Vehicle height control apparatus

The vehicle height control apparatus according to the present invention comprises, vehicle height detecting unit (M3) provided at an appropriate position of a vehicle (M1) for detecting the distance between a body (M2) of the vehicle (M1) and the surface of road; vehicle height adjusting members (M5) provided between the body (M2) of the vehicle (M1) and wheels (M4) of the vehicle (M1) for adjusting the height of the a vehicle (M1); vehicle height control unit (M6) for obtaining controlled variable of the vehicle height adjusting members (M5) so that the actual vehicle height detected by the vehicle height detecting unit (M3) equals the predetermined target height and for driving the vehicle height adjusting members (M5), the vehicle height control unit (M6) being formed as an integral-added optimal regulator which determines the controlled variable of the vehicle height adjusting members (M5) on the basis of an optimal feedback gain predetermined in accordance with dynamic model of the system relating to the height of the vehicle (M1 ).

BACKGROUND OF THE INVENTION 
This invention relates generally to vehicle height control apparatus, and, 
more particularly, to such apparatus which is capable of appropriate 
control of vehicle height in accordance with a dynamic model of a system 
relating to the height of a vehicle. 
Various types of vehicle height control apparatus have been devised and 
manufactured where the vehicle height control apparatus is developed so 
that a vehicle always keeps a normal attitude with a given height by 
correcting the variation of the vehicle height due to changes in the 
number of passengers or the amount of load, or the stability of the 
vehicle by which running is improved by changing the vehicle height in 
accordance with the travelling state of the vehicle or the state of the 
road surface. 
In such conventional vehicle height control apparatus, vehicle height is 
controlled on the basis of so called classic feedback control theory with 
which vehicle height is controlled in connection with each of the 
respective wheels by driving the vehicle height adjusting members so that 
the vehicle height detected by the various vehicle height sensors, which 
are provided for the respective wheels, equals the therefor target vehicle 
height. 
However, since respective vehicle height adjusting members are 
independently controlled in the conventional vehicle height control 
apparatus, there has been a problem that vehicle height control at an 
arbitrary position cannot be effected, since the independent adjustment of 
one vehicle height adjusting member effects the others. Furthermore, there 
has been a problem in connection with response time such that it takes a 
relatively long period of time until a vehicle body assumes a stable 
attitude after control is started since vehicle height control is 
performed without considering the mutual interference between the 
respective vehicle height adjusting members, such that driving of one 
vehicle height adjusting member affects the other vehicle height adjusting 
members. 
SUMMARY OF THE INVENTION 
The present invention has been developed in order to remove the 
above-described drawbacks inherent to the conventional vehicle height 
control apparatus. 
It is, therefore, an object of the present invention, among others, to 
provide a new and useful vehicle height control apparatus which is capable 
of controlling vehicle height in a smooth and stabile manner on the basis 
of so called modern control theory by controlling respective vehicle 
height adjusting members with the vehicle height control being considered 
in the context of the entire vehicle. 
According to a feature of the present invention a vehicle height control 
unit is formed as an integral-added optimal regulator which determines the 
controlled variable of a vehicle height adjusting member on the basis of 
an optimal feedback gain predetermined in accordance with a dynamic model 
of the system relating to the height of a vehicle whose height is to be 
controlled.

DETAILED DESCRIPTION OF THE INVENTION 
The structure of the present invention is schematically shown in FIG. 1. 
The vehicle height control apparatus according to the present invention 
comprises vehicle height detecting means M3 provided to an appropriate 
position of a vehicle M1 for detecting the distance between a body M2 of 
said vehicle M1 and the surface of road; vehicle height adjusting members 
M5 provided between said body M2 of said vehicle M1 and wheels M4 of said 
vehicle M1 for adjusting the height of said vehicle M1; vehicle height 
control means M6 for obtaining controlled variable of said vehicle height 
adjusting members M5 so that the actual vehicle height detected by said 
vehicle height detecting means M3 equals said predetermined target height 
and for driving said vehicle height adjusting members M5; characterized in 
that said vehicle height control means M6 is formed as an integral-added 
optimal regulator which determines the controlled variable of said vehicle 
height adjusting members M5 on the basis of an optimal feedback gain F 
predetermined in accordance with a dynamic model of the system relating to 
the height of said vehicle M1. 
In the above, the vehicle height adjusting member M5 is provided between 
the vehicle body M2 and the wheel M4 for adjusting the vehicle height, and 
may be an air suspension which adjusts vehicle height using gas pressure, 
a hydraulic pneumatic suspension or hydraulic cylinder provided in series 
with conventional suspension structure independent therefrom. 
