Sprung- and unsprung-structure relative-velocity computing apparatus for vehicle

A sprung structure is provided with an acceleration computing section. A damping force estimating section (16) of a relative velocity estimating section (12) estimates a damping force by reading information from a damping force characteristic storing section (14) in accordance with a valve opening degree instruction and the relative velocity between sprung and unsprung structures estimated in the last control cycle. An estimating and computing section 18 estimates the relative velocity between sprung and unsprung structures in accordance with the above acceleration and estimated damping force. A suspension system is controlled in accordance with the relative velocity.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to an apparatus for computing the relative 
velocity between sprung and unsprung structures constituting factors of 
damping-force control in a suspension system using a variable 
damping-force shock absorber. 
2. Description of the Prior Art 
The suspension of a vehicle is a system for connecting a sprung structure 
such as a chassis with an unsprung structure such as a wheel, which 
supports the sprung structure and greatly influences vibration, riding 
comfort, and maneuvering stability. The suspension includes such parts as 
a spring for moderating shocks from a road and a shock absorber for 
damping free vibration of the spring and controlling the velocity of 
attitude transition of the vehicle. As described above, there are various 
requirements for the suspension. However, these requirements conflict with 
each other. Therefore, in the case of design, an attempt is made to find a 
compromise by considering these requirements. 
In order to achieve the above suspension requirements at a high level, a 
technique is known which makes it possible to vary suspension 
characteristics. For example, there is a technique for varying the damping 
forces of a shock absorber in accordance with the state of a vehicle. For 
example, in a frequency region near a sprung-structure resonance 
frequency, damping force is increased so as to converge the free vibration 
in its early stage, otherwise in regions other than the above region, the 
damping force is decreased so as to absorb an input from the road surface 
by the suspension much more. 
This type of variable damping-force suspension is disclosed in the official 
gazette of Japanese Patent Laid-Open Publication No. Hei 6-106937. 
According to the art disclosed in this official gazette, a varying value 
of the damping force of a shock absorber is obtained to control the 
damping force by assuming that the damping force is generated 
proportionally to a certain parameter indicating a vehicle moving state 
shown by the vertical velocity of a sprung structure. By controlling the 
damping force, it is possible to decrease the number of sensors needed to 
detect the vehicle moving state. Moreover, to obtain the parameter showing 
the vehicle moving state, operations are performed by assuming that each 
operation factor varies linearly. 
As the characteristics of the damping force of a shock absorber, the 
damping force is generated depending on the velocity of a stroke including 
the direction and the valve opening degree of an orifice portion. 
According to the art disclosed in the official gazette, the damping force 
is generated proportionally to the parameter. Actually, however, the 
damping force is not generated proportionally to the parameter. Therefore, 
there is a problem that the damping force cannot necessarily be controlled 
at a high accuracy. Moreover, there is a problem that the parameter cannot 
be computed by a linear observer at a high accuracy because each operation 
factor actually changes in a nonlinear manner. 
SUMMARY OF THE INVENTION 
The present invention is made to solve the above problems and its object is 
to provide a sprung- and unsprung-structure relative-velocity computing 
apparatus for accurately computing a stroke velocity serving as a factor 
for determining the damping force of a shock absorber, that is to say, the 
relative velocity between a sprung structure and an unsprung structure in 
order to perform a high-accuracy control while decreasing the number of 
sensors for detecting the moving state of a vehicle. 
A sprung- and unsprung-structure relative-velocity computing apparatus of 
the present invention computes the relative velocity between the sprung 
structure and unsprung structure of a vehicle connected through a shock 
absorber making it possible to vary damping forces by adjusting the valve 
opening degree of a fluid channel and a spring and particularly, has the 
following structures. 
(1) A configuration of the present invention has acceleration computing 
means for computing the vertical acceleration of a sprung structure and 
relative velocity estimating means for estimating the relative velocity 
between a sprung structure and an unsprung structure in accordance with 
the acceleration computed by the acceleration computing means and the 
valve-opening-degree command value of the orifice portion of a shock 
absorber. 
According to the above structure, it is possible to estimate a relative 
velocity in accordance with the valve opening degree and the vertical 
acceleration of the sprung structure. Therefore, because a damping force 
is obtained in accordance with a valve opening degree serving as one of 
the factors for determining the damping force of a shock absorber, it is 
possible to estimate a relative velocity at a high accuracy. Moreover, 
because it is assumed that a valve opening degree is controlled in 
accordance with a control command of the valve opening degree of a 
damping-force-variable shock absorber, it is unnecessary to newly use 
means for detecting an actual valve opening degree, and therefore the 
structure is advantageous from the viewpoints of cost and weight. 
(2) A preferable structure of relative velocity estimating means has 
damping-force characteristic storing means, damping-force estimating 
means, and estimate-computing means. These means will be described below. 
