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| United States Patent |
6,243,631
|
|
Ohsaku
|
June 5, 2001
|
Damping force control device and method
Abstract
A damping force control device and method controls damping forces of
dampers at locations of respective wheels. A first target damping force
that inhibits vibrations of a vehicle body in the heave direction is
calculated for each of the wheels, based on a single wheel model of the
vehicle which employs the skyhook theory. A second target damping force
that inhibits vibrations of the vehicle body in the pitch direction is
calculated for each of the wheels, based on a model of front and rear
wheels of the vehicle. A third target damping force that inhibits
vibrations of the vehicle body in the roll direction is calculated for
each of the wheels, based on a model of left and right wheels of the
vehicle. One of the first through third target damping forces that has the
greatest absolute value is selected for each of the wheels. The damping
force exerted by the damper at the location of each wheel is set to the
selected target damping force. Such a damping force control device
inhibits the vehicle from making pitch or roll movements without damaging
the control performance for attenuating vertical vibrations of the vehicle
body.
| Inventors:
|
Ohsaku; Satoru (Toyota, JP)
|
| Assignee:
|
Toyota Jidosha Kabushiki Kaisha (Toyota, JP)
|
| Appl. No.:
|
541096 |
| Filed:
|
March 31, 2000 |
Foreign Application Priority Data
| Apr 20, 1999[JP] | 11-112865 |
| Intern'l Class: |
B60G 017/015 |
| Field of Search: |
701/36,37,38
280/5.5,6
|
References Cited
U.S. Patent Documents
| 5071157 | Dec., 1991 | Majeed | 280/5.
|
| 5375872 | Dec., 1994 | Ohtagaki et al. | 280/5.
|
| 5638275 | Jun., 1997 | Sasaki et al. | 701/38.
|
| 5701245 | Dec., 1997 | Ogawa et al. | 701/37.
|
| 5794168 | Aug., 1998 | Sasaki et al. | 701/37.
|
| 5802478 | Sep., 1998 | Iwasaki | 701/37.
|
| 5832389 | Nov., 1998 | Sasaki et al. | 701/37.
|
| 5950776 | Sep., 1999 | Iwasaki et al. | 188/299.
|
| Foreign Patent Documents |
| 5-294122 | Nov., 1993 | JP.
| |
| 6-344743 | Dec., 1994 | JP.
| |
Primary Examiner: Cuchlinski, Jr.; William A.
Assistant Examiner: Marc-Coleman; Marthe
Attorney, Agent or Firm: Oliff & Berridge, PLC
Claims
What is claimed is:
1. A damping force control device for controlling damping forces of dampers
disposed between a vehicle body and respective wheels of a vehicle,
comprising a controller that:
calculates, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculates, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a pitch direction, based on a
model of front and rear wheels of the vehicle;
determines an ultimate target damping force for each of the wheels, based
on the calculated first and second target damping forces; and
outputs a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
2. The damping force control device according to claim 1, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body; and
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the pitch direction.
3. The damping force control device according to claim 1, wherein the
controller:
determines the ultimate target damping force by selecting the greater one
of the calculated first and second target damping forces for each of the
wheels.
4. The damping force control device according to claim 3, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body; and
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the pitch direction.
5. The damping force control device according to claim 1, wherein the
controller:
judges a relation in degree of magnitude of absolute values of the first
and second target damping forces;
weights the target damping force of the greater absolute value with a
greater weight; and
summatively synthesizes the respectively weighted first and second target
damping forces, and thereby determines the ultimate target damping force.
6. A damping force control device for controlling damping forces of dampers
disposed between a vehicle body and respective wheels of a vehicle,
comprising a controller that:
calculates, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculates, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a roll direction, based on a
model of left and right wheels of the vehicle;
determines an ultimate target damping force for each of the wheels, based
on the calculated first and second target damping forces; and
outputs a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
7. The damping force control device according to claim 6, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body; and
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the roll direction.
8. The damping force control device according to claim 6, wherein the
controller:
determines the ultimate target damping force by selecting the greater one
of the calculated first and second target damping forces for each of the
wheels; and
outputs the selected control signal to each of the dampers such that the
damping force exerted by each of the dampers is set to the selected target
damping force.
9. The damping force control device according to claim 8, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body; and
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the roll direction.
10. The damping force control device according to claim 6, wherein the
controller:
judges a relation in degree of magnitude of absolute values of the first
and second target damping forces;
weights the target damping force of the greater absolute value with a
greater weight; and
summatively synthesizes the respectively weighted first and second target
damping forces, and thereby determines the ultimate target damping force.
11. A damping force control device for controlling damping forces of
dampers disposed between a vehicle body and respective wheels of a
vehicle, comprising a controller that:
calculates, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculates, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a pitch direction, based on a
model of front and rear wheels of the vehicle;
calculates, for each of the wheels, a third target damping force that
inhibits vibrations of the vehicle body in a roll direction, based on a
model of left and right wheels of the vehicle;
determines an ultimate target damping force for each of the wheels, based
on the calculated first, second and third target damping forces;
outputs a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
12. The damping force control device according to claim 11, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body;
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the pitch direction; and
calculates the third target damping force in accordance with a kinetic
state quantity of the vehicle body in the roll direction.
13. The damping force control device according to claim 11, wherein the
controller:
selects the greatest one of the calculated first, second and third target
damping forces for each of the wheels; and
outputs a control signal corresponding to the selected target damping force
to each of the dampers and performs control such that the damping force
exerted by each of the dampers is set to the selected target damping
force.
14. The damping force control device according to claim 13, wherein the
controller:
calculates the first target damping force in accordance with a vertical
kinetic state quantity of the vehicle body;
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the pitch direction; and
calculates the third target damping force in accordance with a kinetic
state quantity of the vehicle body in the roll direction.
15. The damping force control device according to claim 11, wherein the
controller:
judges a relation in degree of magnitude of absolute values of the first,
second and third target damping forces;
increases weights with which the target damping forces are weighted as the
absolute values increase; and
summatively synthesizes the respectively weighted first, second and third
target damping forces, and thereby determines the ultimate target damping
force.
16. The damping force control device according to claim 11, wherein the
controller
judges a relation in degree of magnitude of absolute values of the first,
second and third target damping forces;
chooses the target damping forces of the greatest two absolute values; and
summatively synthesizes the chosen target damping forces, and thereby
determines the ultimate target damping force.
17. The damping force control device according to claim 11, wherein the
controller:
judges a relation in degree of magnitude of absolute values of the first,
second and third target damping forces;
chooses the target damping forces of the greatest two absolute values;
weights one of the chosen target damping forces that has the greater
absolute value with a greater weight; and
summatively synthesizes the chosen target damping forces, and thereby
determines the ultimate target damping force.
18. A damping force control method for controlling damping forces of
dampers disposed between a vehicle body and respective wheels of a
vehicle, comprising:
calculating, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculating, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a pitch direction, based on a
model of front and rear wheels of the vehicle;
determining an ultimate target damping force for each of the wheels, based
on the calculated first and second target damping forces; and
outputting a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
19. A damping force control method for controlling damping forces of
dampers disposed between a vehicle body and respective wheels of a
vehicle, comprising:
calculating, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculating, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a roll direction, based on a
model of left and right wheels of the vehicle;
determining an ultimate target damping force for each of the wheels, based
on the calculated first and second target damping forces; and
outputting a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
20. A damping force control method for controlling damping forces of
dampers disposed between a vehicle body and respective wheels of a
vehicle, comprising:
calculating, for each of the wheels, a first target damping force that
inhibits vibrations of the vehicle body in a heave direction, based on a
single wheel model of the vehicle;
calculating, for each of the wheels, a second target damping force that
inhibits vibrations of the vehicle body in a pitch direction, based on a
model of front and rear wheels of the vehicle;
calculating, for each of the wheels, a third target damping force that
inhibits vibrations of the vehicle body in a roll direction, based on a
model of left and right wheels of the vehicle;
determining an ultimate target damping force for each of the wheels, based
on the calculated first, second and third target damping forces; and
outputting a control signal corresponding to the determined ultimate target
damping force to each of the dampers such that a damping force exerted by
each of the dampers is set to the determined ultimate target damping
force.
Description
INCORPORATION BY REFERENCE
The disclosure of Japanese Patent Application No. HEI 11-12865 filed on
Apr. 20, 1999 including the specification, drawings and abstract is
incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION
1. Field of Invention
The invention relates to a damping force control device and a damping force
control method for controlling damping forces of dampers disposed between
a vehicle body and respective wheels of a vehicle.
2. Description of Related Art
As a first related art of this kind, there is known a damping force control
device which determines an actual damping coefficient based on the skyhook
theory, that is, in accordance with a ratio between a vertical speed of
the vehicle body and a vertical speed of the vehicle body relative to a
wheel (e.g. Japanese Patent Application Laid-Open No. HEI 5-294122). This
device is designed to decompose a vertical speed of the vehicle body at
the location of each wheel into a roll movement speed, a pitch movement
speed, a heave movement speed and a warp movement speed of the vehicle
body. The pitch movement speed is multiplied by a pitch gain which changes
in accordance with a differential value of a longitudinal acceleration.
The roll movement speed is multiplied by a roll gain which changes in
accordance with a differential value of a lateral acceleration. The heave
and warp movement speeds are multiplied by constant gains respectively.
The roll movement speed, the pitch movement speed, the heave movement
speed and the warp movement speed that have thus been gain-adjusted are
re-synthesized into a vertical speed of the vehicle body at the location
of each of the wheels. The actual damping coefficient is determined
according to a ratio between the re-synthesized vertical speed of the
vehicle body at the location of each of the wheels and a speed of the
vehicle body at the location of the wheel relative to the wheel. Thus the
vehicle body at the location of each of the wheels is inhibited from
vibrating vertically, and is effectively inhibited from making pitch or
roll movements.
According to a second related art, an amount of vertical displacement of
the vehicle body at the location of each of the wheels relative to the
wheel is detected. Based on various equations of motion which consider
pitch and roll movements of the vehicle body and the like, a vertical
speed of the vehicle body at the location of each of the wheels is
calculated by means of the aforementioned amount of relative displacement.
By differentiating the aforementioned amount of relative displacement, a
vertical speed of the vehicle body at the location of each of the wheels
relative to the wheel is calculated. The actual damping coefficient is
determined according to a ratio between the vertical speed and the
relative speed for each of the wheels. In short, there is also known a
damping force control device for controlling damping forces of the dampers
based on the skyhook theory, by merely detecting the amount of relative
displacement as mentioned above (Japanese Patent Application Laid-Open No.
HEI 6-344743).
However, according to the aforementioned first and second related art, the
algorithm for performing control to inhibit vertical vibrations of the
vehicle body, namely, the algorithm based on the skyhook theory is
directly corrected in accordance with pitch and roll movements of the
vehicle body. Although the effect of inhibiting the vehicle body from
vibrating in the pitch and roll directions can be accomplished through
such correction, the basic performance of the damping force control for
inhibiting vertical vibrations of the vehicle body is adversely affected.
SUMMARY OF THE INVENTION
The invention has been made with the aim of solving the above-stated
problem. It is an object of the invention to provide a damping force
control device and a damping force control method which, while ensuring
the control performance for inhibiting vertical vibrations of a vehicle
body, also bring about the effect of inhibiting the vehicle body from
making pitch and/or roll movements.
In order to solve the aforementioned problem, a damping force control
device according to a first aspect of the invention is provided with a
controller that calculates, for each of the wheels, a first target damping
force that inhibits vibrations of the vehicle body in a heave direction
based on a single wheel model of the vehicle; calculates, for each of the
wheels, a second target damping force that inhibits vibrations of the
vehicle body in a pitch direction based on a model of front and rear
wheels of the vehicle; determines an ultimate target damping force for
each of the wheels based on the calculated first and second target damping
forces; outputs a control signal corresponding to the determined ultimate
target damping force to each of the dampers; and controls each damper such
that a damping force exerted by each of the dampers is set to the
determined ultimate target damping force.
In this case, for example, the controller calculates the first target
damping force in accordance with a kinetic state quantity of the vehicle
body in the lateral direction and the second target damping force in
accordance with a kinetic state quantity of the vehicle body in pitch
direction.
According to the first aspect of the invention, the controller calculates
the first and second target damping forces, respectively. Through
operations of the controller, control is performed such that a damping
force exerted by each of the dampers is set to the determined ultimate
target damping force for each of the wheels. In this case, the first
target damping force is calculated to inhibit vibrations of the vehicle
body in the heave direction, based on the single wheel model of the
vehicle. The second target damping force is calculated, independently of
the first target damping force, to inhibit vibrations of the vehicle body
in the pitch direction, based on the model of front and rear wheels of the
vehicle. Therefore, while the control performance intrinsic in the first
target damping force that inhibits vertical vibrations of the vehicle body
is ensured, a deficiency in damping force for pitch movements of the
vehicle body is compensated for. Thus the vehicle body is effectively
inhibited from vibrating vertically and also from making pitch movements.
Consequently the vehicle achieves good riding comfort and high running
stability.
In the aforementioned first aspect of the invention, the controller may be
designed to determine the ultimate target damping force by selecting the
greater one of the calculated first and second target damping forces for
each of the wheels, and to output the selected control signal to each of
the dampers and control each damper such that the damping force exerted by
each of the dampers is set to the selected target damping force.
According to this aspect of the invention, control is performed such that
the damping force of the damper for each of the wheels is set to the
greater one of the first and second target damping forces. Thus, only if
the magnitude of vibrations of the vehicle body in the pitch direction has
increased to some extent, on the condition that the first target damping
force is smaller than the second target damping force, the damping force
of the damper at the location of each of the wheels is set to the second
target damping force to inhibit vibrations of the vehicle body in the
pitch direction, based on the model of front and rear wheels of the
vehicle. Otherwise, the damping force of the damper at the location of
each of the wheels is set to the first target damping force to inhibit
vibrations of the vehicle body in the heave direction, based on the single
wheel model of the vehicle. Accordingly, according to this aspect, while
the control performance for inhibiting vertical vibrations of the vehicle
body, which is intrinsic in the first target damping force calculated by
the controller, is ensured more suitably, a deficiency in damping force
for pitch movements of the vehicle body is compensated for. Thus the
vehicle body is more effectively inhibited from vibrating vertically and
also from making pitch movements. Consequently the vehicle achieves better
riding comfort and higher running stability.
In a second aspect of the invention, the controller calculates, for each of
the wheels, a second target damping force that inhibits vibrations of the
vehicle body in a roll direction, based on a model of left and right
wheels of the vehicle. In this case, for example, the controller
calculates the second target damping force in accordance with a kinetic
state quantity of the vehicle body in the roll direction.
In the second aspect of the invention, the second target damping force that
inhibits vibrations of the vehicle body in the pitch direction in the
first aspect of the invention is replaced by the second target damping
force that inhibits vibrations of the vehicle body in the roll direction.
Therefore, while the control performance for inhibiting vertical
vibrations of the vehicle body, which is intrinsic in the first target
damping force, is ensured, a deficiency in damping force for roll
movements of the vehicle body is compensated for. Thus the vehicle body is
effectively inhibited from vibrating vertically and also from making roll
movements. Consequently the vehicle achieves good riding comfort and high
running stability.
Furthermore, in a third aspect of the invention, the controller calculates
a third target damping force. The controller determines an ultimate target
damping force for each of the wheels, based on the calculated first,
second and third target damping forces. Also in this case, the controller
selects the greatest one of the calculated first, second and third target
damping forces for each of the wheels, and outputs a control signal
corresponding to the selected target damping force to each of the dampers
and controls each damper such that the damping force exerted by each of
the dampers is set to the selected target damping force.
