Quarter car variable force suspension system control

A controller for a quarter car variable force suspension system responds to a signal representative of the system state. In response to the system state signal, the controller provides an actuator force control signal commanding (i) low level damping force when a magnitude value of the system state signal is below a magnitude of a dead zone limit, (ii) maximum available actuator force when the magnitude of the system state signal is above a magnitude of a boundary layer limit and (iii) actuator force proportional to the magnitude of the system state signal when the magnitude of the system state signal is above the magnitude of the dead zone limit and below the magnitude of the boundary layer limit, whereby the suspension system does not chatter and is not affected by system state signal error.

This invention relates to vehicle suspension systems and more particularly 
to actuator control of variable force semi-active and active quarter car 
suspension through modified Lyapunov control methods. The subject of this 
application is related to following copending patent applications: U.S. 
Ser. No. 07/702,875, filed May 20, 1991, entitled "Suspension System State 
Observer," and U.S. Ser. No. 07/702,874, filed May 20, 1991, entitled 
"Full Car Semi-Active Suspension Control Based on Quarter Car Control," 
both filed concurrently with this specification and assigned to the 
assignee of this invention. The disclosures of patent applications Ser. 
Nos. 07/702,875 and 07/702,874 are incorporated into this document by 
reference. 
BACKGROUND OF THE INVENTION 
In the field of vehicle suspensions, the phrase "quarter car suspension" 
refers to the components of the vehicle suspension relating to one of the 
four wheels of the typical automotive vehicle. These components include 
the particular wheel with a tire that is in contact with the road, a 
spring that transfers the road force to the vehicle body (sprung mass) and 
suspends the vehicle body, and a damper or actuator that reduces 
undesirable relative movement between the vehicle body and wheel. The 
complete suspension system of an automotive vehicle comprises four quarter 
car suspensions. 
In recent years, vehicle manufacturers have dedicated significant effort to 
developing suspension systems responsive to the driving conditions of the 
vehicle. This effort is triggered by desire to incorporate the best 
features of soft and stiff suspension systems into a single vehicle 
suspension system. The best feature of a soft vehicle suspension is the 
smooth ride it provides for the vehicle passengers. The best feature of a 
stiff vehicle suspension is the increased handling performance it provides 
for the vehicle. 
The theory of semi-active suspension systems is to selectively switch 
between stiff suspension and soft suspension in response to the particular 
driving conditions of the vehicle. Selection between stiff suspension and 
soft suspension may be obtained by altering the damping force of the 
suspension system, e.g., a greater damping force for a stiffer suspension 
and a lower damping force for a softer suspension. With correct control of 
suspension damping force, a vehicle can provide both optimum driving 
comfort and optimum handling performance. 
The theory of active suspension system controls is to provide an actuator 
force to the suspension system to reduce wheel hop and improve vehicle 
body attitude control beyond that achievable by damping forces alone. The 
actuator force is applied in equal and opposite directions between the 
wheel and vehicle body. Active and semi-active suspension systems can be 
commonly referred to as variable force suspension systems. 
Difficulties in designing variable force suspension systems lie partially 
in system controls. A suspension system may, at any given time, be said to 
have a state. The suspension system state for a particular quarter of the 
vehicle includes the position of the vehicle body (the sprung mass), the 
position of the wheel (the unsprung mass), the velocity of the sprung 
mass, and the velocity of the unsprung mass. From these four components, 
the other characteristics of the quarter car suspension system may be 
determined. For example, the relative velocity between the sprung mass and 
the unsprung mass is equal to the velocity of the sprung mass subtracted 
by the velocity of the unsprung mass. The relative position of the sprung 
mass and unsprung mass is equal to the position of the sprung mass 
subtracted by the position of the unsprung mass. The relative velocity 
between the sprung and unsprung masses and/or the relative position of the 
sprung and unsprung masses may be included in what is referred to below as 
the relative system state. 