The damping-force characteristic storing means stores the damping force 
characteristic of a shock absorber for valve opening degree and stroke 
velocity in the form of map data. This damping-force characteristic is 
previously measured. The damping-force estimating means obtains the valve 
opening degree command for a shock absorber and the relative velocity 
between a sprung structure and an unsprung structure estimated in the 
previous control cycle, preferably in the last control cycle, reads the 
damping force generated at the then valve opening degree and relative 
velocity from the data stored in the damping-force characteristic storing 
means, and estimates the read damping force as the present damping force 
of the shock absorber. In this case, because the relative velocity between 
the sprung structure and unsprung structure becomes equal to the stroke 
velocity of the shock absorber, it is possible to use the characteristic 
stored in the damping-force characteristic storing means. Moreover, the 
estimate-computing means estimates the relative velocity between the 
sprung structure and unsprung structure in accordance with the 
acceleration computed by the acceleration computing means and the damping 
force estimated by the damping-force estimating means. 
According to the above structure, when the damping-force characteristic of 
a shock absorber for a valve opening degree and velocity are stored, it is 
possible to estimate a damping force in accordance with the information on 
a valve opening degree and the relative velocity estimated in the previous 
control cycle. Moreover, it is possible to estimate the relative velocity 
in accordance with the estimated damping force and the vertical 
acceleration of the sprung structure. Therefore, because a damping force 
is obtained in accordance with a valve opening degree and a relative 
velocity which are factors for determining the damping force of a shock 
absorber, it is possible to estimate a relative velocity at a high 
accuracy. 
(3) Another preferable structure of the relative velocity estimating means 
is provided with vibration characteristic storing means, deviation 
computing means, amplifying means, and vibration analyzing means. These 
means will be described below. In the case of the relative velocity 
estimating means, the deviation of the vertical acceleration of the sprung 
structure computed by the acceleration computing means from the estimated 
vertical acceleration of a sprung structure are first computed. The 
deviation is amplified at a predetermined rate corresponding to the valve 
opening degree command by the deviation amplifying means. Vibration 
characteristics of the vehicle are previously stored in the vibration 
characteristic storing means. The stored vibration characteristics include 
sprung mass, unsprung mass, and spring constant and are stored as 
vibration models in accordance with these constants. 
The acceleration of a sprung structure and the relative velocity between 
sprung and unsprung structures are computed by the analyzing means in 
accordance with the amplified acceleration deviation and the stored 
vibration models. In this case, the computed acceleration is used for 
operations by the deviation computing means. 
According to the above structure, it is possible to compare the estimated 
vertical acceleration of the sprung structure with the acceleration 
computed by the acceleration computing means and reflect the error between 
both accelerations on subsequent estimation, and moreover to vary the 
influence of the error on the estimating operation in accordance with a 
valve opening degree. Thereby, it is possible to compute a more accurate 
relative velocity. 
(4) As still another preferable structure of the relative velocity 
estimating means is provided with vibration characteristic storing means, 
deviation computing means, damping-coefficient estimating means, 
amplifying means, and vibration analyzing means. The damping-coefficient 
estimating means estimates a damping coefficient based on previously 
stored damping-force characteristics in accordance with a valve opening 
degree command and the relative velocity between sprung and unsprung 
structures estimated in the previous control cycle, preferably the last 
control cycle. Moreover, the deviation computing means computes the 
deviation of the vertical acceleration of the sprung structure computed by 
the acceleration computing means from an estimated vertical acceleration 
of the sprung structure. The amplifying means amplifies the deviation at a 
predetermined rate corresponding to a damping coefficient estimated by the 
damping-coefficient estimating means. Moreover, vibration characteristics 
of the vehicle are previously stored in the vibration characteristic 
storing means. The vibration characteristics include sprung mass, unsprung 
mass, and spring constant and are stored as vibration models in accordance 
with these constants. 
The analyzing means computes the acceleration of a sprung structure and the 
relative velocity between sprung and unsprung structures in accordance 
with the amplified acceleration deviation and the stored vibration models. 
In this case, the computed acceleration is used for the computation by the 
deviation computing means. 
According to the above structure, it is possible to compare an estimated 
vertical acceleration of a sprung structure with an acceleration computed 
by the acceleration computing means and reflect the error between both 
accelerations on the subsequent estimation, and moreover to vary the 
influence of the error on the estimating operation in accordance with an 
estimated damping coefficient. Therefore, it is possible to compute a more 
accurate relative velocity. 
(5) In the case of each configuration of the present invention described in 
(1)-(4), the acceleration computing means can be used as an acceleration 
sensor for detecting the acceleration of the shock absorber attachment 
point of the sprung structure. According to this structure, it is possible 
to use the acceleration detected by the acceleration sensor as the 
acceleration of the sprung structure. 
(6) Moreover, in the case of each configuration of the present invention 
described in (1)-(4), it is possible to use the acceleration computing 
means as a structure provided with a plurality of acceleration sensors 
provided for a sprung structure and attachment-point acceleration 
computing means for computing the acceleration of the shock absorber 
attachment point of the sprung structure in accordance with the 
acceleration detected by the acceleration sensors. The attachment-point 
acceleration computing means is able to compute the acceleration at the 
shock absorber attachment point from the position of the center of gravity 
of a vehicle, the shock absorber attachment point, and acceleration sensor 
installation positions by means of proportional computation and from the 
values detected by the acceleration sensors. 