In the third aspect of the invention, instead of the first and second
target damping forces in the first and second aspects of the invention,
the damping force exerted by the damper is so controlled as to be set to a
target damping force that has been determined based on the independently
calculated first through third target damping forces, for example, to the
greatest one of the first, second and third target damping forces. In this
case, the first target damping force is calculated to inhibit vibrations
of the vehicle body in the heave direction, based on the single wheel
model of the vehicle. The second target damping force is calculated to
inhibit vibrations of the vehicle body in the pitch direction, based on
the model of front and rear wheels of the vehicle. The third target
damping force is calculated to inhibit vibrations of the vehicle body in
the roll direction, based on the model of left and right wheels of the
vehicle. These first through third target damping forces are calculated
independently of one another. Hence, according to the third aspect of the
invention, while the control performance for inhibiting vertical
vibrations of the vehicle body, which is intrinsic in the first target
damping force calculated by the controller, is ensured, deficiencies in
damping force for pitch and roll movements of the vehicle body are
compensated for. Therefore the vehicle body is effectively inhibited from
vibrating vertically and also from making pitch or roll movements.
Consequently the vehicle achieves good riding comfort and high running
stability.
According to a damping force control method of a fourth aspect of the
invention, a first target damping force that inhibits vibrations of the
vehicle body in a heave direction is calculated for each of the wheels
based on a single wheel model of the vehicle, and a second target damping
force that inhibits vibrations of the vehicle body in a pitch direction is
calculated for each of the wheels based on a model of front and rear
wheels of the vehicle. An ultimate target damping force is then determined
for each of the wheels, based on the calculated first and second target
damping forces. A control signal corresponding to the determined ultimate
target damping force is then outputted to each of the dampers, and each
damper is controlled such that a damping force exerted by each of the
dampers is set to the determined ultimate target damping force.
In a fifth aspect of the invention, instead of calculating the second
target damping force that inhibits vibrations of the vehicle body in the
pitch direction as in the damping force control method of the fourth
aspect of the invention, a second target damping force that inhibits
vibrations of the vehicle body in the roll direction is calculated for
each of the wheels. An ultimate target damping force is determined for
each of the wheels, based on the aforementioned first and second target
damping forces calculated for each of the wheels.
Furthermore, according to a damping force control method of a sixth aspect
of the invention, a first target damping force that inhibits vibrations of
the vehicle body in a heave direction, a second target damping force that
inhibits vibrations of the vehicle body in a pitch direction, and a third
target damping force that inhibits vibrations of the vehicle body in a
roll direction are calculated for each of the wheels. An ultimate target
damping force is then determined for each of the wheels, based on the
calculated first, second and third target damping forces.
Definitions of vibrations of the vehicle body in the heave, pitch and roll
directions will be given hereinafter. It is assumed herein that X-axis
represents the longitudinal direction of the vehicle body, that Y-axis
represents the lateral direction of the vehicle body, and that Z-axis
represents the vertical direction of the vehicle body. The vibrations of
the vehicle body in the heave direction refer to proper vibrations of the
vehicle body moving parallel to the Z-axis. The vibrations of the vehicle
body in the pitch direction refer to proper vibrations of the vehicle body
rotating around the Y-axis. The vibrations of the vehicle body in the roll
direction refer to proper vibrations of the vehicle body rotating around
the X-axis.
BRIEF DESCRIPTION OF THE DRAWINGS
The foregoing and further objects, features and advantages of the invention
will become apparent from the following description of preferred
embodiments with reference to the accompanying drawings, wherein:
FIG. 1 is a schematic block diagram of a damping force control device for a
vehicle;
FIG. 2 is a flowchart of a program executed by an electric control device
shown in FIG. 1;
FIG. 3 is a detailed flowchart of a first damping force calculating routine
shown in FIG. 2;
FIG. 4 is a model view of a single wheel of the vehicle;
FIG. 5 is a detailed flowchart of a second damping force calculating
routine shown in FIG. 2;
FIG. 6 is a model view of front and rear wheels of the vehicle;
FIG. 7 is a detailed flowchart of a third damping force calculating routine
shown in FIG. 2;
FIG. 8 is a model view of left and right wheels of the vehicle;
FIG. 9 is a graph showing a data property in a table of relative speed
against damping force;
FIG. 10 is a model view of another single wheel of the vehicle and relates
to modifications of the invention;
FIG. 11 is a block diagram of a generalized model of a non-linear H state
feedback control system and relates to a first modification for
calculating a first target damping force;
FIG. 12A is a graph showing a frequency weight for a sprung mass
acceleration as an evaluated output;
FIG. 12B is a graph showing a frequency weight for a sprung mass speed as
an evaluated output;
FIG. 12C is a graph showing a frequency weight for a speed of a sprung
member relative to an unsprung member as an evaluated output;
FIG. 12D is a graph showing a frequency weight for a non-linear damping
coefficient as a control input;
FIG. 13 is an image view showing operation and effect of the control based
on the non-linear H.infin. control theory;
FIG. 14A is a Lissajou's waveform diagram showing a characteristic of
damping force against relative speed (F-V) in the damping force control
according to the modification for calculating the first target damping
force;
FIG. 14B is a Lissajou's waveform diagram showing a characteristic of
damping force against relative speed (F-V) in the previously employed
skyhook control;
FIG. 15 is a flowchart of a first damping force calculating routine
according to the first modification for calculating the first target
damping force;
FIG. 16 is a block diagram of a generalized model of a non-linear H.infin.
output feedback control system and relates to a second modification for
calculating the first target damping force;
FIG. 17 is a flowchart of a first damping force calculating routine
according to second and third modifications for calculating the first
target damping force; and
FIG. 18 is a block diagram of a generalized model of a non-linear H.infin.
control system based on a Kalman filter and relates to the third
modification for calculating the first target damping force.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
Embodiments of the invention will be described hereinafter with reference
to the drawings. FIG. 1 is a schematic block diagram showing a damping
force control device for a vehicle according to the embodiments.
At locations of a front-left wheel FW1, a front-right wheel FW2, a
rear-left wheel RW1 and a rear-right wheel RW2 of this vehicle, suspension
systems 10A, 10B, 10C and 10D are disposed between a vehicle body BD
(shown in FIGS. 4, 6 and 8) and the wheels FW1, FW2, RW1 and RW2
respectively. These suspension systems 10A, 10B, 10C and 10D, which are
disposed between the vehicle body BD and the wheels FW1, FW2, RW1 and RW2
respectively, are provided with springs 11a, 11b, 11c and 11d and dampers
12a, 12b, 12c and 12d respectively. The springs 11a, 11b, 11c and 11d
elastically support the vehicle body BD against the wheels FW1, FW2, RW1
and RW2 respectively. The dampers 12a, 12b, 12c and 12d are disposed in
parallel with the springs 11a, 11b, 11c and 11d respectively and damp
vibrations of the vehicle body BD with respect to the wheels FW1, FW2, RW1
and RW2 respectively. Each pair of the springs and dampers 11a and 12a,
11b and 12b, 11c and 12c, and 11d and 12d constitutes a shock absorber.
The dampers 12a, 12b, 12c and 12d are designed to be able to control a
damping coefficient by changing an orifice opening degree. This vehicle is
also provided with an electric control device 20 for variably setting
damping coefficients (damping forces) of the respective dampers 12a, 12b,
12c and 12d. The electric control device 20 is composed of a
microcomputer, its marginal circuits and the like, and repeatedly executes
a program shown in FIG. 2 (including sub-routines in FIGS. 3, 5 and 7) at
intervals of a predetermined period of time by means of a built-in timer,
thus controlling orifice opening degrees of the respective dampers 12a,
12b, 12c and 12d. Sprung mass acceleration sensors 21a through 21d,
relative displacement amount sensors 22a through 22d, a pitch angular
velocity sensor 23 and a roll angular velocity sensor 24 are connected to
the electric control device 20.
The sprung mass acceleration sensors 21a through 21d, which are mounted to
the vehicle body BD (the sprung member) at the locations of the wheels
FW1, FW2, RW1 and RW2 respectively, detect vertical accelerations Xpb1",
Xpb2", Xpb3" and Xpb4" of the vehicle body BD relative to absolute space
at the locations of the wheels FW1, FW2, RW1 and RW2 respectively, and
output detection signals indicative of the vertical accelerations Xpb1",
Xpb2", Xpb3" and Xpb4" respectively. The vertical accelerations Xpb1",
Xpb2", Xpb3" and Xpb4" assume positive values when the vehicle body BD is
accelerated upwards and assume negative values when the vehicle body BD is
accelerated downwards. The relative displacement amount sensors 22a
through 22d, which are mounted between the vehicle body BD (the sprung
member) at the locations of the wheels FW1, FW2, RW1 and RW2 and the
wheels FW1, FW2, RW1 and RW2 (unsprung members) respectively, detect
amounts of vertical displacement (Xpw1-Xpb1), (Xpw2-Xpb2), (Xpw3-Xpb3) and
(Xpw4-Xpb4) of the vehicle body BD at the locations of the wheels FW1,
FW2, RW1 and RW2 relative to the wheels FW1, FW2, RW1 and RW2
respectively, and output detection signals indicative of the amounts of
displacement (Xpw1-Xpb1), (Xpw2-Xpb2), (Xpw3-Xpb3) and (Xpw4-Xpb4)
respectively. The amounts of relative displacement (Xpw1-Xpb1),
(Xpw2-Xpb2), (Xpw3-Xpb3) and (Xpw4-Xpb4), which represent amounts of
displacement with respect to a predetermined reference amount of
displacement, assume positive values if they proceed in a decreasing
direction (in which the dampers contract) and assume negative values if
they proceed in an increasing direction (in which the dampers extend).
The pitch angular velocity sensor 23, which is composed of a rate sensor
installed in the vicinity of the center of gravity of the vehicle body BD,
detects a pitch angular velocity Pa' of the vehicle body BD and outputs a
detection signal indicative of the pitch angular velocity Pa'. The roll
angular velocity sensor 24, which is composed of a rate sensor installed
in the vicinity of the center of gravity of the vehicle body BD, detects a
roll angular velocity Ra' of the vehicle body BD and outputs a detection
signal indicative of the roll angular velocity Ra'.
Next, it will be described how the thus-constructed vehicular damping force
control device operates. After an ignition switch (not shown) has been
turned on, the electric control device 20 starts repeatedly executing the
program shown in FIG. 2 at intervals of a predetermined period of time.
The execution of this program is started in step 100, and the first
through third damping force calculating routines are executed in steps
102, 104 and 106 respectively.
The first damping force calculating routine, which is shown in detail in
FIG. 3, is intended to calculate a first target damping force exerted by
each of the dampers 12a, 12b, 12c and 12d for inhibiting (vertical)
vibrations of the vehicle body BD in the heave direction, based on a model
of a single wheel of the vehicle.
Explanation of the first damping force calculating routine will be preceded
by the description of how to calculate a first target damping force. FIG.
4 shows a model of a single wheel of the vehicle with one degree of
freedom. Referring to FIG. 4, Mb denotes a mass of the vehicle body BD.
Xpb denotes an amount of vertical displacement of the vehicle body BD (the
sprung member) relative to a reference position in absolute space. Xpw
denotes an amount of vertical displacement of the wheel W (the unsprung
member) relative to a reference position in absolute space. These amounts
Xpb and Xpw of displacement assume positive values when the vehicle body
BD and the wheel W move upwards respectively. Ks denotes a spring constant
of a spring 11, which comprehensively represents the springs 11a, 11b, 11c
and 11d. Cs denotes a damping coefficient of a damper 12, which
comprehensively represents the dampers 12a, 12b, 12c and 12d. Csk denotes
a damping coefficient of a virtual damper 12A that has been sky-hooked
according to the skyhook theory and is a preliminarily determined constant
of an appropriate value.
First of all, a virtual model employing the virtual damper 12A instead of
the damper 12 will be considered. Given that Xpb" denotes a vertical
acceleration of the vehicle body BD and that Xpb' denotes a vertical speed
of the vehicle body BD, an equation of motion of the vehicle body BD in
the heave direction of the virtual model is expressed by a formula (1)
shown below.
MbXpb"=Ks(Xpw-Xpb)-CskXpb' (1)
Considering an actual model employing the existing damper 12, an equation
of vertical motion of the actual model is expressed by a formula (2) shown
below.
MbXpb"=Ks(Xpw-Xpb)+Cs(Xpw'-Xpb') (2)
A formula (3) shown below is derived from the aforementioned formulas (1)
and (2). In accordance with a relation defined by the formula (3), an
ideal damping force Fd applied to the vehicle body BD by the damper 12 (or
the damper 12A) based on the skyhook theory is expressed by a formula (4)
shown below.
Cs(Xpw'-Xpb')+CskXpb'=0 (3)
Fd=Cs(Xpw'-Xpb')=-CskXpb' (4)
Next the first damping force calculating routine will be described. The
execution of the first damping force calculating routine is started in
step 150 in FIG. 3. In step 152, vertical accelerations Xpb1", Xpb2",
Xpb3" and Xpb4" of the vehicle body BD at the locations of the wheels FW1,
FW2, RW1 and RW2 are inputted from the sprung mass acceleration sensors
21a through 21d respectively. Next in step 154, the inputted vertical
accelerations Xpb1", Xpb2", Xpb3" and Xpb4" are integrated, whereby
vertical speeds Xpb1', Xpb2', Xpb3' and Xpb4' of the vehicle body BD at
the locations of the wheels FW1, FW2, RW1 and RW2 are calculated
respectively.
Next in step 156, the calculated vertical speeds Xpb1', Xpb2', Xpb3' and
Xpb4' are multiplied by the skyhook coefficient Csk that has appropriately
been determined in advance through execution of a calculation expressed by
a formula (5) shown below, whereby first target damping forces Fd1, Fd2,
Fd3 and Fd4 exerted by the dampers 12a, 12b, 12c and 12d respectively are
calculated.
Fdi=-CskXpbi' (5)
In the aforementioned formula (5), "i" denotes a positive integer from 1 to
4. In this example, although the skyhook coefficient Csk is commonly used
for the wheels FW1, FW2, RW1 and RW2, the front wheels FW1 and FW2 may
employ a skyhook coefficient different from that of the rear wheels RW1
and RW2. In step 158, the execution of the first damping force calculating
routine is terminated.
The second damping force calculating routine, which is shown in FIG. 5 in
detail, is intended to calculate a second target damping force exerted by
each of the dampers 12a, 12b, 12c and 12d for inhibiting vibrations of the
vehicle body BD in the pitch direction, based on a model of front and rear
wheels of the vehicle.