As the vehicle height detecting means M3, a potentiometer may be used which 
detects the variation of the distance between the wheels and the vehicle 
body in the same manner as the above-mentioned vehicle height adjusting 
member M5, as a variation in electrical resistance, or an optical vehicle 
height sensor, where the vehicle height detecting means M4 is provided at 
an arbitrary position of the vehicle body M1 for detecting the distance 
between the vehicle body M2 and the road surface. Furthermore, an 
ultrasonic vehicle height sensor, which emits ultrasonic waves toward the 
road surface to detect a period of time required for its reflected waves 
to be received, may also be used. 
In the above, when an air suspension system using no hydraulic pressure is 
used in the above-mentioned vehicle height adjusting member M5, since the 
spring constant is also changed by the adjustment of the vehicle height, 
it is preferable to use hydraulic pneumatic suspension, which is capable 
of controlling only vehicle height by way of hydraulic pressure, or a 
hydraulic cylinder provided in series with a suspension structure 
independent therefrom. 
The vehicle height control means M6 is arranged to transmit a control 
signal to the vehicle height adjusting member M5 so that the vehicle 
height equals the target vehicle height in receipt of a detection signal 
from the vehicle height detecting means M3. The vehicle height control 
means M6 comprises a microcomputer having a microprocessor, a ROM, a RAM, 
peripheral elements, and input/output circuits. In constrast with 
conventional vehicle height control apparatus, the vehicle height control 
means M6 is arranged to output the control signal by obtaining the 
controlled variable of the vehicle height adjusting member M5 on the basis 
of an optimal feedback gain F determined in accordance with a dynamic 
model of the system relating to the height of the vehicle M1. 
More specifically, the vehicle height control means M6 is formed as an 
integral-added optimal regulator which determines an optimal controlled 
variable using a predetermined target vehicle height and actual vehicle 
height detected by the vehicle height detecting means M3. The 
above-mentioned target vehicle height may be a given value or may be 
determined by various vehicle travelling states, such as vehicle speed, 
steering angle, and the inclination of road surface. In this case, the 
height of the vehicle is suitably set in accordance with the travelling 
state of the vehicle and thus it is possible to improve the stability in 
travelling and steering and to provide a more comfortable ride. 
A method of constituting such integral-added optimal regulator is described 
in detail in documents, such as "Linear System Control Theory" written by 
Katsuhisa FURUTA published by Shokodo Japan in 1976. An outlook for the 
method of actually forming of such regulator will be given hereinbelow. In 
the following description, the references F, X, A, B, C, y, u, L, G, Q, R, 
T, P indicate vectors (matrix), a superscript .sup.T such as A.sup.T 
indicating transposed matrix, a superscript .sup.-1 such as A.sup.-1 
indicating inverse matrix, a symbol such as X indicating an estimate, a 
symbol .sup.- such as C indicating an amount handled by another system, 
i.e. a state observer (which will be simply referred to as observer 
hereinafter) which amount is generated by way of transform or the like 
from the system which is controlled object, a symbol * such as y.sup.* 
indicating a target value respectively. 
It is known in modern control theory that in the control of a controlled 
object, i.e. the control of the height of the vehicle M1 in this case, the 
dynamic behavior of the controlled object is described in a discrete-time 
system as: 
EQU X(k)=A.multidot.X(k-1)+B.multidot.u(k-1) (1) 
EQU y(k)=C.multidot.X(k) (2) 
The above Eq. (1) is called a state equation, and Eq. (2) is called an 
output equation, and the term X(k) indicates state variables which 
represent the internal state of the system relating to the height of the 
vehicle M1, the term u(k) indicates vectors comprising variables 
indicative of the driving condition of the respective vehicle height 
adjusting members M5, and the term y(k) indicates vectors comprising 
vectors representative of vehicle height (actual vehicle height) at an 
arbitrary position of the vehicle M1 detected by the vehicle height 
detecting means M2. Eqs. (1) and (2) are both described in the 
discrete-time system, and a subscript "k" indicates that the value is of 
the present time, while a subscript "k-1" indicates that the value is of 
an instant that is one sampling cycle before the present time. 
The state variable X(k) indicating the internal state of the vehicle M1 
represents information relating to the history of the system which is 
necessary and sufficient for predicting the influence in the future in the 
control system. Therefore, the dynamic model of the system relating to the 
height of the vehicle M1 will be clear, and if we can determine vectors A, 
B and C of Eqs. (1) and (2), then it is possible to optimally control the 
height of the vehicle using the state variables X(k). 
It is difficult to accurately and theoretically obtain dynamic models of a 
complex object such as an automobile in which respective vehicle height 
adjusting members M5 influence the vehicle height as well as the vehicle 
attitude, and, therefore, it is necessary to obtain the same through 
experiments. This is a method of constructing a model, which method is so 
called system identification, and in the case that the vehicle M1 is left 
or driven under a given condition, the model is constructed according to 
state equation (1) and output equation (2) with which a linear 
approximation is satisfied around the given condition. Therefore, even in 
the case that the dynamic model related to the height of the vehicle M1 is 
nonlinear, a linear approximation can be performed by dividing into a 
plurality of conditions, i.e., weight due to passengers and load or 
travelling condition or the like, and therefore it is possible to 
determine each dynamic model. 