By locating two acceleration sensors at the front and the rear, it is 
possible to detect not only heaving in which the whole of a vehicle 
(sprung structure) is vertically displaced but also pitching in which the 
vehicle tilts forward and backward. Moreover, by locating two acceleration 
sensors at the right and the left, it is possible to detect not only 
heaving but also rolling in which the vehicle tilts rightward and 
leftward. Furthermore, by locating three acceleration sensors so that they 
are not located on the same straight line, it is possible to detect 
heaving, pitching, and rolling.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The preferred embodiments of the present invention will be described below 
by referring to the accompanying drawings. FIG. 1 is an illustration 
showing the layout of parts of a vehicle provided with a 
variable-damping-force shock absorber. A chassis 50 serving as a sprung 
structure is connected with wheels 51 serving as unsprung structures by 
suspensions including shock absorbing systems 52a, 52b, 52c and 52d. (Four 
shock absorbing systems are hereafter described with only symbol 52 when 
it is unnecessary to distinguish between them). The shock absorbing system 
52 further includes springs 54a, 54b, 54c and 54d, and shock absorbers 
56a, 56b, 56c and 56d. (Four springs and four shock absorbers are 
hereafter also described with only symbols 54 and 56 when it is 
unnecessary to distinguish between them.) 
The shock absorber 56 generates a damping force using a resistance 
generated when fluid sealed inside the shock absorber 56 passes through an 
orifice. This embodiment makes it possible to adjust a damping force by 
controlling a valve opening degree and thereby varying the channel cross 
sections of the orifice. That is to say, when the valve opening degree is 
large and the channel cross section is large, the damping force decreases 
because the fluid passes smoothly through the channel. However, when the 
valve opening degree is small, the damping force increases because the 
fluid resistance increases. The valve opening degree can be varied by an 
actuator provided in a shock absorber and it is controlled in accordance 
with an instruction sent from a control unit 58. Moreover, the control 
unit 58 computes the relative velocity between the chassis 50 and the 
wheels 51 from the vertical acceleration of a vehicle detected by 
acceleration sensors 60a, 60b and 60c in accordance with the arithmetic 
processing to be mentioned later and outputs an instruction to the 
actuator in accordance with the relative velocity. 
FIG. 2 shows a single wheel model including a variable-damping-force shock 
absorber. In FIG. 2, symbol Mu denotes the mass of a sprung structure 
(hereafter referred to as sprung mass) and Mw denotes the mass of an 
unsprung structure (hereafter referred to as unsprung mass). The masses of 
an arm and the spring 54 constituting a suspension and the shock absorber 
5 are distributed to the sprung mass and the unsprung mass at an 
appropriate ratio. Symbol Ks denotes the spring constant of the spring 56, 
Kt denotes the spring constant of a tire, Cs denotes the fixed damping 
force of the shock absorber 56, and fc denotes the variable damping force 
of a shock absorber. Moreover, symbol Zu denotes the vertical displacement 
of a sprung structure, Zw denotes the vertical displacement of an unsprung 
structure, and Zr denotes the displacement of the surface of a road. 
Furthermore, in the subsequent description, a symbol ' denotes time 
differentiation of a variable provided with the symbol and a symbol " 
denotes double time differentiation. Therefore, Zu' denotes the velocity 
of a sprung structure and Zu" denotes the vertical acceleration of the 
sprung structure. Furthermore, a symbol .sup.T denotes the transposed 
matrix of a matrix provided with the symbol. 
The sprung- and unsprung-structure relative-velocity computing apparatus of 
this embodiment computes the relative velocity between sprung and unsprung 
structures of a vehicle connected through a shock absorber capable of 
varying damping forces by adjusting the valve opening degree of a fluid 
channel and a spring, and particularly has the following structure. 
FIG. 3 is a block diagram of arithmetic processing of the apparatus of this 
embodiment. Acceleration computing means 10 computes the vertical 
acceleration of a sprung structure. A relative velocity estimating section 
12 estimates the relative velocity between sprung and unsprung structures 
in accordance with the acceleration computed by the acceleration computing 
means and the valve-opening-degree command value of the orifice portion of 
a shock absorber. 
FIG. 4 shows a relative-velocity estimating section 12A serving as a 
preferred structure of the relative velocity estimating section 12 shown 
in FIG. 3. A damping-force characteristic storing section 14 stores the 
previously measured damping-force characteristics of a shock absorber for 
a valve opening degree and stroke velocity in the form of the map data 
shown in FIG. 5. A damping-force estimating section 16 obtains the valve 
opening degree command for a shock absorber and the relative velocity 
between sprung and unsprung structures estimated in a previous control 
cycle, preferably in the last control cycle, reads the damping force 
generated due to the valve opening degree at that time and relative 
velocity from the data stored in the damping-force characteristic storing 
section 14, and estimates the read damping force as the present damping 
force of the shock absorber. In this case, because the relative velocity 
between sprung and unsprung structures becomes equal to the stroke 
velocity of the shock absorber, it is possible to use the characteristics 
stored in the damping-force characteristic storing section 14. Moreover, 
an estimate-computing section 18 estimates the relative velocity between 
sprung and unsprung structures in accordance with the acceleration 
computed by an acceleration computing section 10 and the damping force 
estimated by the damping-force estimating section 16. 