Explanation of the second damping force calculating routine will be
preceded by the description of how to calculate a second target damping
force. FIG. 6 shows a model of front and rear wheels of the vehicle with
two degrees of freedom. Referring to FIG. 6, Xbf denotes an amount of
vertical displacement of the vehicle body BD (the sprung member) at the
locations of the front wheels FW1 and FW2 relative to a reference
position. Xbr denotes an amount of vertical displacement of the vehicle
body BD (the sprung member) at the locations of the rear wheels RW1 and
RW2 relative to a reference position. Xwf denotes an amount of vertical
displacement of the front wheels FW1 and FW2 (the unsprung members)
relative to a reference position. Xwr denotes an amount of vertical
displacement of the rear wheels RW1 and RW2 (the unsprung members)
relative to a reference position. These amounts Xbf, Xwf, Xbr and Xwr of
displacement assume positive values when the vehicle body BD, the front
wheels FW1 and FW2 and the rear wheels RW1 and RW2 move upwards
respectively. Ksf denotes a spring constant of a spring 11f, which
comprehensively represents the springs 11a and 11b at the locations of the
front wheels FW1 and FW2. Ksr denotes a spring constant of a spring 11r,
which comprehensively represents the springs 11c and 11d at the locations
of the rear wheels RW1 and RW2. Csf denotes a damping coefficient of a
damper 12f, which comprehensively represents the dampers 12a and 12b at
the locations of the front wheels FW1 and FW2. Csr denotes a damping
coefficient of a damper 12r, which comprehensively represents the dampers
12c and 12d at the locations of the rear wheels RW1 and RW2. Cp denotes a
damping coefficient of a virtual damper 12p for damping vibrations of the
vehicle body BD in the pitch direction and is a preliminarily determined
constant of an appropriate value.
First of all, a virtual model employing the virtual damper 12p instead of
the actual dampers 12f and 12r will be considered. Given that Xpb" denotes
a vertical acceleration of the vehicle body BD and that Pa" and Pa' denote
an angular acceleration and an angular velocity of the vehicle body BD in
the pitch direction respectively, equations of motion of the vehicle body
BD in the heave and pitch directions of the virtual model are expressed
respectively by formulas (6) and (7) shown below. The angular acceleration
Pa" and the angular velocity Pa' assume positive values in a rotational
direction in which the vehicle body BD rises on the side of the front
wheels FW1 and FW2 and falls on the side of the rear wheels RW1 and RW2.
MbXpb"=Ksf(Xwf-Xbf)+Ksr(Xwr-Xbr) (6)
IpPa"=-LfKsf(Xwf-Xbf)+LrKsr(Xwr-Xbr)-CpPa' (7)
In the aforementioned formula (7), Ip denotes a moment of inertia of the
vehicle body BD in the pitch direction, Lf a distance between a front axle
and the center of gravity, and Lr a distance between a rear axle and the
center of gravity.
Considering an actual model employing the existing dampers 12f and 12r,
equations of motion of the actual model in the heave and pitch directions
are expressed respectively by formulas (8) and (9) shown below.
MbXpb"=Ksf(Xwf-Xbf)+Csf(Xwf'-Xbf') +Ksr(Xwr-Xbr)+Csr(Xwr'-Xbr') (8)
IpPa"=-Lf{Ksf(Xwf-Xbf)+Csf(Xwf'-Xbf')}+Lr{Ksr(Xwr-Xbr)+Csr(Xwr'-Xbr')} (9)
Formulas (10) and (11) shown below are derived from the aforementioned
formulas (6) through (9).
Csf(Xwf'-Xbf')+Csr(Xwr'-Xbr')=0 (10)
LfCsf(Xwf'-Xbf')-LrCsr(Xwr'-Xbr')+CpPa'=0 (11)
In accordance with a relation defined by these formulas (10) and (11),
ideal damping forces PFf and PFr applied to the vehicle body BD by the
damper 12f for the front wheels and by the damper 12r for the rear wheels
(or the damper 12p) for the purpose of damping vibrations of the vehicle
body BD in the pitch direction are expressed respectively by formulas (12)
and (13) shown below.
PFf=Csf(Xwf'-Xbf')=CpPa'/(Lf+Lr) (12)
PFr=Csr(Xwr'-Xbr')=-CpPa'/(Lf+Lr) (13)
Next the second damping force calculating routine will be described. The
execution of the second damping force calculating routine is started in
step 160 in FIG. 5. In step 162, a pitch angular velocity Pa' of the
vehicle body BD is inputted from the pitch angular velocity sensor 23.
Next in step 164, a target damping force PFf of the damper 12f for the
front wheels and a target damping force PFr of the damper 12r for the rear
wheels are calculated with a view to inhibiting vibrations of the vehicle
body BD in the pitch direction, by making calculations according to
after-mentioned formulas (14) and (15) respectively, wherein a damping
coefficient Cp which is ideal for inhibiting vibrations of the vehicle
body BD in the pitch direction and has appropriately been determined in
advance, the inputted pitch angular velocity Pa', the predetermined
distance Lf between the front axle and the center of gravity, and the
predetermined distance Lr between the rear axle and the center of gravity
are used.
PFf=CpPa'/(Lf+Lr) (14)
PFr=-CpPa'/(Lf+Lr) (15)
Next in step 166, the calculated target damping force PFf of the damper 12f
for the front wheels is set as second target damping forces PFd1 and PFd2
for the front-left and front-right wheels FW1 and FW2 respectively, and
the calculated target damping force PFr for the damper 12r for the rear
wheels is set as second target damping forces PFd3 and PFd4 for the
rear-right and rear-left wheels RW1 and RW2 respectively. In step 168, the
execution of the second damping force calculating routine is terminated.
The third damping force calculating routine, which is shown in FIG. 7 in
detail, is intended to calculate a third target damping force exerted by
each of the dampers 12a, 12b, 12c and 12d for inhibiting vibrations of the
vehicle body BD in the roll direction, based on a model of left and right
wheels of the vehicle.
Explanation of the third damping force calculating routine will be preceded
by the description of how to calculate a third target damping force. FIG.
8 shows a model of left and right wheels of the vehicle with two degrees
of freedom. Referring to FIG. 8, Xbm denotes an amount of vertical
displacement of the vehicle body BD (the sprung member) at the locations
of the right wheels FW2 and RW2 relative to a reference position. Xbh
denotes an amount of vertical displacement of the vehicle body BD (the
sprung member) at the locations of the left wheels FW1 and RW1 relative to
a reference position. Xwm denotes an amount of vertical displacement of
the right wheels FW2 and RW2 (the unsprung members) relative to a
reference position. Xwh denotes an amount of vertical displacement of the
left wheels FW1 and RW1 (the unsprung members) relative to a reference
position. These amounts Xbm, Xwm, Xbh and Xwh of displacement assume
positive values when the vehicle body BD, the right wheels FW2 and RW2 and
the left wheels FW1 and RW1 move upwards respectively. Ks denotes a spring
constant of a spring 11m, which comprehensively represents the springs 11b
and 11d at the locations of the right wheels FW2 and RW2, and also denotes
a spring constant of a spring 11h, which comprehensively represents the
springs 11a and 11c at the locations of the left wheels FW1 and RW1. Cs
denotes a damping coefficient of a damper 12m, which comprehensively
represents the dampers 12b and 12d at the locations of the right wheels
FW2 and RW2, and also denotes a damping coefficient of a damper 12h, which
comprehensively represents the dampers 12a and 12c at the locations of the
left wheels FW1 and RW1. Cr denotes a damping coefficient of a virtual
damper 12r for damping vibrations of the vehicle body BD in the roll
direction and is a preliminarily determined constant of an appropriate
value.
First of all, a virtual model employing the virtual damper 12r instead of
the dampers 12m and 12h will be considered. Given that Xpb" denotes a
vertical acceleration of the vehicle body BD and that Ra" and Ra' denote
an angular acceleration and an angular velocity of the vehicle body BD in
the roll direction respectively, equations of motion of the vehicle body
BD in the heave and roll directions of the virtual model are expressed
respectively by formulas (16) and (17) shown below. The angular
acceleration Ra" and the angular velocity Ra' assume positive values in a
rotational direction in which the vehicle body BD rises on the side of the
left wheels FW1 and RW1 and falls on the side of the right wheels FW2 and
RW2.
MbXpb"=Ks(Xwm-Xbm)+Ks(Xwh-Xbh) (16)
IrRa"=(Ks+K)(Xwh-Xbh-Xwm+Xbm)T/2-CrRa' (17)
In the aforementioned formula (17), Ir denotes a moment of inertia of the
vehicle body BD in the roll direction, K a spring constant of the
stabilizer, and T a tread of the vehicle.
Considering an actual model employing the existing dampers 12m and 12h,
equations of motion of the actual model in the heave and roll directions
are expressed respectively by formulas (18) and (19) shown below.
MbXpb"=Ks(Xwm-Xbm)+Cs(Xwm'-Xbm')+Ks(Xwh-Xbh)+Cs(Xwh'-Xbh') (18)
IrRa"=((Ks+K)(Xwh-Xbh-Xwm+Xbm)+Cs(Xwh'-Xbh'-Xwm'+Xbm'))T/2 (19)
Formulas (20) and (21) shown below are derived from the aforementioned
formulas (16) through (19).
Cs(Xwh'-Xbh'+Xwm'-Xbm')=0 (20)
Cs(Xwh'-Xbh'-Xwm'+Xbm')T/2+CrRa'=0 (21)
In accordance with a relation defined by these formulas (20) and (21),
ideal damping forces applied to the vehicle body BD by the damper 12m for
the right wheels and the damper 12h for the left wheels (or the damper
12r) for the purpose of inhibiting vibrations of the vehicle body BD in
the roll direction are expressed respectively by formulas (22) and (23)
shown below.
RFm=Cs(Xwm'-Xbm')=CrRa'/T (22)
RFh=Cs(Xpwh'-Xpbh')=-CrRa'/T (23)
Next the third damping force calculating routine will be described. The
execution of the third damping force calculating routine is started in
step 170 in FIG. 7. In step 172, a roll angular velocity Ra' of the
vehicle body BD is inputted from the roll angular velocity sensor 24. Next
in step 174, a target damping force RFm of the damper 12m for the right
wheels and a target damping force RFh of the damper 12h for the left
wheels are calculated with a view to inhibiting vibrations of the vehicle
body BD in the roll direction, by making calculations according to
after-mentioned formulas (24) and (25) respectively, wherein a damping
coefficient Cr which is ideal for inhibiting vibrations of the vehicle
body BD in the roll direction and has appropriately been determined in
advance, the inputted roll angular velocity Ra', and the predetermined
tread T are used.
RFm=CrRa'/T (24)
RFh=-CrRa'/T (25)
Next in step 176, the calculated target damping force RFm of the damper 12m
for the right wheels is set as third target damping forces RFd2 and RFd4
for the right wheels FW2 and RW2 respectively, and the calculated target
damping force RFh for the damper 12h for the left wheels is set as third
target damping forces RFd1 and RFd3 for the left wheels FW1 and RW1
respectively. In step 178, the execution of the third damping force
calculating routine is terminated.
Referring back to the description of the program shown in FIG. 2, after the
first target damping forces Fd1, Fd2, Fd3 and Fd4, the second target
damping forces PFd1, PFd2, PFd3 and PFd4, and the third target damping
forces RFd1, RFd2, RFd3 and RFd4 have been calculated through the
aforementioned processings of steps 102 through 106, one of the first
through third target damping forces that has the greatest absolute value
is selected for each of the wheels FW1, FW2, RW1 and RW2 in step 108. That
is, respective absolute values .vertline.Fd1.vertline.,
.vertline.PFd1.vertline., .vertline.RFd1.vertline. of the first through
third target damping forces Fd1, PFd1 and RFd1 for the front-left wheel
FW1 are compared with one another. One of the first through third target
damping forces Fd1, PFd1 and RFd1, which corresponds to the greatest one
of the absolute values .vertline.Fd1.vertline., .vertline.PFd1.vertline.
and .vertline.RFd1.vertline., is set as a target damping force F1 for the
damper 12a. Processings substantially identical to those for the
front-left wheel FW1 are also carried out sequentially for the front-right
wheel FW2, the rear-left wheel RW1 and the rear-right wheel RW2. Then the
respective target damping forces Fi ("i" denotes an integer of 2 to 4) for
the dampers 12b, 12c and 12d are sequentially determined.
Next in step 110, amounts (Xpw1-Xpb1), (Xpw2-Xpb2), (Xpw3-Xpb3) and
(Xpw4-Xpb4) of relative displacement are inputted from the relative
displacement amount sensors 22a through 22d respectively. In step 112, the
inputted amounts (Xpw1-Xpb1), (Xpw2-Xpb2), (Xpw3-Xpb3) and (Xpw4-Xpb4) of
relative displacement are differentiated, whereby respective speeds
(Xpw1'-Xpb1'), (Xpw2'-Xpb2'), (Xpw3'-Xpb3') and (Xpw4'-Xpb4') of the
vehicle body BD relative to the wheels FW1, FW2, RW1 and RW2 are
calculated respectively.
After the aforementioned processing in step 112, with reference to a table
of relative speed against damping force, respective orifice opening
degrees OP1, OP2, OP3 and OP4 of the dampers 12a, 12b, 12c and 12d, which
correspond to the target damping forces F1, F2, F3 and F4 determined by
the aforementioned processing in step 108 and to the relative speeds
(Xpw1'-Xpb1'), (Xpw2'-Xpb2'), (Xpw3'-Xpb3') and (Xpw4'-Xpb4') calculated
through the aforementioned processing in step 112 respectively, are
determined in step 114. The table of relative speed against damping force
is preliminarily built into the microcomputer and stores data which
represent, for each of the orifice opening degrees, a characteristic of
change in damping force F of the dampers 12a, 12b, 12c and 12d with
respect to the relative speed (Xpw'-Xpb'). In determining each of the
aforementioned orifice opening degrees OP1, OP2, OP3 and OP4, a curve
which is located closest to a point determined by the damping force Fi and
the relative speed (Xpwi'-Xpbi') ("i" denotes an integer of 2 to 4) in the
graph shown in FIG. 9 is retrieved. An orifice opening degree OP
corresponding to the retrieved curve is selected for each pair of damping
force and relative speed.
After the aforementioned processing in step 114, control signals indicative
of the orifice opening degrees OP1, OP2, OP3 and OP4 determined in step
116 are outputted to the dampers 12a, 12b, 12c and 12d respectively. The
orifice opening degrees of the dampers 12a, 12b, 12c and 12d are
controlled to be set to the aforementioned orifice opening degrees OP1,
OP2, OP3 and OP4 respectively. As a result, the dampers 12a, 12b, 12c and
12d generate the determined target damping forces F1, F2, F3 and F4
respectively.
As described hitherto, according to the aforementioned embodiment, through
the processings of the first damping force calculating routine (FIG. 3),
the first target damping forces Fd1, Fd2, Fd3 and Fd4 for inhibiting
vibrations of the vehicle body in the heave direction are calculated for
the respective wheels, based on the model of a single wheel of the vehicle
using the skyhook theory. Through the processings of the second damping
force calculating routine (FIG. 5), the second target damping forces PFd1,
PFd2, PFd3 and PFd4 for inhibiting vibrations of the vehicle body in the
pitch direction are calculated for the respective wheels, based on the
model of front and rear wheels of the vehicle. Through the processings of
the third damping force calculating routine (FIG. 7), the third target
damping forces RFd1, RFd2, RFd3 and RFd4 for inhibiting vibrations of the
vehicle body in the roll direction are calculated for the respective
wheels, based on the model of left and right wheels of the vehicle.
Through the processing of step 108 in FIG. 2, one of the aforementioned
first through third target damping forces that has the greatest absolute
value is selected as the target damping forces F1, F2, F3 and F4 for the
locations of the wheels FW1, FW2, RW1 and RW2 respectively. The damping
forces of the dampers 12a, 12b, 12c and 12d at the respective locations of
the wheels FW1, FW2, RW1 and RW2 are controlled to be set to the
aforementioned target damping forces F1, F2, F3 and F4 respectively.