The state of the quarter car suspension system is difficult to predict 
because the road surface is always changing and is, itself, not 
predictable. Directly measuring the suspension system state requires many 
sensors, and is difficult to do. What is desired is a controller for a 
variable force suspension system that estimates the quarter car suspension 
system state based on as few sensors as possible while keeping the error 
between the actual and estimated state within reasonable limits. It is 
also desired that the suspension controller not be affected by error in 
the estimated state. 
There is also the desire to eliminate suspension system chatter. Chatter 
occurs when the suspension control system is on the border between 
commanding high actuator force and low damping force and constantly 
switches between the two. 
SUMMARY OF THE PRESENT INVENTION 
The present invention provides an apparatus and a method for controlling 
the quarter car suspension system actuator force in response to a system 
state signal such that errors in the state signal do not noticeably affect 
the suspension control and such that the suspension does not chatter. 
Controlling the quarter car suspension system actuator force according to 
this invention includes use of a modified Lyapunov controller. The 
modified Lyapunov controller provides a control signal controlling the 
actuator force of the system to minimize the difference between the actual 
suspension system state and a zero state or static equilibrium state. The 
controller achieves the desired actuator force control by providing an 
actuator force control signal commanding low level damping force when a 
value of the system state is below a dead zone limit, commanding maximum 
available actuator force when the value of the system state is above a 
boundary layer limit, and commanding actuator force proportional to the 
value of the system state when the value of the system state is above the 
dead zone limit and below the boundary layer limit. With implementation of 
this invention, the suspension system does not chatter and is not affected 
by noise in the system and/or error in the estimated system state. 
Four quarter car suspension system controllers of this invention can be 
used in a complete vehicle suspension system and combined with other 
control methods, such as that disclosed in copending application Ser. No. 
07/702,874, for additional vehicle suspension system control.

DETAILED DESCRIPTION OF THE INVENTION 
A quarter car suspension system of the type in which this invention may be 
implemented to control may be understood with reference to the model 
diagram of FIG. 1. In the Figure, reference numeral 12 generally 
designates the sprung mass, having mass M.sub.s, which is the vehicle body 
supported by the suspension. The sprung mass has a position, x.sub.2, and 
a velocity, x.sub.2 ', both represented by line 14. The sprung mass 12 is 
supported by the spring 16, having a constant k.sub.s. The spring is also 
connected to the unsprung mass 24, which represents the vehicle wheel. The 
unsprung mass 24, having mass M.sub.u, has a position, x.sub.1, and a 
velocity, x.sub.1 ', both represented by line 26. The tire of the vehicle 
is modeled as a spring 28, having a spring constant k.sub.u. The road is 
represented by reference numeral 32 and affects a displacement R (line 30) 
on the tire 28. 
Variable force between the sprung and unsprung masses 12 and 24 is provided 
in the suspension system by actuator 22. Actuator 22 may be an adjustable 
damper, for semi-active systems, or an actuator capable of both damping 
and providing a force independent of damping on the suspension system. 
Actuator 22 may be a dynamoelectric machine, including a linear 
electromechanical machine, hydraulic shock with a flow control or bypass 
valve, or any other means of providing variable force to the suspension. 
The actuator 22 is attached between the unsprung mass 24 and a rubber 
bushing 18 (rubber bushing 18 is similar to bushings used in engine mounts 
and is optional, if the rubber bushing 18 is omitted, the actuator 22 is 
attached directly to the sprung mass 12), modeled as a nonlinear spring in 
parallel with a damper. In general, the actuator 22 exerts a force on the 
unsprung mass 24 and an equal and opposite force on the rubber bushing 18 
in proportion to the relative speed of the sprung and unsprung masses 
and/or an input control signal. 
In the suspension system, the road 32 affects a displacement R on the tire 
28, which in turn applies a force on the unsprung mass 24. The unsprung 
mass 24 transfers force to the spring 16 which in turn applies force on 
the sprung mass 12. The actuator 22 applies force on the sprung mass 12 
(through bushing 18, if used) and unsprung mass 24; in the semi-active 
case, the force is applied in the direction opposite the relative 
direction of travel of the two masses, in the active case, the force may 
be in the same direction or opposite the direction of travel of the two 
masses. The bushing 18 is optional but may be preferable to help reduce 
the effect of high frequency road surface disturbance on the system. In 
the model of the suspension system set forth below, the effect of the 
rubber bushing is ignored and accounted for as a system uncertainty. 