Specifically, the relative velocity estimating section 12A is a part of the 
control unit 58. Moreover, the damping-force characteristic storing 
section 14 is a ROM (read only memory) provided for the control unit 58. 
Furthermore, the estimate-computing section 18 and the damping-force 
estimating section 16 are CPUs (central processing units) for performing 
the above described operations in accordance with a program stored in a 
ROM or the like. 
The arithmetic processing by the relative velocity estimating section 12A 
will be described below in detail. 
When showing the equation of motion of the system in FIG. 2 in the form of 
a state space expression, the following equation (1) is obtained. 
EQU x.sub.c '=A.sub.c .multidot.x.sub.c +B.sub.c .multidot.u+G.sub.c 
.multidot.w(1) 
wherein 
x.sub.c =(Zu' Zu Zw' Zw).sup.T, 
u=f.sub.c, 
w=Z.sub.f, and 
each of A.sub.c, B.sub.c, and G.sub.c is a coefficient matrix. 
This is the state equation of a plant. In this case, x.sub.c denotes a 
parameter showing a moving state of the system. Moreover, because the 
vertical acceleration Zu" of a sprung structure is a variable which can be 
measured in this embodiment, the following equation (2) is obtained as an 
output equation. 
EQU y.sub.1 =C.sub.c1 .multidot.x.sub.c +C.sub.c1 .multidot.u+v(2) 
wherein 
y.sub.1 =Zu", 
v is an measurement noise, and 
each of C.sub.c1 and D.sub.c1 is a coefficient matrix. 
Moreover, an output equation for computing a relative velocity y.sub.2 from 
a parameter is defined as the following equation (3). 
EQU y.sub.2 =C.sub.c2 .multidot.x.sub.c +C.sub.c2 .multidot.u (3) 
wherein 
y.sub.2 =Zw'-Zu', and 
each of C.sub.c2 and D.sub.c2 is a coefficient matrix. 
When the above equations (1) to (3) are represented by discrete systems, 
the following equations (4) to (6) are obtained. 
EQU x(k+1)=A.multidot.x(k)+B.multidot.u(k)+G.multidot.w(k) (4) 
EQU y.sub.1 (k)=C.sub.1 .multidot.x(k)+D.sub.1 .multidot.u(k)+v(k)(5) 
EQU y.sub.2 (k)=C.sub.2 .multidot.x(k)+D.sub.2 .multidot.u(k) (6) 
wherein each of A, B, C.sub.1, C.sub.2, D.sub.1 and D.sub.2 is a 
coefficient matrix. 
x(k) denotes a parameter x.sub.c shown in the form of a discrete system. 
Then, a state observer for the system for estimating the relative velocity 
is defined by the following equations (7) and (8). 
EQU z(k)=(I-L.multidot.C.sub.1)A.multidot.z(k-1)+L.multidot.y.sub.1 (k)(7) 
EQU y.sub.2h (k)=C.sub.2 .multidot.z(k)+D.sub.2 .multidot.u(k) (8) 
wherein z(k) denotes an estimated value of the parameter x(k) computed by 
the defined state observer. Moreover, y.sub.2h (k) denotes an estimated 
value of a relative velocity y.sub.2 (k). FIG. 6 shows a block diagram of 
the observer defined by the equations (7) and (8). 
The symbol L in the equation (7) denotes the gain of a stationary Kalman 
filter, which can be obtained from the following equations (9) and (10). 
EQU P=[(APA.sup.T +BVB.sup.T).sup.-1 +C.sup.T W.sup.-1 C].sup.-1(9) 
EQU L=PC.sub.1.sup.T W.sup.-1 (10) 
Matrices V and W are design parameters which can be set by a designer in 
order to improve the estimation accuracy. A symbol P denotes the only 
positive constant value matrix meeting the equation (9). 
In the equations (7) and (8), the coefficient matrixes A, B, C.sub.1, 
C.sub.2, D.sub.1 and D.sub.2 can be obtained from the constants such as 
the spring constant, sprung mass, and unsprung mass of the system shown in 
FIG. 2. 
Moreover, the vertical acceleration y.sub.1 (k) of a sprung structure can 
be computed in accordance with the output of an acceleration sensor 
provided on the sprung structure. In the case of the single wheel model 
shown in FIG. 2, it is possible to provide an acceleration sensor for a 
sprung structure and directly use the acceleration detected by the sensor 
as the vertical acceleration y.sub.1 (k). In the case of the real vehicle 
shown in FIG. 1 or the like, it is difficult to set an acceleration sensor 
60 to the chassis-side setting point of the shock absorber 56. Therefore, 
it is necessary to obtain the acceleration of a sprung structure by 
applying a predetermined correction to a value detected by the 
acceleration sensor 60. Specifically, three acceleration sensors 60 are 
arranged so that they are not located on the same straight line and the 
attitude of a chassis (sprung structure) is obtained from an acceleration 
at the setting point to perform correction in accordance with the 
distances between the acceleration sensor and shock absorber attachment 
points and the center of gravity of the chassis. 