As a result, only if vibrations of the vehicle body BD in the pitch or roll
direction have become strong to a certain extent, on the condition that
the first target damping forces Fd1, Fd2, Fd3 and Fd4 are smaller than the
second target damping forces PFd1, PFd2, PFd3 and PFd4 or the third target
damping forces RFd1, RFd2, RFd3 and RFd4 respectively, the damping forces
of the dampers 12a, 12b, 12c and 12d at the locations of the respective
wheels FW1, FW2, RW1 and RW2 are respectively set to the second target
damping forces PFd1, PFd2, PFd3 and PFd4 or the third target damping
forces RFd1, RFd2, RFd3 and RFd4 for inhibiting vibrations of the vehicle
body in the pitch or roll direction, based on the model of front and rear
wheels or left and right wheels. Otherwise, the damping forces of the
dampers 12a, 12b, 12c and 12d are respectively set to the first target
damping forces Fd1, Fd2, Fd3 and Fd4 for inhibiting vibrations of the
vehicle body in the heave direction, based on the model of a single wheel
of the vehicle. Thus, this embodiment compensates for a deficiency in
damping force for pitch and roll movements of the vehicle body BD, while
ensuring the control performance intrinsic in the first target damping
forces Fd1, Fd2, Fd3 and Fd4 for inhibiting vertical vibrations of the
vehicle body BD. Therefore, vertical vibrations of the vehicle body BD are
effectively inhibited, and vibrations of the vehicle body BD resulting
from pitch and roll movements thereof are also inhibited. Consequently the
vehicle achieves good riding comfort and high running stability.
In the aforementioned embodiment, one of the first through third target
damping forces that has the greatest absolute value is selected as the
target damping forces F1, F2, F3 and F4 respectively for the locations of
the wheels FW1, FW2, RW1 and RW2. However, in the case where the roll
movements of the vehicle body BD are not very serious, calculation of the
third target damping forces may be omitted, and either the first target
damping forces Fd1, Fd2, Fd3 and Fd4 or the second target damping forces
PFd1, PFd2, PFd3 and PFd4, which have the greater absolute values, may be
selected as the target damping forces F1, F2, F3 and F4 respectively for
the locations of the wheels FW1, FW2, RW1 and RW2. This also compensates
for a deficiency in damping force for the pitch movements of the vehicle
body BD, while ensuring the control performance intrinsic in the first
target damping forces Fd1, Fd2, Fd3 and Fd4 for inhibiting vertical
vibrations of the vehicle body BD. Therefore, vertical vibrations of the
vehicle body BD are effectively inhibited, and vibrations of the vehicle
body BD resulting from pitch movements thereof are also inhibited.
Consequently the vehicle achieves good riding comfort and high running
stability.
Also, in the case where the pitch movements of the vehicle body BD are not
very serious, calculation of the second target damping forces may be
omitted, and either the first target damping forces Fd1, Fd2, Fd3 and Fd4
or the third target damping forces RFd1, RFd2, RFd3 and RFd4, which have
the greater absolute values, may be selected as the target damping forces
F1, F2, F3 and F4 respectively for the locations of the wheels FW1, FW2,
RW1 and RW2. This also compensates for a deficiency in damping force for
the roll movements of the vehicle body BD, while ensuring the control
performance intrinsic in the first target damping forces Fd1, Fd2, Fd3 and
Fd4 for inhibiting vertical vibrations of the vehicle body BD. Therefore,
vertical vibrations of the vehicle body BD are effectively inhibited, and
vibrations of the vehicle body BD resulting from roll movements thereof
are also inhibited. Consequently the vehicle achieves good riding comfort
and high running stability.
In the aforementioned embodiments, one of the first through third target
damping forces that has the greatest absolute value is set as an ultimate
target damping force. However, an ultimate target damping force may be
determined in the following manners by comparing the respective absolute
values of the first through third target damping forces. That is, the
first through third target damping forces may be summatively synthesized
by increasing weights attributed to the first through third target damping
forces in accordance with an increase in the respective absolute values.
Alternatively, the two greatest ones of the first through third target
damping forces may be selected and summatively synthesized. In conducting
summative synthesis, a weight attributed to the greater one of the two
selected target damping forces may be increased. In the aforementioned
modification example, one of the first and second target damping forces
that has the greater absolute value, or one of the first and third target
damping forces that has the greater absolute value is determined as an
ultimate target damping force. However, an ultimate target damping force
may be determined based on the first and second target damping forces or
the first and third target damping forces, by increasing a weight
attributed to the greater one of the two target damping forces in
conducting summative synthesis. This also serves to determine an ultimate
target damping force based on the independently calculated first through
third target damping forces, first and second target damping forces, or
first and third target damping forces. Thus, a deficiency in damping force
for pitch and roll movements of the vehicle body is compensated for, while
the control performance intrinsic in the first target damping force for
inhibiting vertical vibrations of the vehicle body is ensured. Therefore,
vertical vibrations of the vehicle body are effectively inhibited, and
vibrations of the vehicle body resulting from pitch and roll movements
thereof are also inhibited. Consequently the vehicle achieves good riding
comfort and high running stability.
Further, the aforementioned embodiment is designed to detect the vertical
accelerations Xpb1", Xpb2", Xpb3" and Xpb4" of the vehicle body BD as
vertical kinetic state quantities of the vehicle body BD at the locations
of the wheels FW1, FW2, RW1 and RW2 relative to absolute space,
respectively. Apart from such a construction, the aforementioned
embodiment may also be designed to detect the vertical speeds Xpb1',
Xpb2', Xpb3' and Xpb4' of the vehicle body BD relative to the absolute
space. Also, the aforementioned embodiment may be designed to calculate
the vertical speeds Xpb1', Xpb2', Xpb3' and Xpb4' by detecting the amounts
Xpb1, Xpb2, Xpb3 and Xpb4 of vertical displacement of the vehicle body BD
at the locations of the wheels FW1, FW2, RW1 and RW2 relative to the
absolute space, respectively. Also, as regards the amounts (Xpw1-Xpb1),
(Xpw2-Xpb2), (Xpw3-Xpb3) and (Xpw4-Xpb4) of the vehicle body BD (the
sprung member) at the locations of the wheels FW1, FW2, RW1 and RW2
relative to the respective wheels FW1, FW2, RW1 and RW2, the relative
speeds (Xpw1'-Xpb1'), (Xpw2'-Xpb2'), (Xpw3'-Xpb3') and (Xpw4'-Xpb4') may
be detected, or the relative speeds (Xpw1'-Xpb1'), (Xpw2'-Xpb2'),
(Xpw3'-Xpb3') and (Xpw4'-Xpb4') may be calculated by detecting the
relative accelerations (Xpw1"-Xpb1"), (Xpw2"-Xpb2"), (Xpw3"-Xpb3") and
(Xpw4"-Xpb4"), respectively.
In the aforementioned embodiment, the pitch angular velocity sensor 23
includes a rate sensor provided to detect an angular velocity Pa' of the
vehicle body BD in the pitch direction. However, the angular velocity Pa'
may be detected from a difference in amount of vertical displacement
between front and rear parts of the vehicle body BD. Instead of using the
roll angular velocity sensor 24 composed of a rate sensor so as to detect
an angular velocity Ra' in the roll direction of the vehicle body BD, the
angular velocity Ra' may be detected from a difference in amount of
vertical displacement between left and right parts of the vehicle body BD.
Furthermore, the sprung mass acceleration sensors 21a through 21d, the
relative displacement amount sensors 22a through 22d, the pitch angular
velocity sensor 23 and the roll angular velocity sensor 24 for directly
detecting various kinetic state quantities are partially replaced, and the
observer may be used to estimate and thus detect part of the various
kinetic state quantities.
Next, various modifications of the aforementioned first damping force
calculating routine will be described. In these modifications, the
aforementioned first target damping forces Fd1, Fd2, Fd3 and Fd4 are
calculated based on a control theory which can handle a non-linear plant
and provide a design specification in the form of a frequency range.
Because the following description is premised on a single wheel model of
the vehicle, attention will be focused on only one of the wheels FW1, FW2,
RW1 and RW2, and the description will be made as to an embodiment for
calculating only the first target damping force Fd which comprehensively
represents the first target damping forces Fd1, Fd2, Fd3 and Fd4. As for
the other wheels, the first target damping force can be calculated in the
same manner. Prior to the description of the various modifications, the
single wheel model of the vehicle according to the modifications will be
described first.
a. Model
First of all, a model of a suspension system will be considered in an
attempt to express the suspension system in a state space. FIG. 10 is a
functional view of the suspension system for a single wheel of the
vehicle. Mb denotes a mass of the vehicle body (the sprung member) BD, Mw
a mass of a wheel WH (more exactly, an unsprung member including a lower
arm and the like), and Kt a spring constant of a tire TR. Ks denotes a
spring constant of the spring 11, Cs0 a linear portion of a damping
coefficient Cs (hereinafter referred to as a linear damping coefficient)
of a damper provided in the suspension system, and Cv a non-linear portion
of the damping coefficient Cs (hereinafter referred to as a non-linear
damping coefficient). The sum of the linear damping coefficient Cs0 and
the non-linear damping coefficient Cv is an overall damping coefficient of
the damper 12 (Cs=Cs0+Cv). RD denotes a road surface. Given that Xpb, Xpw
and Xpr denote amounts of displacement of the vehicle body BD, the wheel
WH and the road surface RD respectively, equations (26) and (27) of motion
are established as shown below.
MbXpb"=Ks(Xpw-Xpb)+Cs(Xpw'-Xpb')+Cv(Xpw'-Xpb') (26)
MwXpw"=Kt(Xpr-Xpw)-Ks(Xpw-Xpb)-Cs(Xpw'-Xpb')-Cv(Xpw'-Xpb') (27)
In the aforementioned formulas (26) and (27) and after-mentioned respective
formulas, the sign (') indicates single differentiation and the sign (")
indicates double differentiation.
The control input "u" in this suspension system is the non-linear damping
coefficient Cv. Hence, if the suspension system is expressed in a state
space with a road surface disturbance w1 and the non-linear damping
coefficient Cv being used as a road surface speed Xpr' and the control
input "u" respectively, a formula (28) is established as shown below.
Xp'=ApXp+Bp1w1+Bp2(Xp)u (28)
In the aforementioned formula (28), Xp, Ap, Bp1 and Bp2 (Xp) are
respectively expressed according to formulas (29) through (32) shown
below.
##EQU1##
The suspension system of this modification simultaneously restricts a
vertical speed Xpb' of the vehicle body BD (hereinafter referred to as a
sprung mass speed Xpb') which greatly affects vibrations of the vehicle
body BD (the sprung mass member), a vertical acceleration Xpb" of the
vehicle body BD (hereinafter referred to as a sprung mass acceleration
Xpb") which greatly affects riding comfort of the vehicle, and a vertical
speed (Xpw'-Xpb') of the wheel WH relative to the vehicle body BD
(hereinafter referred to as a relative speed (Xpw'-Xpb')) which greatly
affects vibrations of the wheel WH. Accordingly, the sprung mass speed
Xpb', the sprung mass acceleration Xpb" and the relative speed (Xpw'-Xpb')
are used as an evaluated output Zp. In the suspension system, it is easy
to detect the sprung mass acceleration Xpb" and an amount (Xpw-Xpb) of
displacement of the wheel WH relative to the vehicle body BD (hereinafter
referred to simply as a relative displacement amount (Xpw-Xpb)). Therefore
the sprung mass acceleration Xpb" and the relative displacement amount
(Xpw-Xpb) are basically used as an observed output yp. If the observed
output yp is expressed in a state space on the assumption that the
observed output yp includes an observed noise W.sub.2, formulas (33) and
(34) are established as shown below.
Zp=Cp1Xp+Dp12(Xp)u (33)
yp=Cp2Xp+Dp21W2+Dp22(Xp)u (34)
In the aforementioned formulas (33) and (34), Zp, yp, Cp1, Dp12(Xp), Cp2,
Dp21 and Dp22(Xp) are respectively expressed according to formulas (35)
through (41) shown below.
##EQU2##
However, since the coefficient Bp2(Xp) includes the state quantity Xp as
indicated by the aforementioned formula (28), the state space expression
of the aforementioned suspension system is a bilinear system. In the
bilinear system, since Bp2(0)=0 at the origin X=0 despite a change in
control input u, the execution of control is impossible in the vicinity of
the origin. Therefore the control system for the aforementioned suspension
system cannot be designed according to the linear control theory. Hence,
an attempt is made to design the control system by means of the non-linear
H.infin. control theory for the purpose of gaining desired control
performance. In other words, an attempt is made to design a control system
for restricting the sprung mass speed Xpb', the sprung mass acceleration
Xpb" and the relative speed (Xpw'-Xpb'). Hereinafter, various examples of
the non-linear H.infin. control system according to the various
modifications of the invention for calculating the first target damping
force Fd, and concrete examples of calculation of the first target damping
force Fd will be described.
b. First Modification
b1. Designing Example of Non-Linear H.infin. State Feedback Control System
First of all, in order to make an attempt to design the non-linear H.infin.
state feedback control system, a generalized model of a state feedback
control system as shown in FIG. 11 wherein a frequency weight is added to
the evaluated output Zp and the control input "u" is considered. In this
case, the frequency weight means a dynamic weight that changes in
accordance with a frequency and is given in the form of a transfer
function. Use of the frequency weight makes it possible to increase a
weight in a frequency range where the control performance is to be
improved and to reduce a weight in a frequency range where the control
performance is negligible. In addition, the evaluated output Zp and the
control input "u" is multiplied by frequency weights Ws(S) and Wu(S),
respectively, and then multiplied, respectively, by functions a1(X) and
a2(X) of the state quantity X. These functions are non-linear weight
functions. In order to turn to Riccati's equation and find a solution, the
non-linear weights a1(X) and a2(X) demonstrate characteristics defined by
formulas (42) and (43) shown below.
a1(X)>0, a2(X)>0 (42)
a1(0)=a2(0)=1 (43)
These non-linear weights make it possible to design a control system for
restricting an L2 gain more positively. A state space expression of this
system is indicated by a formula (44) shown below.
Xp'=ApXp+Bp1W1+Bp2(Xp)u (44)
A state space expression of the weight Ws(S) by which the evaluated output
Zp is multiplied is indicated by formulas (45) and (46) shown below.
Xw'=AwXw+BwZp (45)
Zw=CwXw+DwZp (46)
Xw denotes a state quantity of the frequency weight Ws(S), and Zw denotes
an output of the frequency weight Ws(S). Aw, Bw, Cw and Dw are constant
matrices determined by a control specification. These constant matrices
Aw, Bw, Cw and Dw are so determined as to reduce a gain for the sprung
mass acceleration Xb" in a frequency range of about 3 to 8 Hz (FIG. 12(A))
with a view to improving riding comfort of the passenger (eliminating a
feeling of cragginess), reduce a gain for the sprung mass speed Xb' in a
frequency range of about 0.5 to 1.5 Hz (FIG. 12(B)) with a view to
inhibiting resonance of the vehicle body BD, and reduce again for the
relative speed (Xw'-Xb') in a frequency range of about 10 to 14 Hz (FIG.
12(C)) with a view to avoiding resonance of the wheel WH. While the
frequency ranges for reducing these respective gains are prevented from
overlapping with one another and thus prevented from interfering with one
another, respective elements constituting the evaluated output Zp, namely,
the sprung mass acceleration Xb", the sprung mass speed Xb' and the
relative speed (Xw'-Xb') are controlled independently.