If the controlled object is of a type such that a physical model can be 
relatively easily constructed, as in the case of a monocycle, then the 
model (i.e. vectors A, B, and C) of a dynamic system can be determined 
through system identification which can be made through a method such as 
frequency response determination or spectrum analysis. However, in the 
case of a controlled object of a multivariable system, such as an 
automobile having a plurality of vehicle height adjusting members M5, it 
is difficult to make a physical model which is accurately approximated, 
and in such a case, the dynamic model is constructed through the least 
squares method, instrumental variable method or on-line identification. 
Once a dynamic model is determined, an amount of feedback is determined 
from the state variables X(x), the variables y(k) of the actual height of 
the vehicle M1 and its target value y (k), so that the controlled 
variables u(k) of the condition of driving the vehicle height adjusting 
members M5 are theoretically and optimally determined. In the system for 
controlling the height of the vehicle M1, as variables directly 
influencing the height of the vehicle M1, the dynamic behavior of a shock 
absorber provided between the vehicle body M2 and the wheels M4 together 
with the vehicle height adjusting members M1, for instance, or the moving 
speed of the fluid of a hydraulic cylinder may be treated as the state 
variables X(k). However, most of such variables are difficult to directly 
measure. Therefore, means called a state observer (observer) is formed 
within the control means M6 so that it is possible to estimate the state 
variables X(k) of the vehicle M1 using the variables of the condition of 
driving the respective vehicle height adjusting members M5 and a detection 
signal (actual vehicle height) from the vehicle height detecting means M4. 
This is the observer according to modern control theory, and various types 
of observers and their designing methods are known. These are described in 
detail, for instance, in "Mechanical System Control" written by Katsuhisa 
Furuta, published from Ohm Co. Ltd. in 1984, and the observer may be 
designed as a minimal order observer or a finite time settling observer in 
correspondence with the fashion of an applied controlled object, i.e., the 
vehicle M1 and apparatus for controlling the height thereof. 
The vehicle height control means M6 controls and drives the vehicle height 
adjusting members M5, in a system expanded using measured state variables 
or state variables X(k) estimated by the above-mentioned observer and an 
accumulated value obtained by accumulating the deviations of actual 
vehicle height detected by the vehicle height detecting means M4 from a 
predetermined target value of the vehicle height, by determining an 
optimal feedback amount from both thereof and also from a predetermined 
optimal feedback gain. The accumulated value is necessary for absorbing 
vibrations occurring during the operation of the vehicle M1, and is a 
value which is necessary for varying the target vehicle height depending 
on the operating state of the vehicle M1. During control of a servo 
system, it is required generally to perform a control for cancelling 
steady-state error between the target value and an actual controlled 
variable, and this corresponds to the necessity of inclusion of 1/S.sup.l 
(integration of l.sup.th order) in a transfer function. In the case that a 
state equation is made with the transfer function of the system being 
determined through system identification, as described above, it is 
preferable to include such an integrated amount in view of stability 
against noise. The accumulated value is used for the above reason. 
Therefore, when the accumulated value is introduced into the 
above-mentioned state variable X(k) to expand the system so as to 
determine the feedback amount from these values and a predetermined 
optimal feedback gain F, the controlled variables of the controlled 
object, i.e., the variables of the condition of driving the respective 
vehicle height adjusting members M1, are determined as an integral-added 
optimal regulator. 
Next, it will be described in connection with optimal feedback gain. In an 
optimal regulator to which an integral element is added as described 
above, the way of finding a control input (the variables of the condition 
of driving the vehicle height adjusting members M1 in this case) which 
minimizes a performance index J is made clear, while it is also known that 
the optimal feedback gain can be obtained from a solution of Riccati 
equation, A, B, C matrixes of the state equation (1) and the output 
equation (2), and the weighted parameter used in performance index (see 
the above-mentioned book). In the above, the weighted parameter is 
initially arbitrarily given so as to change the weighing in the 
regulation, by the performance index J, of the behavior of the variables 
of the condition of driving the vehicle height adjusting members M5. It is 
possible to determine an optimal value through repeated simulation by 
changing the weighted parameter by a given amount from the behavior of the 
state of the vehicle height which is obtained as the result of simulation 
performed by a large computer with an arbitrary weighted parameter being 
given. As a result, an optimal feedback gain F is also determined. 