For example, when the values detected by three acceleration sensors 60 are 
equal to each other, it is found that the chassis performs a heaving 
motion in which all part of the chassis move vertically in parallel. In 
this case, the detected value can directly be used as the vertical 
acceleration y.sub.1 (k). Moreover, when the outputs of the two 
acceleration sensors 60a and 60b located close to the front wheels are 
equal to each other and the phase of this output is reversed to the phase 
of the output of the acceleration sensor 60c located close to the rear 
wheels, it is found that the chassis includes a pitching motion. When the 
chassis performs only a pitching motion, it is only necessary to correct 
an acceleration sensor output in accordance with the ratio of the distance 
between the center of gravity of the chassis and an acceleration sensor, 
to the distance between the center of gravity of the chassis and a shock 
absorber attachment point, and compute the vertical acceleration y.sub.1 
(k). The same is true for the case of a rolling motion. 
Moreover, a damping force u(k) is estimated from the valve opening degree 
of a shock absorber and the output y.sub.2h (k) of a state observer, that 
is to say, the estimated relative velocity between sprung and unsprung 
structures. The valve opening degree uses a valve opening degree command 
sent from the control unit 58 to each shock absorber 56. Therefore, it is 
unnecessary to measure an actual valve opening degree, and thus it is 
unnecessary to use a sensor or the like. Moreover, the relative velocity 
between sprung and unsprung structures uses the data one control cycle 
before. When a control cycle is much smaller than the change of the 
relative velocity between sprung and unsprung structures, it is estimated 
that the difference between the data one control cycle before and the 
present actual relative velocity is very small. Furthermore, the damping 
force characteristic of a shock absorber is previously measured by using a 
stroke velocity and a valve opening degree as parameters and stored in the 
form of characteristic map data as shown in FIG. 5. When a valve opening 
degree and a stroke velocity are known, it is possible to estimate the 
damping force u(k) of a shock absorber at that time from the 
characteristic map data. As described above, because the valve opening 
degree is known from the valve opening degree command and the stroke 
velocity equals the relative velocity between sprung and unsprung 
structures, it is possible to estimate the damping force at that time from 
these pieces of data. Strictly speaking, the estimated damping force is 
the damping force one control cycle before. However, as described above, 
when a control cycle is much smaller than the cycle of relative velocity 
change, it is possible to make the difference between the damping force 
one control cycle before and its actual value very small. Particularly, 
for the cycle of the vibration generated in a suspension of a passenger 
car, approx. 10 Hz, which is the resonance frequency of an unsprung 
structure, and approx. 1 Hz, which is the resonance frequency of a sprung 
structure, are predominant. Therefore, by performing control at a 
frequency much higher (a cycle much shorter) than the above resonance 
frequencies, the problem caused by using the data one cycle before does 
not occur. 
The relative velocity y.sub.2h (k) is estimated by using the above 
described vertical acceleration y.sub.1 (k) of a sprung structure and the 
damping force u(k) in accordance with the equations (7) and (8). 
FIG. 7 shows estimated relative velocity (continuous line) and actual 
relative velocity (broken line) between sprung and unsprung structures of 
a vehicle to which the apparatus of this embodiment is applied when 
vibrating the vehicle only in the heaving direction. 
In the case of the above-described equations (7) and (8) or the state 
observer shown in FIG. 6, a model is analyzed by assuming that an observer 
gain L is constant. However, when the tilt of the damping force of a shock 
absorber, that is to say, the damping coefficient of the shock absorber 
changes greatly depending on the valve opening degree and stroke velocity 
of the shock absorber as shown in FIG. 8, it is not necessarily possible 
to estimate a parameter such as a relative velocity at a high accuracy in 
the case of a state observer with a constant observer gain L, that is to 
say, in the case of a linear state observer. A Kalman filter is one 
example of a linear state observers. 
FIGS. 9A, 9B, 10A and 10B show the results of trial computation of the 
vibration when using a shock absorber having the damping force 
characteristics shown in FIG. 8 for the single-wheel model with 2 degrees 
of freedom shown in FIG. 2. In the case of this trial computation, an 
observer gain is computed at a damping coefficient of 1,000 N.multidot.s/m 
by using a Kalman filter theory. In this case, vibration is executed by 
sine waves with a frequency of 0.5 to 5 Hz and an amplitude of 10 mm. FIG. 
9A shows the relative velocity between sprung and unsprung structures 
actually measured at a valve opening degree of 100%. FIG. 9B shows an 
estimated value under the same condition. FIG. 10A shows a measured value 
when the valve opening degree is fixed to an intermediate stage, and FIG. 
10B shows an estimated value under the same condition. Though the damping 
coefficient at a valve opening degree of 100% depends on the stroke 
velocity, it approximately ranges between 1,000 and 2,800 N.multidot.s/m. 
Moreover, the damping coefficient at the intermediate stage of the valve 
opening degree approximately ranges between 1,700 and 18,000 
N.multidot.s/m. 