A state space expression of the weight Wu(S) by which the control input "u"
is multiplied is indicated by formulas (47) and (48) shown below.
Xu'=AuXu+BuU (47)
Zu=CuXu+DuU (48)
Xu denotes a state quantity of the frequency weight Wu(S), and Zu denotes
an output of the frequency weight Wu(S). Au, Bu, Cu and Du are constant
matrices determined by a control specification. In order to consider
responding performance of an electric actuator for controlling the damping
coefficient, the constant matrices Au, Bu, Cu and Du are determined such
that a gain for the control input "u" is restricted in a high frequency
range in accordance with a frequency characteristic of the actuator (FIG.
12(D)).
At this moment, a state space expression of a generalized model in the
non-linear H.infin. state feedback control system is indicated by formulas
(49) through (51) shown below.
X'=AX+B1w1+B2(X)u (49)
Z1=a1(X)(C11X+D121(X)u) (50)
Z2=a2(X)(C12X+D122u) (51)
In the aforementioned formulas (49) through (51), X, A, B1, B2(X), C11,
D121(X), C12 and D122 are expressed respectively by formulas (52) through
(59) shown below.
##EQU3##
C11=[DwCp1Cw 0 ] (56)
D121(X)=[DwDp12(Xp)] (57)
C12=[00Cu] (58)
D122=Du (59)
Next, in order to find a solution based on Riccati's equation, if the state
space expression of the generalized model expressed by the aforementioned
formulas (49) through (51) is rewritten under the condition defined by a
formula (60) shown below, formulas (60) through (63) are obtained as shown
below.
DwDp12(X)=0 (60)
X'=Ax+B1w+B2(X)u (61)
Z1=a1(X)C11X (62)
Z2=a2(X)C12X+a2(X)D122u (63)
Because A is a stable matrix indicative of a damping force control system,
an attempt is made to design, for the aforementioned generalized model, a
non-linear H.infin. state feedback control rule u=k(X) which satisfies the
condition (1) that the closed-loop system has a stable internal exponent
and the condition (2) that the L2 gain from the road surface disturbance
w1 to the evaluated output Z is equal to or smaller than a positive
constant .gamma..
The aforementioned non-linear H.infin. state feedback control rule u=k(X)
can be obtained if the following conditions are established. That is, (1)
if D122.sup.-1 exists and a positive constant .gamma. is given, a positive
definite symmetric solution P satisfying the after-mentioned Riccati's
equation (64) exists for the positive constant .gamma., and (2) if the
non-linear weights a1(X) and a2(X) satisfy a restrictive condition
expressed by a formula (65) shown below, one of the control rules u=k(X)
for internally stabilizing the closed-loop system and making the L2 gain
equal to or smaller than .gamma. is given by a formula (66) shown below.
##EQU4##
The non-linear weights a1(X) and a2(X) satisfying the restrictive condition
of the formula (66) are exemplified respectively in formulas (67) and (68)
shown below.
##EQU5##
In the aforementioned formulas (67) and (68), m1(X) is an arbitrary
positive definite function. As a result of calculations made by the
computer, it has been made possible to find the positive definite
symmetric solution P as described above. By using the aforementioned
formula (68), the aforementioned formula (66) is converted into a formula
(69) shown below.
##EQU6##
This means that although a partial differential inequality called
Hamilton-Jacobi's inequality must be solved in general in order to design
a control system using the non-linear H.infin. control theory, the control
rule can be designed by solving Riccati's inequality instead of
Hamilton-Jacobi's inequality, by imposing the restrictive condition of the
aforementioned formula (65) on the non-linear weights a1(X) and a2(X) as
described above. Riccati's inequality can be solved easily by using a
known software, such as Matlab. Thus, this method makes it possible to
easily find a positive definite symmetric solution P and to derive the
control rule u=k(X).
The aforementioned D.sub.122 does not exist in Riccati's inequality and
relates only to the restrictive condition imposed on the non-linear
weights and the control rule. This means that the control rule using
D.sub.122 can be adjusted to some extent without solving Riccati's
inequality again. In other words, adjustment of the aforementioned control
rule means the scaling of the control input "u". If the scaling ratio is
multiplied by 10, D.sub.122 is multiplied by 1/10 and the terms of B.sub.2
(X) and C.sub.12 in the aforementioned formula (66) are multiplied by 100
and 10, respectively.
Next, in order to confirm a role played by the non-linear weights, a
generalized model of a bilinear system that does not employ any non-linear
weight will be considered and compared with the aforementioned generalized
model that employs the non-linear weights. That is, the aforementioned
non-linear weights a1(X) and a2(X) are defined as a1(X)=1 and a2(X)=1
respectively. Also, for the sake of simplification, it is determined that
C.sub.12 =0 and that D.sub.122 =1, on the assumption that an orthogonal
condition is satisfied. The state space expression indicated by the
aforementioned formulas (61) through (63) is expressed according to
formulas (70) through (72) shown below.
X'=AX+B1W+B2(X)u (70)
Z1=C11X (71)
Z2=u (72)
Thus, the control rule u=k(X) for the generalized model is expressed
according to a formula (73) shown below.
u=B.sub.2.sup.T (X)PX (73)
P is a positive definite symmetric solution that satisfies Riccati's
inequality (74) shown below.
##EQU7##
A linear approximation system in the vicinity of the origin of the
generalized model indicated by the aforementioned formulas (70) through
(72) is expressed according to formulas (75) through (77) shown below.
X'=AX+B1W (75)
Z1=C11X (76)
Z2=u (77)
Riccati's inequality in the aforementioned formula (74) means that the
closed-loop system is internally stable for the generalized model and that
the L2 gain is equal to or smaller than .gamma.. That is, the L2 gain of
the bilinear system is determined by a value at the origin (Z=0) shown in
FIG. 13. This is because the bilinear system is B2(0)=0 at the origin and
therefore the control input "u" is so ineffective that the L2 gain cannot
be improved in the vicinity of the origin. The generalized model with the
control input u being equal to 0 (the formulas (70) through (72)) also
coincides with the linearly approximated generalized model (the formulas
(75) through (77)). Hence, Riccati's inequality in the formula (74) means
that even in the case where the control input "u" is equal to 0 for the
generalized model (the formulas (70) through (72)), the closed-loop system
is internally stable and the L2 gain is equal to or smaller than .gamma..
That is, even if the state quantity X has increased and the control input
u has become effective, in the case where a control system is designed for
the generalized model (the formulas (70) through (72)) with a control
output expressed by formulas (78) and (79) shown below, it is merely
guaranteed that the L2 gain does not become greater than go even after
being multiplied by the control input "u".
Z1=C11X (78)
Z2=u (79)
That is, if the control output is expressed as in the aforementioned
formulas (78) and (79), the control performance may improve through the
use of the control input "u" but may not make any difference in comparison
with the case of u=0. Thus, the non-linear weights a1(X) and a2(X) are
applied to control outputs Z1 and Z2 respectively, whereby formulas (80)
and (81) are established as shown below. This makes it possible to design
a control system for making the L2 gain of the plant closer to the X axis
which represents the origin level by means of the non-linear weights at
locations remote from the origin, as indicated by a line gi in FIG. 13.
Z1=a1(X)C11X (80)
Z2=a2(X)u (81)
In this control, the damping coefficient Cs of the damper 12 is divided
into the linear damping coefficient Cs0 and the non-linear damping
coefficient Cv, and the control system has been designed with the
non-linear damping coefficient Cv being used as the control input "u". As
shown in FIG. 14A, the linear damping coefficient Cs0 is approximately set
to the vicinity of the center between a minimum damping force
characteristic curve (corresponding to a maximum orifice opening degree)
of the damper 12 and a maximum damping force characteristic curve
(corresponding to a minimum orifice opening degree) of the damper 12, and
the gain of the control input "u" is controlled in accordance with a
frequency. The damping coefficient Cs changes on opposed sides of the
linear damping coefficient Cs0, and the damping force obtained from the
linear damping coefficient Cs0 is designed to remain between the
aforementioned minimum and maximum damping force characteristic curves.
Accordingly, the non-linear damping coefficient Cv can easily be determined
in accordance with a design specification of the damper 12, and the
damping force control can be performed within a range feasible with the
actual damper 12. Consequently, the damping force control can be performed
as desired. For comparison, FIG. 14B shows Lissajou's waveform diagram in
the case where the damping coefficient of the damper 12 is controlled
based on the skyhook theory. In this case, the control cannot be performed
within the range feasible with the actual damper 12, and it is impossible
to perform the control as desired.
Further, if the damping force (the damping coefficient) of the damper 12 is
designed to be switched stepwise to one of a plurality of stages, the
aforementioned linear damping coefficient Cs0 is set such that the damping
force determined by the linear damping coefficient Cs0 becomes, within a
range of small damping forces, substantially equal to a damping force
generated by a predetermined one of the aforementioned stages of the
damper 12. In the suspension system of this kind, in a range where the
damping force is small, the linearity of the damping force with respect to
the relative speed is strong. In other words, it is quite likely that the
calculated non-linear damping coefficient will be equal to "0". Thus, it
is highly probable that the damper 12 be maintained at the predetermined
one of the stages, and the frequency with which the damping coefficient is
switched decreases. Therefore, high durability is rendered to the damper
12.
b2. Calculation Example of First Modification
Next, a calculation example of the first target damping force Fd using the
aforementioned non-linear H.infin. state feedback control rule will be
described.
In this case, in addition to the sprung mass acceleration sensors 21a, 21b,
21c and 21d, the relative displacement amount sensors 22a, 22b, 22c and
22d, the pitch angular velocity sensor 23 and the roll angular velocity
sensor 24, tire displacement amount sensors 25a, 25b, 25c and 25d and
unsprung mass acceleration sensors 26a, 26b, 26c and 26d, which are
provided for the wheels FW1, FW2, RW1 and RW2 respectively, are connected
to the electric control device 20, as indicated by broken lines in FIG. 1.
However, the following description will deal with an example of
calculating the first target damping force Fd of a single wheel
representative of the wheels FW1, FW2, RW1 and RW2. Therefore, in the
following description, the tire displacement amount sensors 25a, 25b, 25c
and 25d will be referred to simply as a tire displacement amount sensor
25, and the unsprung mass acceleration sensors 26a, 26b, 26c and 26d will
be referred to simply as an unsprung mass acceleration sensor 26.
Likewise, the sprung mass acceleration sensors 21a, 21b, 21c and 21d and
the relative displacement amount sensors 22a, 22b, 22c and 22d will be
referred to simply as a sprung mass acceleration sensor 21 and a relative
displacement amount sensor 22 respectively.
The tire displacement amount sensor 25 detects an amount (Xpr-Xpw) of
displacement of the tire TR, which is a relative displacement amount
between a road surface displacement Xpr and an unsprung mass displacement
Xpw. For example, the tire displacement amount (Xpr-Xpw) is detected based
on outputs from a strain sensor for detecting a degree of deformation of
the tire, a pressure sensor for detecting an air pressure of the tire and
the like. The unsprung mass acceleration sensor 26 is fixed to the wheel
WH and detects an unsprung mass acceleration Xpw" indicative of a vertical
acceleration of the wheel WH. The microcomputer in the electric control
device 20 executes a first damping force calculating routine shown in FIG.
15 at intervals of a predetermined period of time by means of the built-in
timer, and thereby calculates a first target damping force Fd.
The execution of the first damping force calculating routine is started in
step 200. In step 202, detection signals indicative of the tire
displacement amount (Xpr-Xpw), the relative displacement amount (Xpw-Xpb),
the sprung mass acceleration Xpb" and the unsprung mass acceleration Xpw"
are inputted from the tire displacement amount sensor 25, the relative
displacement amount sensor 22, the sprung mass acceleration sensor 21 and
the unsprung mass acceleration sensor 26 respectively. Then in step 204,
the sprung mass acceleration Xpb" and the unsprung mass acceleration Xpw"
are time-integrated, whereby a sprung mass speed Xpb' and an unsprung mass
speed Xpw' are calculated. Also, the relative displacement amount
(Xpw-Xpb) is time-differentiated, whereby a relative speed (Xpw'-Xpb') is
calculated.
Next in step 206, Bp2(Xp) and Dp12(Xp) are calculated according to
after-mentioned formulas (82) and (83), which are identical to the
aforementioned formulas (32) and (38) using the relative speed
(Xpw'-Xpb'). B2(X) is then calculated according to an after-mentioned
formula (84), which is identical to the aforementioned formula (55) using
Bp2(XP) and Dp12(Xp).
##EQU8##
In the aforementioned formulas (82) and (83), Mw and Mb denote a mass of
the wheel WH and a mass of the vehicle body BD, respectively. In the
aforementioned formula (84), Bw and Wu denote coefficient matrices
relating to the frequency weights Ws(S) and Wu(S) set in the
aforementioned formulas (45) and (47) respectively. These coefficient
matrices are constant matrices that are preliminarily stored in the
microcomputer.
After the aforementioned processing of step 206, a state variable Xw of the
frequency weights is calculated in step 208 according to an
after-mentioned formula (85) identical to the aforementioned formula (45),
using the evaluated output Zp (the sprung mass speed Xpb', the sprung mass
acceleration Xpb" and the relative speed (Xpw'-Xpb')) which is a control
target of this example that has been inputted in the processing of step
202 or calculated in the processing of step 204 and is defined by the
aforementioned formula (35).
Xw'=AwXw+BwZp (85)
In the aforementioned formula (85), Aw and Bw denote coefficient matrices
relating to the frequency weight Ws(S) set in the aforementioned formula
(45). These matrices are constant matrices that are preliminarily stored
in the microcomputer.
Next in step 210, a state variable Xu of the frequency weight relating to
the control input "u", an extended state quantity X and a control input
"u" are calculated, using formulas (86) through (88) which are identical
to the aforementioned formulas (47), (52) and (69) respectively.
Xu'=AuXu+BuU (86)
##EQU9##
In the aforementioned formula (86), Au and Bu are coefficient matrices
relating to the frequency weight Wu(S) set in the aforementioned formula
(47). These matrices are constant matrices that are preliminarily stored
in the microcomputer. D.sub.122 in the aforementioned formula (88), which
is defined by the aforementioned formula (59), is a coefficient matrix
relating to the frequency weight Wu(S) set in the aforementioned formula
(48) and is a constant matrix preliminarily stored in the microcomputer.
m1(X) is an arbitrary positive definite function, and an algorithm
concerning the function is preliminarily stored in the microcomputer. The
positive definite function m1(X) may be set to a positive constant, for
example, "1.0". C11 is defined by the aforementioned formulas (37) and
(56). In other words, C11 is a constant matrix which is preliminarily
stored in the microcomputer and which is defined by the mass Mw of the
wheel, the mass Mb of the vehicle body BD, the spring constant Ks of the
spring 11, the linear damping coefficient Cs0 of the damper 12 and the
coefficient matrices Cw and Dw relating to the frequency weight Ws(S) set
in the aforementioned formula (46). B2(X) is a matrix calculated in the
aforementioned step 206. P is a positive definite symmetric solution
satisfying the aforementioned formulas (64) and (65) and is a constant
matrix that is preliminarily stored in the microcomputer. C12, which is
defined by the aforementioned formula (58), is a constant matrix that
includes the coefficient matrix Cu relating to the frequency weight Wu(S)
set in the aforementioned formula (48) and is preliminarily stored in the
microcomputer.