Therefore, the vehicle height control means M6 in the vehicle height 
control apparatus according to the present invention is formed as an 
integral-added optimal regulator using a dynamic model relating to the 
height of the vehicle M1 which dynamic model is determined in advance 
through system identification, and the parameter of the observer therein 
and an optimal feedback gain F and so on are determined in advance through 
simulation using the dynamic model of the vehicle M1. 
While it has been described that the state variable X(k) is an amount 
indicating the internal state of the vehicle M1, this is not required to 
be a variable corresponding to an actual physical amount, and, therefore, 
this may be designed as a vector of an appropriate order which is suitable 
for indicating the state of the vehicle M1. 
In the vehicle height control apparatus having the above-described 
structure according to the present invention, the vehicle height control 
means M6 formed as an integral-added optimal regulator operates so as to 
drive the vehicle height adjusting members M5 with the controlled variable 
of the vehicle height adjusting members M5 being obtained so that the 
actual vehicle height at an arbitrary position in the vehicle M1 detected 
by the vehicle height detecting means M3 equals the target vehicle height. 
Accordingly, it is possible to control the vehicle height to be a target 
vehicle height all the time without being influenced by the passengers, 
load or travelling state of the vehicle. As a result, the steering 
characteristics and stability of the vehicle are ensured. 
FIG. 2 is a block diagram showing the entire structure of an embodiment of 
the vehicle height control apparatus according to the present invention. 
The reference numerals 1 to 4 respectively indicate vehicle height sensors 
which are provided between respective wheels (not shown) and a vehicle 
body. The vehicle height sensors 1 to 4 may be potentiometers, and in 
detail, the reference character 1 indicating the vehicle height sensor for 
a front-left wheel, the reference character 2 indicating another sensor of 
a front-right wheel, the reference character 3 indicating another sensor 
for a rear-left wheel, and the reference character 4 indicating another 
sensor for a rear-right wheel. The reference characters 5 to 8 are vehicle 
height adjusting members provided between the respective wheels and the 
vehicle body for adjusting the vehicle height. In detail, the reference 
character 5 indicates a vehicle height adjusting member for the front-left 
wheel, the reference character 6 indicating another vehicle height 
adjusting member for the front-right wheel, the reference character 7 
indicating another vehicle height adjusting member for the rear-left 
wheel, and the reference character 8 indicating another vehicle height 
adjusting member of the rear-right wheel. 
The reference character 10 indicates a control circuit comprising a CPU 11, 
a ROM 12, a RAM 13, an input port 14, an output port 15, a data bus 16, a 
power circuit 17 and so on. Detection signals from the vehicle height 
sensors 1 to 4 are received by the input port 14, and the CPU 11 computes 
the controlled variables of the respective vehicle height adjusting 
members 5 to 8 in accordance with a control program prestored in the ROM 
12. As a result, control signals are produced and fed from the output port 
15 to the respective vehicle height adjusting members 5 to 8. In this way, 
a series of vehicle height control steps is executed. 
In a preferred embodiment, a hydraulic cylinder is provided between each 
wheel and the vehicle body in series separately from a suspension 
structure as each of the vehicle height adjusting members. The vehicle 
height adjusting members 5 to 8 comprise hydralic cylinders 21 to 24 and 
electromagnetic changeover valves 25 to 28 as shown in FIG. 3. Each of the 
electromagnetic changeover valves 25 to 28 is driven by a drive signal 
from the control circuit 10 so as to make communication between an oil 
supply pipe 29 or drain pipe 30 and hydraulic cylinders 21 to 24 so as to 
adjust oil pressure in the hydraulic cylinder to control the vehicle 
height at the respective wheels. An oil pressure pump 33 is connected to 
the oil supply pipe 29 for pumping up oil stored in a reservoir 32 via an 
adjusting valve 31 used for adjusting oil pressure. Furthermore, an 
accumulator 35 for preventing pulsation of oil pressure is connected via a 
normally-open electromagnetic valve 34 to the oil supply pipe 29. The oil 
in the drain pipe 30 as well as unnecessary oil whose pressure has been 
adjusted by the adjusting valve 31 is returned to the reservoir 32 to be 
stored therein. 
The period of time for communication between the respective electromagnetic 
changeover valves 25 to 28 and the oil supply pipe 29 or drain pipe 30 is 
controlled by the drive signal from the control circuit 10 so that the 
hydraulic pressure within the respective hydraulic cylinders 21 to 24 is 
controlled to a given value. 
FIG. 4 shows a control system diagram of the control circuit 10. While FIG. 
4 shows the control system, the hardware structure thereof is not shown by 
FIG. 4. This control system is executed by a control program for vehicle 
height control shown in a flowchart of FIG. 8. 