In the case of FIGS. 9A and 9B showing values close to the damping 
coefficient of 1,000 N.multidot.s/m which is a design condition, the 
measured value is almost equal to the estimated value and therefore a 
preferable result is obtained. In the case of a value separate from the 
design condition, however, a measured value is different from an estimated 
value. As described above, when a damping coefficient changes greatly, it 
is impossible to obtain a high accuracy from estimation by a linear 
observer, that is to say, a Kalman filter. 
The estimation of a relative velocity capable of corresponding to a case in 
which a damping coefficient varies greatly will be described below. 
FIG. 11 shows a relative velocity estimating section 12B which is another 
preferable structure of the relative velocity estimating section 12 shown 
in FIG. 3. A damping-coefficient estimating section 28 estimates a damping 
coefficient based on the previously-stored damping force characteristics 
in accordance with the relative velocity between sprung and unsprung 
structures estimated in a previous control cycle, preferably the last 
control cycle. Moreover, a deviation computing section 30 computes the 
deviation of the vertical acceleration of the sprung structure computed by 
the acceleration computing section 10 from the estimated vertical 
acceleration of the sprung structure. An amplifying section 32 amplifies 
the deviation at a predetermined rate corresponding to the damping 
coefficient estimated by the damping-coefficient estimating section 28. A 
vibration characteristic storing section 34 previously stores vibration 
characteristics of the vehicle. The vibration characteristics include a 
sprung mass, unsprung mass, and spring constant and are stored as 
vibration models in accordance with these constants. 
An analyzing section 36 computes the acceleration of a sprung structure and 
the relative velocity between sprung and unsprung structures in accordance 
with the amplified acceleration deviation and the stored vibration models. 
In this case, the computed acceleration is used for operations by the 
deviation computing section 30. 
Specifically, the relative velocity estimating section 12B is a part of the 
control unit 58. Moreover, the vibration characteristic storing section 34 
is a ROM provided for the control unit 58. Furthermore, the deviation 
computing section 30, amplifying section 32, and analyzing section 36 use 
a CPU to be operated by a predetermined program and a circuit element for 
performing predetermined operations. 
The arithmetic processing by the relative velocity estimating section 12B 
will be described below in detail. 
When showing the above-described equation of motion of the system in FIG. 2 
in the form of a state space expression, the following equation (11) is 
obtained. 
EQU X.sub.c '=A.sub.c .multidot.x.sub.c +B.sub.c .multidot.f.sub.c +G.sub.c 
.multidot.w (11) 
wherein 
x.sub.c =(Zu' Zu Zw' Zw).sup.T, 
w=Z.sub.r, and 
each of A.sub.c, B.sub.c and G.sub.c is a coefficient matrix. 
This is the state equation of a plant. In this case, x.sub.c denotes a 
parameter showing a moving state of the above-described system. Moreover, 
because the vertical acceleration Zu" of a sprung structure is a variable 
which can be measured in the vehicle shown in FIG. 1, the following 
equation (12) is obtained as an output equation. 
EQU y.sub.1 =C.sub.c1 .multidot.x.sub.c +D.sub.c1 .multidot.f.sub.c +v(12) 
wherein 
y.sub.1 =Zu", 
v is an measurement noise, and 
each of C.sub.c1 and D.sub.c1 is a coefficient matrix. 
Moreover, an output equation for computing a relative velocity y.sub.2 from 
a parameter is defined as the following equation (13). 
EQU y.sub.2 =C.sub.c2 .multidot.x.sub.c (13) 
wherein 
y.sub.2 =Zw'-Zu', and 
C.sub.c2 is a coefficient matrix. 
When assuming a damping coefficient as Cs and a valve opening degree 
command as ar, a damping force f.sub.c is shown by the following equation 
(14). 
EQU f.sub.c =Cs(Zs',ar)Zs' (14) 
wherein 
Zs=Zw-Zu. 
In the equation (14), Cs(Zs', ar) denotes that the damping coefficient Cs 
is a value determined by a relative velocity Zs and a valve opening degree 
ar. Moreover, it is assumed that the minimum value of the damping 
coefficient Cs is Cs.sub.min and the maximum value is Cs.sub.max. 
When rewriting the equations (11) to (13) by using the damping coefficient 
Cs, the following equations (15), (16) and (17) are obtained. 
EQU x.sub.c '=Av(q).multidot.x.sub.c +G.sub.c .multidot.w (15) 
EQU y.sub.1 =C.sub.V1 (q).multidot.x.sub.c +v (16) 
EQU y.sub.2 =C.sub.C2 .multidot.X.sub.c (17) 
wherein 
##EQU1## 
A.sub.V (q)=q.times.A.sub.Vmax +(1-q).times.A.sub.vmin C.sub.V1 
(q)=q.times.C.sub.V1max +(1-q).times.C.sub.v1min. 
When Cs=Cs.sub.max, A.sub.V (q) and C.sub.V1 (q) are assumed as A.sub.Vmax 
and C.sub.V1max, respectively. 