In calculating the state variable Xu relating to the frequency weight of
the control input u, the extended state quantity X and the control input
"u" in step 210, the respective values Xu, X and u are supplied with
initial values, and calculations according to the aforementioned formulas
(85) through (88) are repeatedly made until the respective values Xu, X
and u converge. In this manner, the values Xu, X and u are determined.
After the aforementioned processing in step 210, since the control input
"u" is equal to the non-linear damping coefficient Cv, an overall target
damping coefficient Cs of the damper 12 is calculated in step 212
according to an after-mentioned formula (89) wherein the linear damping
coefficient Cs0 is added to the control input "u". In step 216, the
execution of the first damping force calculating routine is terminated.
Cs=Cs0+Cv=Cs0+u (89)
Next in step 214, the first target damping force Fd is calculated according
to an after-mentioned formula (90) wherein the calculated target damping
coefficient C is multiplied by the relative speed (Xpw'-Xpb') calculated
in the aforementioned processing of step 204.
Fd=Cs(Xpw'-Xpb') (90)
c. Second Modification
c1. Designing Example of Non-Linear H.infin. Output Feedback Control System
Next, the designing of the aforementioned non-linear H.infin. state
feedback control system will be further explained. That is, an estimated
value will be obtained from an observer which includes part (e.g. the tire
displacement amount (Xpr-Xpw) and the relative displacement amount
(Xpw-Xpb) or the tire displacement amount (Xpr-Xpw), the relative
displacement amount (Xpw-Xpb) and the unsprung mass speed Xpw') of the
state quantity Xp (the tire displacement amount (Xpr-Xpw), the relative
displacement amount (Xpw-Xpb), the unsprung mass speed Xpw' and the sprung
mass acceleration Xpb") in the control system, and the estimated value
will be used in an attempt to design a non-linear H output feedback
control system. In this case, a generalized model of an output feedback
control system as shown in FIG. 16 wherein frequency weights are added to
the evaluated output Zp and the control input "u" will be considered. In
this case, the evaluated output Zp is multiplied by a non-linear weight
function a1(X,X ) after being multiplied by the frequency weight Ws(S),
and the control input "u" is multiplied by a non-linear weight function
a2(X,X ) after being multiplied by the frequency weight Wu(S). These
non-linear weight functions a1(X,X ) and a2(X,X ) have characteristics
indicated by formulas (91) and (92) shown below. This makes it possible to
design a control system for restricting the L2 gain more positively. As
described above, X denotes a state quantity partially including an
estimated value.
a1(X,X )>0, a2(X,X )>0 (91)
a1(0,0)=a2(0,0)=1 (92)
A state space expression of this system, as well as a state space
expression of the frequency weight Ws(S) by which the evaluated output Zp
is multiplied and a state space expression of the frequency weight Wu(S)
by which the control input "u" is multiplied, is expressed according to
formulas (93) through (97) shown below, as is the case with the
aforementioned state feedback control system.
Xp'=ApXp+Bp1W1+Bp2(Xp)u (93)
Xw'=AwXw+BwZp (94)
Zw=CwXw+DwZp (95)
Xu'=AuXu+BuU (96)
Zu=CuXu+DuU (97)
The state variable Xw, the evaluated function Zw and the constant matrices
Aw, Bw, Cw and Dw are the same as in the case of the aforementioned state
feedback control system.
However, a state space expression of the generalized model in this
non-linear H.infin. output feedback control system is indicated by
formulas (98) through (101) shown below.
X'=AX+B1w+B2(X)u (98)
Z1=a1(X,X )(C.sub.11 X+D.sub.121 (X (99)
Z2=a2(X,X )(C.sub.12 X+D.sub.1 (100)
y=C2X+D21W+D22(X)u (101)
X, W, A, B1, B2(X), C.sub.11, D.sub.121 (X), C12, D.sub.122, C2, D21 and
D22(X) in the aforementioned formulas (98) through (101) are respectively
expressed according to formulas (102) through (113) shown below.
##EQU10##
C11=[DwCp1Cw0 ] (107)
D.sub.121 (X)=[DwDp12(Xp)] (108)
C12=[00Cu] (109)
D122=Du (110)
C2=[Cp200] (111)
D21=[0 Dp21] (112)
D22(X)=Dp22(Xp) (113)
Next, in order to find a solution based on Riccati's equation, the state
space expression of the generalized model expressed by the aforementioned
formulas (98) through (101) is converted under the condition prescribed in
a formula (114) shown below, whereby formulas (115) through (118) are
established as shown below.
DwDp12(X)=0 (114)
X'=AX+B1w+B2(X)u (115)
Z1=a1(X,X )C11X (116)
Z2=a2(X,X )C12X+a2(X,X )D.sub.122 u (117)
y=C2X+D21W+D22(X)u (118)
As is the case with the aforementioned state feedback control system, for
the aforementioned generalized model, an attempt is made to design a
non-linear H.infin. output feedback control rule u=k(y) which satisfies
the condition (1) that the closed-loop system has a stable internal
exponent and the condition (2) that the L2 gain from w to Z is equal to or
smaller than a positive constant .gamma.. Furthermore, in the following
description, the non-linear H.infin. output feedback control will be
classified into first through third types.
c1-1) Designing Example of Control System of First Type
The first type refers to a case where B2(X) in the formula (106) and D22(X)
in the formula (113) are known functions, that is, a case where at least
the relative speed (Xpw'-Xpb') is observable and the observer gain L is a
constant matrix.
The aforementioned non-linear H.infin. output feedback control rule u=k(y)
can be obtained if the following conditions are established. That is, (1)
if D122.sup.-1 exists, .gamma..sub.1 is a positive constant satisfying
.gamma..sub.1.sup.2 I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.12 >0,
.gamma..sub.2 >1, and positive definite symmetric matrices P, Q and a
positive definite matrix .THETA. satisfying Riccati's inequality for
designing an observer (observer gain) of an after-mentioned formula (119)
and Riccati's inequality for designing a controller (control apparatus) of
an after-mentioned formula (120) exist, and (2) if the non-linear weights
a1(X, X ) and a2(X, X ) satisfy a restrictive condition expressed by
formulas (121) and (122) shown below, one of the control rules according
to an after-mentioned formula (123) is given by formulas (124) and (125)
shown below.
AQ+QA.sup.T +Q(C.sub.11.sup.T C.sub.11 +C.sub.12.sup.T C.sub.12
-C.sub.2.sup.T.THETA..sup.T.THETA.C.sub.2)Q B.sub.1 (.gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.21).sup.-1 B.sub.1.sup.T <0
(119)
##EQU11##
The observer gain L is expressed by a formula (126) shown below.
L=-QC.sub.2.sup.T.THETA..sup.T.THETA. (126)
The sign ".parallel..parallel." denotes a Euclid-norm, and the sign
".parallel..parallel..sub.2 " denotes a norm in a square integrable
function space L.sub.2 and is defined by an after-mentioned formula (127)
for f(t).epsilon.L.sub.2.
##EQU12##
.THETA. is a positive definite matrix and .THETA..sup.-1 exists. The use of
.THETA. permits adjustment of the observer gain L. As is the case with the
aforementioned state feedback control rule, the gain L of the controller
can be adjusted using D.sub.122. Furthermore, .gamma..sub.1 is an L2 gain
of the observer and .gamma..sub.2 is an L2 gain of the controller. An L2
gain of the closed-loop system is determined as a product of .gamma..sub.1
and .gamma..sub.2. Accordingly, the L2 gain of the system must be
determined by suitably adjusting the observer and the controller.
The non-linear weights a1(X, X ) and a2(X, X ) satisfying the restrictive
conditions of the aforementioned formulas (121) and (122) respectively are
exemplified below.
a1(X,X )=(.gamma..sub.2.sup.2 +(.gamma..sub.2.sup.2
-1).gamma..sub.2.sup.2.epsilon.m.sub.1 (X,X )X T
.times.PB.sub.2 (X)D.sub.122.sup.-1 D.sub.122.sup.-T B.sub.2.sup.T (X)PX
).sup.1/2
/(.gamma..sub.2.sup.2 +(.gamma..sub.2.sup.2 -1)m.sub.1 (X,X )X T
.times.PB.sub.2 (X)D.sub.122.sup.-1 D.sub.122 -TB.sub.2 T(X)PX ).sup.1/2
(128)
##EQU13##
In the aforementioned formulas (128) and (129), m1(X,X ) is an arbitrary
positive definite function, and .epsilon. is a positive constant
satisfying inequalities .epsilon.<1 and .epsilon..gamma..sub.2.sup.2 >1.
As a result of calculations made by the computer, it has been made
possible to find the positive definite symmetric solution P as described
above. Using the aforementioned formulas (128) and (129), the
aforementioned formulas (124) and (125) are respectively converted into
formulas (130) and (131) shown below.
X' =(A+LC.sub.2)X +(B.sub.2 (X)+LD.sub.22 (X))u-Ly (130)
##EQU14##
Consequently, also in this case, a solution can easily be found by means of
a known software in the same manner as in the case of the aforementioned
state feedback control system. Therefore, this method makes it possible to
easily find the positive definite symmetric solution P and to derive the
estimated state quantity X' and the control rule u=k(y).
c1-2) Calculation Example of First Type
Next, a calculation example of the first target damping force Fd using the
aforementioned control rule of the first type will be described. In this
case, the tire displacement amount sensor 25 (the tire displacement amount
sensors 25a, 25b, 25c and 25d in FIG. 1) and the unsprung mass
acceleration sensor 26 (the unsprung mass acceleration sensors 26a, 26b,
26c and 26d in FIG. 1) are omitted, and the microcomputer executes a first
damping force calculating routine shown in FIG. 17 instead of the first
damping force calculating routine shown in FIG. 15. In other respects,
this example is identical to the aforementioned first modification.
Also in this case, the execution of the first damping force calculating
routine in FIG. 17 is started in step 200. In step 202a, detection signals
indicative of a relative displacement amount (Xpw-Xpb) and a sprung mass
acceleration Xpb" are inputted from the relative displacement amount
sensor 22 and the sprung mass acceleration sensor 21 respectively. In step
204a, as is the case with the aforementioned first modification example, a
relative speed (Xpw'-Xpb') and a sprung mass speed Xpb' are calculated.
Next in step 206a, Bp2(Xp) and Dp12(Xp) are calculated according to
after-mentioned formulas (132) and (133), which are identical to the
aforementioned formulas (32) and (38) using the relative speed
(Xpw'-Xpb'). B2(X) is then calculated according to an after-mentioned
formula (134), which is identical to the aforementioned formula (106)
using Bp2(XP) and Dp12(Xp). D22(X) is calculated according to
after-mentioned formulas (135) and (136), which are identical to the
aforementioned formulas (41) and (113) using the relative speed
(Xpw'-Xpb').
##EQU15##
D22(X)=Dp22(Xp) (136)
In the aforementioned formulas (132) through (135), Mw, Mb, Bw and Bu
denote the same values or constant matrices as in the aforementioned first
modification example.
After the aforementioned processing of step 206a, an estimated state
quantity X and a control input u are calculated using formulas (137) and
(138) which are identical to the aforementioned formulas (130) and (131),
in the same manner as in the aforementioned first modification example.
X' =(A+LC2)X +(B2(X)+TD22(X))u-Ly (137)
##EQU16##
In the aforementioned formula (137), A is a constant matrix that is
preliminarily stored in the microcomputer and determined by the
aforementioned formulas (104), (30) and (37). L is a constant matrix that
is preliminarily stored in the microcomputer and defined by the
aforementioned formula (126), and is a gain of the observer that is
determined by the positive definite symmetric matrix Q, the constant
matrix C2 determined by the aforementioned formulas (39) and (111), and
the positive definite matrix .THETA.. C2 is also the aforementioned
constant matrix that is preliminarily stored in the microcomputer. B2(X)
and D22(X) are matrices calculated in the aforementioned step 206a.
Further, y is an observed value which represents, in the first type, the
relative displacement amount (Xpw-Xpb) inputted through the processing of
the aforementioned step 202a and the sprung mass speed Xpb' calculated
through the processing of the aforementioned step 204a.
In the aforementioned formula (138), D.sub.122 is a coefficient matrix that
is defined by the aforementioned formula (110) and relates to the
frequency weight Wu(S) set in the aforementioned formula (48), and is a
constant matrix that is preliminarily stored in the microcomputer.
.gamma..sub.2 is a positive constant satisfying the aforementioned
inequality .gamma..sub.2 >1. m1(X,X ) is an arbitrary positive definite
function, and an algorithm concerning the function is preliminarily stored
in the microcomputer. The positive definite function m1(X) may be set to a
positive constant, for example, "1.0". C11 is defined by the
aforementioned formulas (37) and (107). In other words, C11 is a constant
matrix which is preliminarily stored in the microcomputer and which is
defined by the mass Mw of the wheel WH, the mass Mb of the vehicle body
BD, the spring constant Ks of the spring 11, the linear damping
coefficient CS0 of the damper 12 and the coefficient matrices Cw and Dw
relating to the frequency weight Ws(S) set in the aforementioned formula
(46). B2(X) is a matrix calculated in the aforementioned step 206a. P is a
positive definite symmetric solution satisfying the aforementioned
formulas (119) and (120) and is a constant matrix that is preliminarily
stored in the microcomputer. C12, which is defined by the aforementioned
formula (109), is a constant matrix that includes the coefficient matrix
Cu relating to the frequency weight Wu(S) set in the aforementioned
formula (48) and is preliminarily stored in the microcomputer.
After the processing of the aforementioned step 210a, through processings
of the same steps 212 and 214 as in the first modification example, an
overall target damping coefficient Cs of the damper 12 and a first target
damping force Fd are calculated. In step 216, the execution of the first
damping force calculating routine is terminated.
c2-1) Designing Example of Control System of Second Type
The second type refers to a case where B2(X) in the aforementioned formula
(106) and D22(X) in the aforementioned formula (113) are unknown
functions, that is, a case where the relative speed (Xpw'-Xpb') is unknown
and the observer gain L is a constant matrix.
In a bilinear system of this kind, B2(X) and D22(X) are linear functions of
X. In consideration of this, the generalized model expressed by the
aforementioned formulas (115) through (118) is rewritten, whereby formulas
(139) through (142) are established as shown below. It is to be noted
herein that B20, D220 and d122 are constant matrices.
X'=AX+B1w+B20Xu (139)
Z1=a1(X )C.sub.11 X (140)
Z2=a2(X )C.sub.12 X+a2(X)d.sub.122 u (141)
y=C.sub.2 X+D.sub.21 W+D.sub.220 Xu (142)
An attempt will be made to design a non-linear H.infin. output feedback
control rule for this generalized model. In the case where the observer
gain L is given as a constant matrix, an output feedback control rule can
be designed according to the following theorem. That is (1) if, given that
.gamma..sub.1 is a positive constant satisfying an inequality
.gamma..sub.1.sup.2 I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.12 >0, that
.gamma..sub.2 is a positive constant satisfying an inequality
.gamma..sub.2 >1 and that a positive constant .epsilon. satisfying an
inequality .epsilon..sup.2 -u.sup.2 >0 exists, positive definite symmetric
matrices P and Q and a positive definite matrix .THETA. which satisfy
Riccati's inequality for designing the observer (observer gain) of an
after-mentioned formula (143) and Riccati's inequality for designing the
controller of an after-mentioned formula (144) exist, and (2) if the
non-linear weights a1(X, X ) and a2(X, X ) satisfy restrictive conditions
prescribed in formulas (145) and (146) shown below, one of the control
rules according to an after-mentioned formula (147) is given by formulas
(148) and (149) shown below.