In FIG. 4, the references Hfl, Hfr, Hrl, Hrr represent actual vehicle 
heights respectively detected at the position of the respective wheels by 
the vehicle height sensors 1 to 4. The references Hfl.sup.*, Hfr.sup.*, 
Hrl.sup.*, Hrr.sup.* represent target vehicle heights predetermined in 
correspondence with the detected actual vehicle heights. The reference P1 
is an integrator for obtaining accumulated values Zfl, Zfr, Zrl, Zrr by 
accumulating the deviations of the respective actual vehicle heights Hfl, 
Hfr, Hrl, Hrr from the respective target vehicle heights Hfl.sup.*, 
Hfr.sup.*, Hrl.sup.*, Hrr.sup.*. The reference P2 is an observer for 
obtaining state estimated variable X(k) by estimating the state variable 
X(k) which represents the internal state of the vehicle, i.e., the state 
of the suspension provided between the respective wheels and the vehicle 
body, or the varying state of the oil pressure within the hydraulic 
cylinders 21 to 24 from the detected vehicle heights Hfl, Hfr, Hrl, Hrr at 
the respective wheels and oil pressures Pfl, Pfr, Prl, Prr of the 
hydraulic cylinders 21 to 24. The reference P3 is a feedback amount 
determining portion for computing oil pressures Pfl, Pfr, Prl, Prr of the 
hydraulic cylinders 21 to 24 by obtaining the product of the accumulated 
values Zfl, Zfr, Zrl, Zrr obtained by the integrator P1, and an optimal 
feedback gain F. The reference P4 is a drive signal outputting portion 
which outputs drive signals Tfl, Tfr, Trl, Trr of normally-closed 
electromagnetic values 25 to 28 in accordance with the detected oil 
pressures Pfl, Pfr, Prl, Prr of the hydraulic cylinders 21 to 24. 
While the structure of the control system has briefly been described 
hereinabove, the construction of the dynamic model through actual system 
identification, the designing of the observer P3, and the manner of 
providing the optimal feedback gain F will be described hereinbelow. 
First of all, a dynamic model of the system relating to the vehicle height 
is constructed. For instance, in the case that the vehicle is monocycle, 
its physical model can be expressed, as shown in FIG. 5, by a hydraulic 
cylinder 42 provided between a vehicle body 40 and road surface 41 and a 
suspension 45 comprising a spring 43 and a damper 44. In this case, the 
vehicle height "h" is obtained as a sum of the length X1 of the suspension 
45 and the length X2 of the hydraulic cylinder 42 as follows: 
EQU h(t)=X1(t)+X2(t) 
wherein (t) indicates time function. 
The dynamic behavior of the suspension 45 and the hydraulic cylinder 42 is 
obtained from the following equations: 
EQU F=P.multidot.S=m1.multidot.X1+f1.multidot.X1+k.multidot.X1 
EQU F=P.multidot.S=m2.multidot.X2+f2.multidot.X2 
wherein 
P is the pressure of the hydraulic cylinder; 
S is the cylinder area; 
m1 is mass of the suspension; 
f1 is the damping coefficient of the damper; 
k is the spring constant of the suspension; 
m2 is the mass of the vehicle body; and 
f2 is the coefficient of viscosity of the hydraulic cylinder. 
Therefore, when using P(t) as an input variable, X1(t), X1(t), X2(t), X2(t) 
as state variables, and h(t) as an output variable, the state equation and 
the output equation of the system are respectively given as a system of 
the fourth order by: 
##EQU1## 
However, when the control system has four inputs and four outputs as in the 
present embodiment so that there is interference between variables 
representing the inputs and the outputs, it is difficult to derive the 
state equation by constructing a physical model as described above. 
Therefore, in the present embodiment the transfer function is obtained 
through a sort of simulation called system identification so as to obtain 
system parameters A, B and C. 
FIG. 6 is a diagram showing a control system of the present embodiment, 
i.e., a system having four inputs and four outputs by way of transfer 
functions G1(z) through G16(z). The reference z indicates z transformation 
of sampled values of the input/output signals, and it is assumed that 
G1(z) through G16(z) have appropriate order. Therefore, the entire 
transfer function matrix G(z) is given by: 
##EQU2## 
The method of system identification is described in detail in "System 
Identification" written by Setsuo SAGARA published by Measurement and 
Automatic Control Society of Japan in 1981, and identification is 
performed here through the least squares method. 
The vehicle is left or driven under a predetermined condition, and the oil 
pressure Pfl of the hydraulic cylinder 21 is being charged with oil 
pressures Pf4, Prl, Prr of remaining hydraulic cylinders 22, 23 and 24 
being fixed to predetermined values. At this time, the data of the vehicle 
height is sampled N times. This is expressed as an input data series of 
{u(i)}={Pfl(i)} and as an output data series of {y(i)}={Hfl(i)} wherein 
i=1, 2, 3 . . . N. Here, the system can be regarded as having one input 
and one output, and thus the transfer function G1(z) is given by: 
EQU G1(z)=B(z.sup.-1)/A(z.sup.-1) (3) 
Therefore, 
EQU G1(z)=(b0+b1.multidot.z.sup.-1 + . . . 