When Cs=Cs.sub.min, A.sub.V (q) and C.sub.V1 (q) are assumed as A.sub.Vmin 
and C.sub.V1min, respectively. 
A.sub.Vmax =A.sub.C +Cs.sub.max .multidot.BcN 
A.sub.Vmin =A.sub.C +Cs.sub.min .multidot.BcN 
C.sub.V1max =C.sub.C1 +Cs.sub.max .multidot.DuN 
C.sub.V1min =C.sub.C1 +Cs.sub.min .multidot.DuN 
N=(-1 0 1 0). 
Then, a state observer for the above-described system for estimating the 
above relative velocity is defined by the following equations (19) and 
(20). 
EQU X.sub.ch '=A.sub.V (q).multidot.x.sub.ch +L(q).multidot.(y.sub.1 -C.sub.V1 
(q).multidot.x.sub.ch) (19) 
EQU y.sub.2h =C.sub.V2 (q).multidot.x.sub.ch (20) 
In this case, x.sub.ch denotes an estimated signal of a parameter x.sub.c 
of a system to be computed by the defined state observer. Moreover, 
y.sub.2h denotes an estimated signal of a relative velocity y.sub.2. 
L(q) in the equation (7) shows an observer gain and it is defined as shown 
below. It is assumed that the stationary Kalman filter gain for the 
equations (15) and (16) when a damping coefficient is equal to the minimum 
value Cs.sub.min is L.sub.min and the stationary Kalman filter gain for 
the equations (15) and (16) when the damping coefficient is equal to the 
maximum value Cs.sub.max is L.sub.max. Moreover, for observer gains 
computed at these end points, observer gains are set in accordance with 
the following equation (21) at points other than the end points: 
EQU L(q)=q.times.L.sub.max +(1-q).times.L.sub.min (21) 
In order to compute the estimated value y.sub.2h of the relative velocity 
between sprung and unsprung structures in accordance with the observers 
defined by the equations (19) and (20), it is necessary to obtain fixed 
coefficient matrixes A.sub.c, B.sub.c, G.sub.c, C.sub.c1, C.sub.c2 and 
D.sub.c1 depending on the characteristic value of a system, the vertical 
acceleration y.sub.1 of a sprung structure, and the damping force f.sub.c. 
In this case, a coefficient matrix can easily be obtained from the mass of 
a sprung structure and a spring constant similarly to the above case in 
which the observer gain is constant and the acceleration y.sub.1 can be 
obtained from an acceleration sensor provided for a sprung structure. 
Moreover, the damping force f.sub.c is obtained by using the 
previously-measured damping force characteristics of a shock absorber 
shown in FIG. 8. Though a valve opening degree can actually be measured, 
this embodiment uses the valve opening degree command ar. 
Moreover, it is possible to obtain the damping force f.sub.c and damping 
coefficient Cs of a shock absorber based on the characteristic diagram in 
FIG. 8 by using the estimated value y.sub.2h of the relative velocity 
between sprung and unsprung structures one control cycle before. 
Furthermore, it is possible to obtain q from the equation (18) by using 
the damping coefficient Cs and obtain the observer gain L(q) from the 
equation (21). 
Thus, it is possible to estimate the relative velocity y.sub.2h between 
sprung and unsprung structures from the equations (19) and (20). 
In the case of detection of a sprung acceleration, it is possible to 
compute the acceleration of the chassis-side setting point of the shock 
absorber 56 by arranging three acceleration sensors so that they are not 
located on the same straight line. 
FIGS. 12A, 12B, 13A and 13B show the results of trial computation of the 
relative velocity between sprung and unsprung structures of the 
single-wheel model with two degrees of freedom shown in FIG. 2 by using 
the above state observers. Moreover, FIG. 8 shows the damping 
characteristics of a shock absorber. 
FIGS. 12A, 12B, 13A and 13B show trial computation results when computing 
the observer gain L(q) in accordance with the damping coefficient Cs. The 
observer gain L(q) is computed by using the stationary Kalman filter 
theory at damping coefficients of 1,000 N.multidot.s/m and 65,600 
N.multidot.s/m. Moreover, FIGS. 12A and 12B show the case of a valve 
opening degree of 100%, and FIGS. 13A and 13B show the case of fixing a 
valve opening degree to an intermediate stage. FIGS. 12A and 13A show 
measured values, and FIGS. 12B and 13B show estimated values. The damping 
coefficients in the case of FIGS. 12A and 12B show approx. 1,000 to 2,800 
N.multidot.s/m and those in the case of FIGS. 13A and 13B show approx. 
1,700 to 18,000 N.multidot.s/m. Moreover, sine-wave vibration is executed 
at a frequency of 0.5 to 5 Hz and an amplitude of 10 mm. From these 
trial-computation results, it is found that a preferable estimation result 
can be obtained even if a damping coefficient changes greatly. 