AQ+QA.sup.T +Q(C.sub.11.sup.T C.sub.11 +C.sub.12.sup.T C.sub.12
-C.sub.2.sup.T.THETA..sup.T.THETA.C.sub.2
+.epsilon..sup.2 I+.epsilon..sub.1.sup.2 D.sub.220.sup.T.THETA..sup.T
(I+.THETA.D.sub.21.times.(.gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.21).sup.-1
D.sub.21.sup.T.THETA..sup.T).THETA.D.sub.220)Q
+B.sub.1 (.gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.21).sup.-1 B.sub.1.sup.T
+(B.sub.1 (.gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.21).sup.-1 D.sub.21).sup.-1
D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.220 +B.sub.20)
.times.(D.sub.220.sup.T.THETA..sup.T.THETA.D.sub.21 (.gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.21).sup.-1 B1.sup.T
+B.sub.20.sup.T)<0 (143)
##EQU17##
The observer gain L(u) is expressed by a formula (150) shown below.
L(u)=-QC.sub.2.sup.T.THETA..sup.T.THETA. (150)
.THETA. is a positive definite matrix and .THETA..sup.-1 exists. The use of
.THETA. permits adjustment of the observer gain L(u). As is the case with
the aforementioned state feedback control rule, the gain L of the
controller can be adjusted using d.sub.122.
The non-linear weights a1(X, X ) and a2(X, X ) satisfying the restrictive
conditions of the aforementioned formulas (145) and (146) respectively are
exemplified in formulas (151) and (152) shown below.
a1(X,X )=(.gamma..sub.2.sup.2 d.sub.122.sup.2 +(.gamma..sub.2.sup.2
-1).gamma..sub.2.sup.2.epsilon.m1(X,X )
.times.X .sup.T PB.sub.20 X X .sup.T B.sub.20.sup.T PX ).sup.1/2
/(.gamma..sub.2.sup.2 d.sub.122.sup.2 +(.gamma..sub.2.sup.2 -1)m1(X,X )
.times.X .sup.T PB.sub.20 X X .sup.T B.sub.20.sup.T PX ).sup.1/2 (151)
##EQU18##
In the aforementioned formulas (151) and (152), m1(X, X ) is an arbitrary
positive definite function, and .epsilon. is a positive constant
satisfying inequalities .epsilon.<1 and .epsilon..gamma..sub.2.sup.2 >1.
As a result of calculations made by the computer, it has been made
possible to find the positive definite symmetric solution P as described
above. Using the aforementioned formulas (151) and (152), the
aforementioned formulas (148) and (149) are respectively converted into
formulas (153) and (154) shown below.
X' =(A+L(u)C2)X +(B20+L(u)D220)X u-L(u)y (153)
##EQU19##
Consequently, also in this case, a solution can easily be found by means of
a known software in the same manner as in the case of the aforementioned
state feedback control system. Therefore, this method makes it possible to
easily find the positive definite symmetric solution P and to derive the
estimated state quantity X' and the control rule u=k(y).
c2-2) Calculation Example of Second Type
Next, a calculation example of the first target damping force Fd using the
control rule of the second type will be described. In this case, the
relative displacement amount sensor 22 of the first type shown in FIG. 6
(the relative displacement amount sensors 22a, 22b, 22c and 22d shown in
FIG. 1) is omitted. The inputting of the relative displacement amount
(Xpw-Xpb) from the relative displacement amount sensor 22 in step 202a of
FIG. 17, the calculation of the relative speed (Xpw'-Xpb') in step 204a of
FIG. 17, and the arithmetic processing in step 206a are omitted. Then
calculations are made according to the aforementioned control rule of the
second type.
Also in this case, the execution of the first damping force calculating
routine in FIG. 17 is started in step 200. A sprung mass acceleration Xpb"
is inputted in step 202a, and a sprung mass speed Xpb' is calculated in
step 204a. In step 210a, a control input u and an estimated state quantity
X' including an estimation of the relative speed (Xpw'-Xpb') are
calculated using formulas (155) and (156) which are identical to the
aforementioned formulas (153) and (154) respectively.
X' =(A+L(u)C.sub.2)X +(B.sub.20 +L(u)D.sub.220)X u-L(u)y (155)
##EQU20##
In the aforementioned formulas (155) and (156), A, L, C.sub.2,
.gamma..sub.2, m1(X, X ), C.sub.11, P and C.sub.12 are the same as in the
case of the first type. B.sub.20, D.sub.220, d.sub.122 are the
aforementioned appropriate matrices that are preliminarily stored in the
microcomputer. In this case, y is an observed value which represents the
sprung mass speed Xpb' calculated through the aforementioned processing of
step 204a.
After the aforementioned processing of step 210a, through the processings
of steps 212 and 214 substantially identical to those of the first type,
an overall damping force Cs of the damper 12 is calculated and a first
target damping force Fd is calculated. In this case, when calculating the
first target damping force Fd in step 214, the estimated relative speed
(Xpw' -Xpb' ) calculated in step 210a is utilized.
c3-1) Designing Example of Control System of Third Type
The third type also refers to a case where B.sub.2 (X) in the
aforementioned formula (106) and D.sub.22 (X) in the aforementioned
formula (113) are unknown functions, that is, a case where the relative
speed (Xpw'-Xpb') is unknown and the observer gain L is a function matrix.
Also in the third type, an attempt will be made to design a non-linear
H.infin. output feedback control rule for the generalized model expressed
by the aforementioned formulas (139) through (142) of the second type. In
the case where the observer gain L is given as a function of the control
input u, an output feedback control rule can be designed according to the
following theorem. That is (1) if, given that .gamma..sub.1 is a positive
constant satisfying an inequality .gamma..sub.1.sup.2
I-D.sub.21.sup.T.THETA..sup.T.THETA.D.sub.12 >0, that .gamma..sub.2 is a
positive constant satisfying an inequality .gamma..sub.2 >1 and that a
positive constant .epsilon. satisfying an inequality .epsilon..sub.1.sup.2
-u.sup.2 >0 exists, positive definite symmetric matrices P and Q and a
positive definite matrix .THETA. which satisfy Riccati's inequality for
designing the observer (observer gain) of an after-mentioned formula (157)
and Riccati's inequality for designing the controller of an
after-mentioned formula (158) exist, and (2) if the non-linear weights
a1(X, X ) and a2(X, X ) satisfy restrictive conditions prescribed in
formulas (159) and (160) shown below, one of the control rules according
to an after-mentioned formula (161) is given by formulas (162) and (163)
shown below.
AQ+QA.sup.T +Q(C11.sup.T C11+C12.sup.T C12+.epsilon..sup.2
I)Q+B1(.gamma..sub.1.sup.2 I-D21.sup.T.THETA..sup.T.THETA.D21).sup.-1
B1.sup.T +B20B20.sup.T <0 (157)
##EQU21##
The observer L(u) is expressed by a formula (164) shown below.
L(u)=-QC.sub.2.sup.T.THETA..sup.T.THETA.-uQD.sub.220.sup.T.THETA..sup.
T.THETA.=L.sub.1 +uL.sub.2 (164)
L.sub.1 and L.sub.2 shown in the aforementioned formula (164) are
respectively expressed by formulas (165) and (166) shown below.
L.sub.1 =-QC.sub.2.sup.T.THETA..sup.T.THETA. (165)
L.sub.2 =-QD.sub.220.sup.T.THETA..sup.T.THETA. (166)
.THETA. is a positive definite matrix and .THETA..sup.-1 exists. The use of
.THETA. permits adjustment of the observer gain L. As is the case with the
aforementioned state feedback control rule, the gain L of the controller
can be adjusted using d.sub.122.
The non-linear weights a1(X, X ) and a2(X, X ) satisfying the restrictive
conditions of the aforementioned formulas (159) and (160) respectively are
exemplified respectively in formulas (167) and (168) shown below.
a1(X,X )=(.gamma..sub.2.sup.2 d122.sup.2 +(.gamma..sub.2.sup.2
-1).gamma..sub.2.sup.2.epsilon.m1(X,X )X .sup.T P
.times.(B20+L1.THETA..sup.-1.THETA..sup.-T L2.sup.T P)X X .sup.T
.times.(B20T+PL2.THETA..sup.-1.THETA..sup.-T)PX ).sup.1/2
/(.gamma..sub.2.sup.2 d122.sup.2 +(.gamma..sub.2.sup.2 -1)m1(X,X )X TP
.times.(B20+L1.THETA..sup.-1.THETA..sup.-T L2.sup.T P)X X .sup.T
.times.(B20.sup.T +PL2.THETA..sup.-1.THETA..sup.-T L1.sup.T)pX ).sup.1/2
(167)
##EQU22##
In the aforementioned formulas (167) and (168), m1(X, X ) is an arbitrary
positive definite function, and .epsilon. is a positive constant
satisfying inequalities .epsilon.<1 and .epsilon..gamma..sub.2.sup.2 >1.
As a result of calculations made by the computer, it has been made
possible to find the positive definite symmetric solution P as described
above. Using the aforementioned formulas (167) and (168), the
aforementioned formulas (162) and (163) are respectively converted into
formulas (169) and (170) shown below.
##EQU23##
Consequently, also in this case, a solution can easily be found by means of
a known software in the same manner as in the case of the aforementioned
state feedback control system. Therefore, this method makes it possible to
easily find the positive definite symmetric solution P and to derive the
estimated state quantity X' and the control rule u=k(y).
c3-2) Calculation Example of Third Type
Next, a calculation example of the first target damping force Fd using the
control rule of the third type will be described. In this case, the
construction is the same as in the aforementioned case of the second type.
Also in this case, the execution of the first damping force calculating
routine is started in step 200. After processings in steps 202a and 204a
which are substantially identical to those of the aforementioned first
type, an estimated state quantity X and a control input u are calculated
using formulas (171) and (172) which are identical to the aforementioned
formulas (169) and (170), in the same manner as in the aforementioned case
of the second type.
##EQU24##
In the aforementioned formulas (171) and (172), A, C.sub.2, B.sub.20,
D.sub.220, .gamma..sub.2, m1(X, X ), C.sub.11, d.sub.122, P, C.sub.12 are
the same as those in the aforementioned case of the second type. L,
L.sub.1 and L.sub.2 are gains defined by the aforementioned formulas (164)
through (166). Furthermore, also in this case, y is an observed value
which represents the sprung mass speed Xpb' calculated through the
aforementioned processing of step 204a.
After the aforementioned processing in step 210a, through the processings
of steps 212 and 214 substantially identical to those of the second type,
an overall damping force Cs of the damper 12 is calculated and a first
target damping force Fd is calculated. In step 216, the execution of the
first damping force calculating routine is terminated.
d. Third Modification
d1. Designing Example of Non-Linear H.infin. Control System of Kalman
Filter Base
For the aforementioned model marked with a, an attempt will be made to
design an output feedback system which employs a Kalman filter as an
observer, on the condition that the bilinear terms B.sub.p2 (X.sub.p) and
D.sub.p2 (X.sub.p) be known, namely, that the relative speed (Xpw'-Xpb')
be observable.
In the third modification, the same reference characters as in the
aforementioned case of the second modification are used, and the
coefficients and variables concerning the model are accompanied by a
suffix p. A state space expression of the suspension system is indicated
by formulas (173) and (174) shown below.
X.sub.p '=A.sub.p X.sub.p +B.sub.p1 W.sub.1 +B.sub.p2 (X.sub.p)u (173)
y.sub.p =C.sub.p X.sub.p +D.sub.p1 W.sub.2 +D.sub.p2 (X.sub.p)u (174)
If D.sub.p1 =I, the Kalman filter in the case of t.fwdarw..infin. is
expressed according to a formula (175) shown below.
X.sub.0 'A.sub.p X.sub.0 +B.sub.p2 u+K(C.sub.p X.sub.0 +D.sub.p2
(X.sub.p)u-y) (175)
X.sub.0 and X.sub.0 ' are estimated state quantities in the Kalman filter,
and the filter gain K is expressed by a formula (176) shown below.
K=-.SIGMA.C.sub.p.sup.T W.sup.-1 (176)
The estimated error covariance .SIGMA. is a positive definite symmetric
solution of Riccati's equation (177) shown below.
A.sub.p.SIGMA.+.SIGMA.A.sub.p.sup.T +B.sub.p1 VB.sub.p1.sup.T
-.SIGMA.C.sub.p.sup.T W.sup.-1 C.sub.p.SIGMA.=0 (177)
V is a covariance matrix of w1, and W is a covariance matrix of w2.
FIG. 18 shows a block diagram of a generalized model of this system. In
this case, "a product obtained by multiplying the estimated state quantity
X.sub.0 by the frequency weight W(S)", which is an output from the
observer, and "a product obtained by multiplying the control input u by
the frequency Wu(S)" are used as evaluated outputs Z. In other words, the
Kalman filter is used herein as a detector, and the control system is so
designed as to reduce an output from the Kalman filter. The third
modification is different from the aforementioned first and second
modifications in this respect. However, if the state has been estimated
successfully, it is considered that the performance equivalent to that of
the first and second modifications will be obtained. A state space
expression of the system indicated by the block diagram in FIG. 18 is
expressed according to formulas (178) through (184) shown below.
X.sub.p '=A.sub.p X.sub.p +B.sub.p1 W.sub.1 +B.sub.p2 (X.sub.p)u (178)
X.sub.0 '=A.sub.p X.sub.0 +B.sub.p2 (X.sub.p)u+L(C.sub.2 X.sub.0 +D.sub.p2
(X.sub.p)u-y) (179)
y=C.sub.p X.sub.p +D.sub.p1 W.sub.2 +Dp.sub.2 (X.sub.p)u (180)
X.sub.w '=A.sub.w X.sub.w +B.sub.w C.sub.s X.sub.0 (181)
Z.sub.1 =a.sub.1 (X.sub.p,X.sub.0,X.sub.w,X.sub.u)(C.sub.w X.sub.w +D.sub.w
C.sub.s X.sub.0) (182)
X.sub.u '=A.sub.u X.sub.u +B.sub.u u (183)
Z.sub.2 =a2(X.sub.p,X.sub.0,X.sub.w,X.sub.u)(C.sub.u X.sub.u +D.sub.u u)
(184)
X.sub.p denotes a state quantity of the system, the formula (178)
represents a state space expression of the system, X.sub.0 denotes an
estimated state quantity, the formula (179) represents a state space
expression of the observer, y denotes an observed output, and X.sub.w
denotes a state of frequency weight. Evaluated outputs Z.sub.1 and Z.sub.2
are to be weighted later with non-linear weights.
For this system, a control rule u=k(X.sub.0) which performs feedback
control of a state of the observer satisfying the condition that the
closed-loop system has a stable internal exponent and the condition that
the L2 gain from w to Z is equal to or smaller than a positive constant
.gamma. is designed. As indicated by a formula (185) shown below, this
system is characterized in that X.sub.0 is an input for the frequency
weight Ws(S).
##EQU25##
First of all, if the error variable is defined as in a formula (186) shown
below, the error system is expressed according to formulas (187) and (188)
shown below.
X.sub.e =X.sub.p -X.sub.0 (186)
X.sub.e '=(A.sub.p +LC.sub.p)X.sub.e +B.sub.p1 W.sub.1 +LD.sub.p W.sub.2
(187)
y.sub.e =y-C.sub.p X.sub.0 -D.sub.p2 (X.sub.p)u=C.sub.p X.sub.0 +D.sub.p1
W.sub.2 (188)
Furthermore, the error system expressed by the aforementioned formulas
(187) and (188) is converted by multiplying ye by a constant matrix
.THETA. (a scaling matrix) which has its inverse matrix. The converted
system is indicated by formulas (189) and (190) shown below.