Suspension systems of the type represented by FIG. 1 are easily 
implemented by those skilled in the art. 
Referring to FIG. 2a, one example of the actuator 22 may be the unit 22a, 
including an electromechanical machine 42. In the Figure, the 
electromechanical machine 42 comprises a linear to rotary motion converter 
60 and a rotary multi-phase alternator 52. The linear to rotary motion 
converter 60 includes a ball screw cage 58, hollow connector 62, screw 56 
and lower connector 66. The rotary multi-phase alternator 52 is rotatably 
mounted through bearings 44 and 54 to the upper connector 40. The lower 
connector 66 is mounted to the unsprung mass 24 (FIG. 1) and the upper 
connector 40 is mounted to the sprung mass 12 (FIG. 1), through rubber 
bushing 18, if used. 
Through the relative movement of the sprung mass 12 and the unsprung mass 
24 acting on the connectors 40 and 66, the ball screw 56 is forced to 
rotate, rotating the rotary multi-phase alternator 52 and creating 
electric potential on lines A, B, and C, which are connected to the 
rectifier and chopper apparatus 48. In response to the controller 50, 
which generates a pulse width modulated control signal on line PWM, the 
rectifier and chopper 48 selectively dissipates the power generated by 
alternator 52 through load resistor 46, providing the damping force for 
actuator 22a. During high frequency movements of the unsprung mass 24, 
e.g., on a very bumpy road, the rubber bushing 18 (FIG. 1) attenuates the 
inertial effect of actuator 22a on the suspension system performance. 
Optionally, the actuator 22a may be used as a brushless DC motor by 
including hall effect sensors 344, 362 and 366 (FIG. 12) and used with an 
inverter circuit 390 (also in FIG. 12). When used as a brushless motor, 
actuator 22a can not only dampen the suspension system, but apply a force 
between the sprung and unsprung masses 12 and 24, both counter to and in 
the direction of travel of the two masses (damping force can only be 
opposite the relative direction of travel of the two masses 12 and 24). 
The rectifier and chopper 48 and the controller 50 can be better understood 
with reference to FIG. 3. Coils 120, 121, and 122 of the alternator 52 are 
connected to a rectifier bridge 140 which rectifies the three phase 
voltage on lines A, B, and C. In response to a control signal on line PWM, 
the circuit comprising operational amplifier 136, transistors 130 and 146, 
and resistors 132, 134, 138, 144, 148, and 150 control MOSFET 128, 
selectively closing a DC circuit between resistors 46 and 142, dissipating 
the power generated by alternator 52. The duty cycle of the signal on line 
PWM determines the amount of damping force. Example values for the 
resistors and capacitor are as follows: resistor 46, 1.67 .OMEGA., 150W; 
resistor 142, 2 m.OMEGA.; resistor 124, 50 .OMEGA.; capacitor 33, 0.1 uF; 
resistors 134, 138, and 150, 10K; resistor 148, 100K; resistor 132, 1.5K; 
and resistor 144, 100 .OMEGA.. 
Line I may be implemented as an option to provide a damping force feedback 
loop for electromechanical implementations. There will probably be 
sufficient inductance in the circuit of alternator 52, rectifier bridge 
140 and load resistor 46 that the duty cycle modulation of MOSFET 128 
produces an average DC current with a small ripple. If so, the current 
signal I read into microcomputer 174 is already averaged. If any 
additional averaging is required, it can easily be done by one skilled in 
the art with a standard digital averaging algorithm in microcomputer 174 
applied to successive values of I. 
As will be explained below, it is desirable for successful implementation 
of this invention to detect the relative velocity of the sprung and 
unsprung masses 12 and 24, otherwise known as the rattle space velocity, 
or the relative position of the sprung and unsprung masses 12 and 24. 