FIG. 14 shows a relative velocity estimating section 12c which is still 
another preferable structure of the relative velocity estimating section 
12 sown in FIG. 3. In the case of the relative velocity estimating section 
12, a deviation computing section 20 first computes the deviation of the 
vertical acceleration of a sprung structure computed by the acceleration 
computing section 10 from the estimated vertical acceleration of the 
sprung structure. A deviation amplifying section 22 amplifies the 
deviation at a predetermined rate corresponding to the above valve opening 
degree instruction. Moreover, the vibration characteristics of the vehicle 
are previously stored in a vibration characteristic storing section 24. 
The vibration characteristics include a sprung mass, unsprung mass, and 
spring constant and are stored as vibration models in accordance with 
these constants. 
An analyzing section 26 computes the acceleration of a sprung structure and 
the relative velocity between sprung and unsprung structures in accordance 
with the amplified acceleration deviation and the stored vibration models. 
In this case, the computed acceleration is used for operations by the 
deviation computing section 20. 
Specifically, the relative velocity estimating section 12C is a part of the 
control unit 58. Moreover, the vibration characteristic storing section 24 
is a ROM provided for the control unit 58. Furthermore, the deviation 
computing section 20, amplifying section 22, and analyzing section 36 use 
a CPU to be operated by a predetermined program and a circuit element for 
performing predetermined operations. 
The arithmetic processing by the relative velocity estimating section 12C 
will be described below in detail. 
The relative velocity estimating section 12C computes an observer gain L(p) 
in accordance with only the valve opening degree command ar. The observer 
gain L(p) is computed in accordance with the following equations (22) and 
(23). 
EQU L(q)=p.times.L.sub.max +(1-p).times.L.sub.min (22) 
wherein 
##EQU2## 
In this case, ar.sub.min denotes a valve opening degree command when fully 
opening a valve and ar.sub.max denotes a valve opening degree command when 
fully closing the valve. 
Other operations are the same as those carried out by the relative velocity 
estimating section 12B shown in FIG. 11. 
FIGS. 15A, 15B, 16A and 16B show the results of trial computation of the 
relative velocity between sprung and unsprung structures of the 
single-wheel model with two degrees of freedom shown in FIG. 2 by using 
the above observers. The damping characteristics of a shock absorber are 
shown in FIG. 8. 
FIGS. 15A, 15B, 16A and 16B show the results of trial computation the 
observer gain L(p) in accordance with the valve opening degree command ar. 
The observer gain L(p) is computed at damping coefficients of 1,000 
N.multidot.s/m and 65,600 N.multidot.s/m by using the stationary Kalman 
filter theory. Moreover, FIGS. 15A and 15B show the case of a valve 
opening degree of 100%, and FIGS. 16A and 16B show the case of fixing the 
valve opening degree to an intermediate stage. FIGS. 15A and 16A show 
measured values, and FIGS. 15B and 16B show estimated values. The damping 
coefficients in the case of FIGS. 15A and 15B show approx. 1,000 to 2,800 
N.multidot.s/m and those in the case of FIGS. 16A and 16B show approx. 
1,700 to 6,500 N.multidot.s/m. Moreover, sine-wave vibration is executed 
at a frequency of 0.5 to 5 Hz and a amplitude of 10 mm. From these trial 
computation results, it is found that a preferable estimation result can 
be obtained even if a damping coefficient varies greatly. 
In FIGS. 17 and 18, the results of vibration tests on the actual vehicle 
shown in FIG. 1 in its heaving direction are shown by continuous lines. 
For estimation of a relative velocity, an observer gain is L(q) of the 
equation (21) computed in accordance with a damping coefficient and 
computed at damping coefficients of 1,000 N.multidot.s/m and 65,600 
N.multidot.s/m by using the stationary Kalman filter theory. FIG. 17 shows 
the case of a valve opening degree of 100%, and FIG. 18 shows the case of 
a valve opening degree of 0%. The damping coefficient reaches approx. 
1,000 to 2,800 N.multidot.s/m in the case of a valve opening degree of 
100% and 65,600 N.multidot.s/m at most in the case of a valve opening 
degree of 0%. Moreover, sine-wave vibration is executed at an amplitude of 
10 mm and a frequency of 1 Hz. The broken lines in FIGS. 17 and 18 denote 
the values obtained by differentiating the outputs of vehicle height 
sensors and show actual relative velocities between sprung and unsprung 
structures. From FIGS. 17 and 18, it is found that a preferable estimation 
result can be obtained even if a damping coefficient varies greatly. 
Each of the above embodiments estimates a damping force from the 
information on valve opening degree or the relative velocity between 
sprung and unsprung structures computed in accordance with the information 
for valve opening degree and in a previous control cycle. Therefore, a 
high estimation accuracy is obtained. Moreover, by estimating the above 
relative velocity in accordance with an estimated value of the above 
damping force, a more-accurate relative velocity can be obtained. 
Furthermore, by measuring only the acceleration of a sprung structure in 
accordance with previously-measured damping force characteristics of a 
shock absorber and a valve opening degree instruction, it is possible to 
estimate the above relative velocity and moreover, to obtain a damping 
force in accordance with the estimated relative velocity. Therefore, no 
pressure sensor or vehicle height sensor in a shock absorber or no 
unsprung acceleration sensor is necessary. Thus, it is possible to 
decrease the cost and vehicle weight.