+bn.multidot.z.sup.-n)/(1+a1.multidot.z.sup.-1 +a2.multidot.z.sup.-2 + . . 
. +an.multidot.z.sup.-n) (4) 
In the above, z.sup.-1 is a unit shift operator indicating z.sup.-1 
.multidot.x(k)=x(k-1). 
When we determine parameters a1 to an and b0 to bn of Eq. (4) from the 
input and output data series {u(i)} and {y(i)}, transfer function G1(z) 
can be obtained. These parameters are determined in system identification 
using the least squares method so that the following assumes a minimal 
value: 
##EQU3## 
When obtaining respective parameters assuming that n=2, a signal flow 
diagram of the system shown in FIG. 7 would result, and using [X1(k)] as 
state variables, state and output equations thereof can be expressed by 
Eqs. (6) and (7): 
##EQU4## 
Therefore, using system parameters A1', B1', C1' for the parameters A, B, C 
in the case that the system is regarded as of one input and one output, we 
obtain: 
##EQU5## 
In this way, the transfer functions G1(z) to G16(z) and system parameters 
A2' to A16', B2' to B16', C2' to C16' for each of the same can be 
obtained. 
Now the way of designing the observer P6 will be described. While the way 
of designing is known as the Gopinath method, which is described in detail 
in "Basic System Theory" written by katsuhisa FUTURA and Akira SANO 
published from Corona Co. Ltd. in 1978, the observer is designed as a 
finite time settling observer in this embodiment. 
The observer P2 is used for estimating the internal state variable X(k) of 
the vehicle from the vehicle heights Hfl, Hfr, Hrl, Hrr at the respective 
wheels, and oil pressures Pfl, Pfr, Prl, Prr of the respective hydraulic 
cylinders 21 to 24, and the reason why the state estimated variables X(k) 
obtained by the observer P2 can be handled as actual state variable X(k) 
in the control of the vehicle height will be made clear hereinbelow. Let 
us assume that the output X from the observer P2 is constructed as the 
following Eq. (9): 
EQU X(k)=(A-L.multidot.C).multidot.X(k-1)+B.multidot.u(k-1)+L.multidot.y(k-1) 
(9) 
In Eq. (9), L is a matrix arbitrarily given. Modifying Eqs. (1), (2) and 
(9), we obtain: 
EQU [X(k)-X(k)]=(A-L.multidot.C)[X(k-1)-X(k-1)] 10) 
Therefore, if the matrix L is selected so that an eigenvalue of the matrix 
(A-L.multidot.C) is located within a unit circle, X(k).fwdarw.X(k) with 
k.fwdarw..infin., and thus it is possible to accurately estimate the 
internal state variable X(k) of the controlled object using series u(*), 
y(*), from the past, of the input control vector u(k) and the output 
vector y(k). 
The vectors A, B, C of the state equation (1) and the output equation (2), 
both determined through system identification through the least squares 
method, can be similarity transformed into the following observable 
canonical structure considering the new state variable X(k)=T.sup.-1 
.multidot.X(k) using nonsingular matrix T because the system is 
observable. 
EQU X(k)=A0.multidot.X(k-1)+B0.multidot.u(k-1) (11) 
EQU y(k)=C0.multidot.X(k) (12) 
In the above, A0=T.sup.-1 .multidot.A.multidot.T, B0=T.sup.-1. B, 
C0=C.multidot.T, and we obtain the following equations by selecting 
appropriate nonsingular T. 
##EQU6## 
Then, let L matrix be replaced as L=[-.alpha.1-.alpha.2 . . . 
-.alpha.n].sup.T, and we can now design a finite time settling observer as 
follows using equations (13), (14) and (15): 
##EQU7## 
In the above, A0, B0 and C0 are obtained through similarity transformation 
using A, B, and C, and it is also ensured that the control by the state 
equation is correct from this operation. 
While the observer P2 has been designed using the vectors A, B and C of the 
state equation obtained through system identification, the output of the 
observer is now expressed in terms of X(k) hereinafter. 
Now the way of obtaining the optimal feedback gain F will be described. 
Since the way of obtaining optimal feedback gain F is described in detail 
in the above-mentioned "Linear System Control Theory", only the results 
are shown here with the detail thereof being omitted. 
Using 
EQU .delta.u(k)=u(k)-u(k-1) (17) 
EQU .delta.y(k)=y(k)-y(k-1) (18) 
in connection with the operating condition variables u(k) and operating 
state variables y(k), obtaining an optimal control input, i.e. driving 
condition u*(k) of the vehicle height adjusting members (in detail, this 
corresponds to oil pressure of the respective hydraulic cylinders), which 
makes the following performance index J minimal, results in solving a 
control problem as an integral-added optimal regulator related to the 
vehicle height. 