Either implementation is acceptable. 
The rattle space velocity may be determined a variety of ways. The 
preferred implementation is to determine the frequency of the zero 
crossings of the voltages on lines A, B, and C. 
The circuit comprising transformer 152, operational amplifier 158, 
resistors 154, 156, 160, 170, and 172, capacitors 162 and 164, and zener 
diodes 166 and 168 provide a pulse to the microcomputer 174 on line F with 
every zero crossing of the Voltage between lines B and C. Preferably, 
identical circuits are connected between lines A and C and between lines A 
and B to provide zero crossing pulses on lines F' and F", respectively. 
The frequency of the signaIs on Iines F, F' and F" determines the 
magnitude of the rattle space velocity and the direction of the rattle 
space velocity is determined by the order of the signals on lines F, F' 
and F". The calculation of the rattle space velocity is performed by 
microcomputer 174 through a computer routine easily implemented by one 
skilled in the art. Example values for the capacitors and resistors are: 
resistors 154, 156 and 170, 10K; capacitor 162, 0.0015 uF; capacitor 164, 
0.33 uF; resistor 160, 3K; and resistor 172, 470K. A more detailed 
description of the actuator 22a and related circuitry is set forth in U.S. 
Pat. No. 4,815,575, to Murty, assigned to the assignee of this invention, 
and will not be set forth herein. 
If the relative position of the sprung and unsprung masses 12 and 24 is to 
be determined, an LVDT-type sensor (not shown) is attached between the 
sprung and unsprung masses 12 and 24. The LVDT sensor provides an output 
signal linearly related to distance between the sprung and unsprung masses 
and the output signal is provided to an A/D converter (not shown), the 
output of which is connected to the microcomputer 174 for processing. 
In implementation with the actuator 22a, this invention provides a control 
routine for microcomputer 174 to improve the performance of actuator 22a 
in a semi-active quarter car suspension system. To provide optimal damping 
control and suspension system performance, it is desirable to know the 
entire state of the system. The entire state of the system comprises the 
positions and velocities of the sprung and unsprung masses (ignoring the 
rubber bushing 18). The relative velocity of the sprung and unsprung 
masses is easily derived from the absolute velocities and the relative 
position of the sprung and unsprung masses is easily derived from the 
absolute positions. In the case where the rubber bushing 18 is ignored, 
the system state may be set forth as a vector X as follows: 
##EQU1## 
where x.sub.1 and x.sub.1 ' are the position and velocity of the unsprung 
mass 24 (FIG. 1) and x.sub.2 and x.sub.2 ' are the position and velocity 
of the sprung mass 12. The positions of the unsprung and sprung masses 24 
and 12 are preferably determined relative to an at rest position for the 
system. 
To dispense with the expensive requirement of separate sensors to measure 
each component of the quarter car system state along with the difficulties 
in obtaining absolute state measurements, this invention is implemented 
with a means for estimating the entire system state requiring the input of 
only one sensor which measures the relative system state. The system state 
estimation means (e.g., observer) is the subject of copending patent 
application Ser. No. 07/702,875. The single sensor may be a sensor that 
measures the relative velocity of the sprung and unsprung masses 12 and 24 
or the relative position of the masses 12 and 24. One example of a sensor 
for measuring the relative velocity is the inherent inductance of the 
actuator 22a described above with reference to FIG. 3, providing the 
pulses on lines F, F' and F". Another example of a sensor for measuring 
the relative velocity is to include three Hall effect sensors in the 
actuator 22a (see, e.g. FIG. 12) and to determine relative velocity 
according to the frequency and direction of signals provided by the Hall 
effect sensors. One example of a sensor for measuring the relative 
position is an LVDT sensor (readily available to those skilled in the art) 
attached to the sprung and unsprung masses 12 and 24. 