X.sub.pe '=(A.sub.p +LC.sub.p)X.sub.pe +B.sub.p1 w.sub.1 +LD.sub.p W.sub.2
(189)
y.sub.e =.THETA.C.sub.p X.sub.e +.THETA.D.sub.p1 W.sub.2 (190)
For this converted error system, an attempt will be made to design an
observer gain L such that a positive constant .gamma..sub.1 exists and
that the L2 gain from a disturbance input w=[W.sub.1.sup.T W.sub.2.sup.T ]
to y.sub.e becomes equal to or smaller than .gamma..sub.1
(.parallel.y.sub.e.parallel..sub.2.ltoreq..gamma..sub.
1.parallel.w.parallel..sub.2).
If it is assumed herein that .gamma..sub.1 is a positive constant
satisfying an inequality .gamma..sub.1
I-D.sub.p1.sup.T.THETA..sup.T.THETA.D.sub.p1 >0, the value of L for
establishing .parallel.y.sub.e.parallel..sub.2.ltoreq..gamma..sub.1
I.parallel.W.parallel..sub.2 is given by a formula (191) shown below.
L=-QC.sub.p.sup.T.THETA..sup.T.THETA. (191)
Q is a positive definite symmetric matrix satisfying Riccati's equation
(192) shown below.
##EQU26##
It is to be noted that the aforementioned Riccati's equation (192), which
is to be solved herein, is an order of the model and is smaller than the
order of the generalized models of the aforementioned first and second
modifications.
The aforementioned formula (179) concerning the observer is then rewritten,
so that a formula (193) shown below is obtained.
##EQU27##
Using the observer expressed by this formula (193), an attempt will be made
to design a controller such that a positive constant .gamma..sub.2 exists
and that the L2 gain from an observer error y.sub.e to an evaluated
output Z becomes equal to or smaller than .gamma..sub.2
(.parallel.Z.parallel..sub.2.ltoreq..gamma..sub.2.parallel.ye.parallel..
sub.2). If a generalized model which combines state variables X.sub.w and
X.sub.u relating to frequency weights is constructed using the observer
expressed by the aforementioned formula (193), a state space expression of
the model is indicated by formulas (194) through (196) shown below.
X.sub.k '=AX.sub.k +B.sub.2 (X.sub.p)u+L.sub.1.THETA..sup.-1 y.sub.e (194)
Z.sub.1 =a1(X.sub.p,X.sub.k)C.sub.11 X.sub.k (195)
Z.sub.2 =a2(X.sub.p,X.sub.k)C.sub.12 X.sub.k +a2(X.sub.p,X.sub.k)D.sub.12 u
(196)
The respective variable matrices and constant matrices in the
aforementioned formulas (194) through (196) are expressed by formulas
(197) through (204) shown below.
##EQU28##
C.sub.11 =[D.sub.w C.sub.s C.sub.w 0] (202)
C.sub.12 =[0 0 C.sub.u ] (203)
D.sub.12 =D.sub.u (204)
The state quantity X.sub.k defined herein does not include the state
quantity X.sub.p.
At this moment, if it is assumed that D.sub.12.sup.-1 exists, a positive
definite symmetric solution P of Riccati's inequality of an
after-mentioned formula (205) exists. Furthermore, if the non-linear
weights a1(X.sub.p, X.sub.k) and a2(X.sub.p, X.sub.k) satisfy a formula
(206) shown below, a positive constant .gamma..sub.2 exists and a
controller for establishing
.parallel.z.parallel..sub.2.ltoreq..gamma..sub.2.parallel.y.sub.
e.parallel..sub.2 is given by a formula (207) shown below.
##EQU29##
Accordingly, it is possible to design an observer and a controller that
satisfy formulas (208) and (209) shown below.
.parallel.y.sub.e.parallel..sub.2.ltoreq..gamma..sub.
1.parallel.W.parallel..sub.2 (208)
.parallel.Z.parallel..sub.2.ltoreq..gamma..sub.2.parallel.ye.parallel..sub.
2 (209)
This reveals that positive definite symmetric matrices Q and P satisfying
Riccati's equation and inequality (210) and (211) shown below exist.
##EQU30##
Then if the non-linear weights a1(X.sub.p, X.sub.k) and a2(X.sub.p,
X.sub.k) satisfy a restrictive condition of a formula (212) shown below, a
control rule according to an after-mentioned formula (213) is given by
formulas (214) and (215) shown below.
##EQU31##
.parallel.Z.parallel..sub.2.ltoreq..gamma..sub.1.gamma..sub.
2.parallel.W.parallel..sub.2 (213)
X.sub.k '=(A+L.sub.1 C.sub.2)X.sub.k +(B.sub.2 (X.sub.p)+L.sub.1 D.sub.p2
(X.sub.p))u-L.sub.1 y (214)
##EQU32##
Riccati's equation of the aforementioned formula (177) that has been used
to design the Kalman filter is herein compared with Riccati's equation of
the aforementioned formula (192). If covariance matrices V and W are
defined by formulas (216) and (217) shown below, positive definite
solutions .SIGMA. and Q of both Riccati's equations coincide with each
other.
W.sup.-1 =.THETA..sup.T.THETA. (216)
##EQU33##
That is, if .THETA. and .gamma..sub.1 satisfying the aforementioned
formulas (216) and (217) are selected by means of the covariance matrices
V and W that have been used to design the Kalman filter, the observer that
is designed herein and expressed by an after-mentioned formula (218)
coincides with the Kalman filter.
X.sub.0 '=AX.sub.0 +B.sub.2 (X.sub.p)u+L(C.sub.2 X.sub.0 +D.sub.p2
(X.sub.p)u-y) (218)
The non-linear weights a1(X.sub.p, X.sub.k) and a2(X.sub.p, X.sub.k)
satisfying the restrictive condition of the aforementioned formula (212)
are respectively exemplified in formulas (219) and (220) shown below.
##EQU34##
In the aforementioned formulas (219) and (220), m1(X, X ) is an arbitrary
positive definite function. As a result of calculations made by the
computer, it is possible to find the positive definite symmetric solution
P as described above. By using the aforementioned formulas (219) and
(220), the aforementioned formulas (214) and (215) are respectively
converted into formulas (221) and (222) shown below.
X.sub.k '=(A+L.sub.1 C.sub.2)X.sub.k +(B.sub.2 (X.sub.p)+L.sub.1 D.sub.p2
(X.sub.p))u-L.sub.1 y (221)
u=-D.sub.12.sup.-1 ((1+m1(X.sub.p,X.sub.k)X.sub.k.sup.T C.sub.11.sup.T
C.sub.11 X.sub.k).times.D.sub.12.sup.-T B.sub.2.sup.T
(X.sub.p)P+C.sub.12)X.sub.k (222)
Consequently, also in this case, a solution can easily be found by means of
a known software in the same manner as in the case of the aforementioned
state feedback control system. Therefore, this method makes it possible to
easily find the positive definite symmetric solution P and to derive the
state quantity X' and the control rule u=k(y).
d2. Calculation Example of Third Modification
Next, a calculation example of the first target damping force Fd using the
control rule of the Kalman filter base will be described. The construction
in this case is also the same as that of the first type of the
aforementioned second modification.
Also in this case, the execution of the first damping force calculating
routine is started in step 200, and processings of steps 202a, 204a and
210a which are substantially identical to those of the first type of the
aforementioned second modification example are performed. However in this
case, a state quantity Xk' and a control input u are calculated in step
210a substantially in the same manner as in the case of the first type of
the aforementioned second modification example, using after-mentioned
formulas (223) and (224) which are identical to the aforementioned
formulas (221) and (222) respectively.
X.sub.k '=(A+L.sub.1 C.sub.2)X.sub.k +(B.sub.2 (X.sub.p)+L.sub.1 D.sub.p2
(X.sub.p))u-L.sub.1 y (223)
u=D.sub.12.sup.-1 ((1+m1(X.sub.p,X.sub.k)X.sub.k.sup.T C.sub.11.sup.T
C.sub.11 X.sub.k).times.D.sub.12.sup.-T B.sub.2.sup.T (X.sub.p)P+C.sub.12
(224)
In the aforementioned formula (223), A is a constant matrix that is
preliminarily stored in the microcomputer and determined by the
aforementioned formulas (198), (185), (30) and (47). L.sub.1 is a constant
matrix that is preliminarily stored in the microcomputer and defined by
the aforementioned formulas (200), (191) and (192), and is a gain of the
observer determined by the positive definite symmetric matrix Q, the
constant matrix C.sub.p, the constant matrix C.sub.2 determined by the
aforementioned formulas (39) and (111), and the positive definite matrix
.THETA.. C.sub.2 is also the aforementioned constant matrix that is
preliminarily stored in the microcomputer. B.sub.2 (X.sub.p) is a constant
matrix that is determined by the aforementioned formulas (199), (32) and
(47). D.sub.p2 (X.sub.p) is a constant matrix that is determined by the
aforementioned formula (38). Further, y is an observed value and
represents the relative displacement amount (Xpw-Xpb) inputted through the
aforementioned processing of step 202a and the sprung mass speed Xpb'
calculated through the aforementioned processing of step 204a.
In the aforementioned formula (224), D.sub.12 is a coefficient matrix that
is defined by the aforementioned formula (204) and relates to the
frequency weight Wu(S) set by the aforementioned formula (48), and is a
constant matrix that is preliminarily stored in the microcomputer.
m1(X.sub.p, X.sub.k) is an arbitrary positive definite function and an
algorithm concerning the function is preliminarily stored in the
microcomputer. This positive definite function m1(X.sub.p, X.sub.k) may be
set to a positive constant, for example, "1.0". C.sub.11 is a constant
matrix that is defined by the aforementioned formula (202), prescribed by
the coefficient matrices Cw, Dw and Cs relating to the frequency weight
Ws(S) set in the aforementioned formula (185), and preliminarily stored in
the microcomputer. B.sub.2 (X.sub.p) is a constant matrix that is
determined by the aforementioned formulas (199), (32) and (47). P is a
positive definite symmetric solution satisfying the aforementioned formula
(211) and is a constant matrix that is preliminarily stored in the
microcomputer. C.sub.12 is a constant matrix which is preliminarily stored
in the microcomputer and which includes the coefficient matrix Cu that is
prescribed by the aforementioned formula (203) and relates to the
frequency weight Wu(S) set in the aforementioned formula (48).
After the processing of the aforementioned step 210a, through processings
of the same steps 212 and 214 as in the first modification and the first
type of the second modification, an overall target damping coefficient Cs
of the damper 12 and a first target damping force Fd are calculated. In
step 216, the execution of the first damping force calculating routine is
terminated.
e. Other Modification
In the aforementioned first through third modifications, the tire
displacement amount (Xpr-Xpw), the relative displacement amount (Xpw-Xpb),
the unsprung mass speed Xpw' and the sprung mass speed Xpb' are used as a
state quantity in the state space expression of the generalized model.
However, as long as the aforementioned state space expression is possible,
other physical quantities concerning vertical movements of the vehicle
body BD and the wheel WH can also be utilized. Further, in the first type
of the aforementioned second modification and the third modification, the
estimation is carried out without detecting the tire displacement amount
(Xpr-Xpw) or the unsprung mass speed Xpw'. In the second and third types
of the aforementioned second modification, the estimation is carried out
even without detecting the relative displacement amount (Xpw-Xpb) (the
relative speed (Xpw'-Xpb')). However, through a slight modification on the
control side, the estimation can also be carried out without detecting
other state variables.
In the aforementioned first through third modifications, three physical
quantities, namely, the sprung mass speed Xpb' which affects resonance of
the vehicle body BD, the relative speed (Xpw'-Xpb') which affects
resonance of the wheel WH, and the sprung mass acceleration Xpb" which
affects a deterioration in riding comfort (a feeling of cragginess) of the
vehicle are used as the evaluated output Zp. However, it is also possible
to use one or two of these physical quantities as the evaluated output Zp.
In addition, as a quantity affecting resonance of the vehicle body BD,
physical quantities closely associated with movements of the vehicle body
BD such as the sprung mass acceleration Xpb" and the sprung mass
displacement amount Xpb may be used instead of the sprung mass speed Xpb'.
As a quantity affecting resonance of the wheel WH, physical quantities
closely associated with movements of the wheel WH such as the unsprung
mass speed Xpw' and the tire displacement amount (Xpr-Xpw) may be used
instead of the relative speed (Xpw'-Xpb').
In the aforementioned various modifications, the non-linear H control
theory is applied as a control theory which can handle a non-linear model
and provide a design specification in the form of a frequency range.
However, as the control theory, the bilinear matrix inequality control
theory, which is an extended version of the linear matrix inequality
control theory, may be employed.
The aforementioned various modifications realize a good damping force
control device which satisfies the control specification (the norm
condition) that is given at the time of designing, has a control input
(the non-linear damping coefficient Cv) that changes continuously, and
performs control without causing a sense of incongruity, also in the
bilinear control system handling the first target damping force Fd=Cs
(Xpw'-Xpb'), which is given as a product of the speed (Xpw'-Xpb') of the
wheel WH (the unsprung mass member) relative to the vehicle body BD (the
sprung mass member) and the damping coefficient Cs that changes in
accordance with the relative speed (Xpw'-Xpb'). Further in the
aforementioned various modification examples, the first target damping
force Fd is calculated by considering a generalized model which employs,
as an evaluated output, the vertical speed Xpb' of the vehicle body BD
which affects resonance of the vehicle body BD, the speed (Xpw'-Xpb') of
the wheel WH relative to the vehicle body BD which affects resonance of
the wheel WH, and the vertical acceleration Xpb" of the vehicle body BD
which affects a deterioration in riding comfort (a feeling of cragginess).
Predetermined frequency weights are then attributed to the vertical speed
Xpb', the relative speed (Xpw'-Xpb') and the vertical acceleration Xpb".
Therefore it is possible to control, in accordance with a frequency range,
the vertical speed Xpb', the relative speed (Xpw'-Xpb') and the vertical
acceleration Xpb" in such a manner as to more effectively inhibit the
vehicle from being adversely affected. Hence, these various modifications
achieve calculation of a first target damping force Fd which improves
running stability and riding comfort of the vehicle.
As shown in FIG. 1, the electronic control device is preferably implemented
on a general purpose computer. However, the electronic control device can
also be implemented on a special purpose computer, a programmed
microprocessor or microcontroller and peripheral integrated circuit
elements, on ASIC or other integrated circuit, a digital signal processor,
a hardwired electronic or logic circuit such as a discrete element
circuit, a programmable logic device such as a PLD, PLA, FPGA or PAL, or
the like. In general, any device capable of implementing a finite state
machine that is in turn capable of implementing the flowcharts shown in
FIGS. 2, 3, 5, 7, 15 and 17, can be used to implement the electronic
control device.
While the invention has been described with reference to what are presently
considered to be preferred embodiments thereof, it is to be understood
that the invention is not limited to the disclosed embodiments or
constructions. On the contrary, the invention is intended to cover various
modifications and equivalent arrangements. In addition, while the various
elements of the disclosed invention are shown in various combinations and
configurations, which are exemplary, other combinations and
configurations, including more, less or only a single embodiment, are also
within the spirit and scope of the invention.
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