##EQU8## 
In the above, Q and R indicate weighted parameter matrixes, and k indicates 
the number of sampling times which is zero at the time of the beginning of 
control, while the right side of Eq. (19) is an expression of so called 
quadratic form using diagonal matrixes of Q and R. 
Here, the optimal feedback gain F is given as follows: 
EQU F=-(R+B.sup.T .multidot.P.multidot.B).sup.-1 .multidot.B.sup.T 
.multidot.P.multidot.A (20) 
In Eq. (20), A and B are given by: 
##EQU9## 
Furthermore, P is a solution of the following Riccati equation: 
##EQU10## 
In the above, the performance index J in Eq. (19) has a meaning that it is 
intended to reduce the deviation of the state variables y(k) of the 
vehicle state as a control output, i.e., vehicle heights Hfl, Hfr, Hfl, 
Hrr at the respective wheels, from the target value y*(k), i.e. Hfl*, 
Hfr*, Hfl*, Hrr*, with the variables as the control inputs to the vehicle, 
i.e., oil pressures Pfl, Pfr, Prl, Prr, being regulated. The weighting of 
the regulation of the respective vehicle heights Hfl, Hfr, Hrl, Hrr can be 
altered by changing the values of the weighted parameter matrixes Q and R. 
Therefore, the state variables X(k) can be obtained as state estimated 
variables X(k) using Eq. (9) if we obtain the optimal feedback gain F 
using Eq. (20) by obtaining P solving Eq. (23) with arbitrarily weighted 
parameter matrixes Q, R being selected using the dynamic model relating to 
the vehicle height, i.e., matrixes A, B, C (which correspond to the 
above-mentioned A, B, C) which is obtained in advance. Therefore, the 
variables u(k) of the control input to the vehicle can be obtained as 
follows: 
EQU u(k)=F.multidot.[X(k).sup.T ZHfl(k) ZHfr(k) ZHrl(k) ZHrr(k)].sup.T (24) 
By repeating simulation with the weighted parameter matrixes Q and R being 
altered until an optimum control characteristic is obtained, the optimal 
feedback gain F is obtained. 
While it has been described about the construction of the dynamic models of 
the height control system of the vehicle made through system 
identification using the least squares method, the designing of the finite 
time settling observer and the computation of the optimal feedback gain F, 
these are obtained in advance so that actual control is performed within 
the electronic control circuit 10 using only the results thereof. 
Now, an actual control performed by the electronic control circuit 10 will 
be described with reference to the flowchart of FIG. 8. In the following 
description, an amount handled in a present processing is expressed by a 
subscript (k) and an amount handled in the latest cycle by another 
subscript (k-1). 
When the ignition switch of the vehicle is turned on to supply electrical 
power to the control circuit 10, the CPU 11 executes repeatedly step 101 
and the following steps. As the processing is started, at first in the 
step 101, drive signals Tfl(k-1), Tfr(k-1), Trl(k-1), Trr(k-1) of the 
electromagnetic changeover valves 25 to 28 obtained by the last series of 
processings are outputted to the respective electromagnetic valves so as 
to control the oil pressure of the respective hydraulic cylinders. Then in 
step 102, the heights Hfl(k-1), Hfr(k-1), Hrl(k-1), Hrr(k-1) of the 
vehicle at the respective wheels are read from the detection signals from 
the respective vehicle height sensors 21 to 24, and then the operational 
flow proceeds to step 103. 
In the step 103, the deviations of the above-mentioned read vehicle 
heights, i.e., actual heights Hfl, Hfr, Hrl, Hrr, from target vehicle 
heights Hfl*, Hfr*, Hrl*, Hrr* which are preset and prestored in the ROM 
12, are computed as SHfl(k-1), SHfr(k-1), SHrl(k-1), SHrr(k-1). Then the 
operation flow proceeds to a step 104. 
In the step 104, the respective deviations obtained in the step 103 are now 
accumulated to obtain accumulated values ZHfl(k), ZHfr(k), ZHrl(k), 
ZHrr(k) by adding the above-mentioned obtained deviations SHfl(k-1), 
SHfr(k-1), SHrl(k-1), SHrr(k-1) to former accumulated values ZHfl(k-1), 
ZHfr(k-1), ZHrl(k-1), ZHrr(k-1) which have been obtained by the latest 
processing. The processing corresponds to the integrator P1 shown in FIG. 
4. 
In a following step 105, a new state variable X(k) is computed using 
parameters A0, B0, L within the observer prestored in the ROM 12 after 
being obtained through the above-mentioned method, the actual vehicle 
heights Hfl(k-1), Hfr(k-1), Hrl(k-1), Hrr(k-1) read in the step 102, state 
variable X(k-1)=[X1(k-1) X2(k-1) . . . X6(k-1)] obtained by the former or 
latest processing, and oil pressures Pfl(k-1), Pfr(k-1), Prl(k-1), 
Prr(k-1) of the respective hydraulic cylinders 21 to 24 detected in the 
latest cycle. This processing corresponds to the observer P2 shown in FIG. 
4, and this observer P2 is constructed as a finite time settling observer. 
The state estimated variable X(k) is computed as follows: 
##EQU11## 
wherein M=A0-LC0. 
In a following step 106, oil pressures Pfl(k), Pfr(k), Prl(k), Prr(k) of 
the respective hydraulic cylinders 21 to 24 by performing vector 
multiplication between the state estimated variable X(k) obtained in the 
step 105, the accumulated values ZHfl(k), ZHfr(k), ZHrl(k), ZHrr(k) 
obtained in the step 104, and the optimal feedback gain F 
##EQU12## 
preset and prestored in the ROM 12 as follows: 
##EQU13## 
This processing corresponds to the feedback amount determining portion P3 
of FIG. 4. 
In a following step 107, drive signals Tfl(k), Tfr(k), Trl(k), Trr(k) for 
driving the normally-closed electromagnetic valves 25 to 28 are computed 
so that the oil pressures of the hydraulic cylinders 21 to 24 equal the 
above-mentioned obtained oil pressures Pfl(k), Prf(k), Prl(k), Prr(k) from 
the following equations: 
EQU Tfl(k)=T.multidot.(Pfl(k)-Pa)/(Pb-Pa) 
EQU Tfr(k)=T.multidot.(Pfr(k)-Pa)/(Pb-Pa) 
EQU Trl(k)=T.multidot.(Prl(k)-Pa)/(Pb-Pa) 
EQU Trr(k)=T.multidot.(Prr(k)-Pa)/(Pb-Pa) 
Then the operational flow goes to a step 108. 
In the above equations, the reference Pa indicates the pressure of the 
drain pipe (atmospheric pressure), the reference Pb indicating the 
pressure of the oil supply pipe, and the reference T indicating a 
predetermined control period of the electromagnetic changeover valve. 
More specifically, the electromagnetic changeover valves are driven and 
controlled through duty cycle control, as shown in FIG. 9 for instance, 
when drive signals are being outputted for a period of time Tx within a 
predetermined period of time T, an average pressure within the hydraulic 
cylinders becomes: 
##EQU14## 
Therefore, assuming that the average pressure P is the target pressure, the 
driving period of time Tx per the predetermined period of time T can be 
obtained through the following equation: 
EQU Tx=T.multidot.(P-Pa)/(Pb-Pa) 
Then in a following step 108, the value of "k" indicative of the number of 
times of sampling is incremented by 1, and the operational flow returns to 
the step 101 to execute the above-mentioned series of processing again. 
As the control is continued, the control circuit 10 performs vehicle height 
control with an optimal feedback gain as an integral-added optimal 
regulator which controls the actual vehicle heights at the respective 
wheels to target vehicle heights. Accordingly, in the vehicle height 
control apparatus according to the present invention, as shown in FIGS. 
10A and 10B, the vehicle height can be controlled to a target vehicle 
height during braking, for instance, quickly and accurately when compared 
with conventional vehicle height control apparatus. As a result, the 
stability in running of the vehicle can be improved. FIG. 10A shows the 
varying state of the vehicle height controlled by the conventional vehicle 
height control apparatus during braking, while FIG. 10B shows the same 
controlled by the present embodiment of the invention. In FIGS. 10A and 
10B, the reference t1 indicates a starting point of braking. 
In the above-embodiment, although it has been described that the target 
vehicle height is predetermined, this target vehicle height may be set in 
accordance with various values, such as the steering angle, vehicle speed 
or acceleration/deceleraton, so that vehicle attitude can be controlled in 
a stable manner suitable to the running state and, therefore, the 
stability during vehicle running can be improved. 
Furthermore, although the vehicle height sensors are provided at each of 
the wheels in the above-described embodiment so that the vehicle height at 
the respective wheels are controlled to be equal to the target vehicle 
heights, the vehicle height sensor(s) is(are) may be installed at an 
arbitrary position of the vehicle body. For instance, the vehicle height 
sensor may be installed at the driver's seat. In this case, the control 
system is actualized as a four-input and one-output system, and the 
observer and the optimal feedback gain are set accordingly. 
The above-described embodiment is just an example of the present invention, 
and therefore, it will be apparent for those skilled in the art that many 
modifications and variations may be made without departing from the scope 
of the present invention.