When the sensor to measure the relative system state measures the relative 
velocity between the sprung and unsprung masses 12 and 24, the estimated 
relative system state includes an estimation of the relative velocity 
between the sprung and unsprung masses 12 and 24. When the sensor to 
measure the relative system state measures the relative position between 
the sprung and unsprung masses 12 and 24, the estimated relative system 
state includes an estimation of the relative position between the sprung 
and unsprung masses 12 and 24. It is preferable to measure relative 
position to minimize the effect of error integration. 
One example of the means for estimating the entire system state includes 
the observer 194 shown in FIG. 4a including a linear Luenberger term and a 
nonlinear signum term. The observer 194 estimates the entire system state 
X.sup.e' (comprising x.sub.1.sup.e, x.sub.1.sup.e', x.sub.2.sup.e and 
x.sub.2.sup.e') and computes the estimated relative system state, y.sup.e 
(t). The estimated system state X.sup.e' is computed according to the 
following model: 
EQU X.sup.e' =AX.sup.e +Bu+L(y(t)-y.sup.e (t))+S(y(t), y.sup.e (t)), 
where A and B are standard model matrices for a suspension system with 
control, X.sup.e is the previous estimated system state, u is the control 
(representing the actuator force of actuator 22), L is a linear Luenberger 
matrix that provides stabilizing linear feedback, y(t) is the measured 
relative system state of the sprung and unsprung masses 12 and 24, and 
S(y(t), y.sup.e (t)) is the nonlinear signum function term, allowing for 
accurate estimations within a defined error limit. For purposes of 
simplification of the model, the characteristics of the rubber bushing 18 
(FIG. 1) are not modeled, but accounted for as error in the uncertainty 
term. The estimated relative system state, y.sup.e (t), is related to the 
state, X.sup.e, as follows: 
EQU y.sup.e (t)=CX.sup.e, 
where the matrix C is a standard suspension system model matrix. 
The matrix A is a standard suspension model matrix easily implemented by 
one skilled in the art as follows: 
##EQU2## 
In implementing the model, those skilled in the art realize that the model 
parameters of matrix A, in a damper where inertial effects are 
significant, are as follows: 
EQU a.sub.1 =(j.sup.2 (k.sub.s M.sub.u -jn.sup.2 k.sub.u) -(k.sub.u 
+k.sub.s)c.sub.1)/((M.sub.u +jn.sup.2)c.sub.1); 
EQU a.sub.2 =(jn.sup.2 b.sub.p M.sub.u -c.sub.1 b.sub.p) /((M.sub.u 
+jn.sup.2)c.sub.1); 
EQU a.sub.3 =(c.sub.1 k.sub.s -jn.sup.2 k.sub.s M.sub.u) /((M.sub.u 
+jn.sup.2)c.sub.1); 
EQU a.sub.4 =(c1bp-jn2bpMu) /((M.sub.u +jn.sup.2)c.sub.1); 
EQU a.sub.5 =(k.sub.s M.sub.u -jn.sup.2 k.sub.u)/c.sub.1 ; 
EQU a.sub.6 =b.sub.p M.sub.u /c.sub.1 ; 
EQU a.sub.7 =-k.sub.s M.sub.u /c.sub.1 ; 
EQU a.sub.8 =-b.sub.p M.sub.u /c.sub.1, 
where b.sub.p is the passive damping force on the system, e.g., when zero 
power is being dissipated in resistor 46 of actuator 22a above, j is the 
rotary inertia of the electromechanical machine 52, n is the gear ratio, 
and c.sub.1 equals the quantity (M.sub.u M.sub.s +jn.sup.2 (M.sub.u 
+M.sub.s)). 
The matrix B is as follows: 
##EQU3## 
where, for the system where inertial effects are significant, b.sub.1 
=(jn.sup.2 M.sub.u -c.sub.1)/ ((M.sub.u +jn.sup.2)c.sub.1) and b.sub.2 
=M.sub.u /c.sub.1. If the relative system state is to comprise the 
relative velocity between the sprung and unsprung masses 12 and 24, the 
matrix C may be described as C=[0 1 0 -1], so that y.sup.e 
(t)=x.sub.1.sup.3' -x.sub.2.sup.3'. If the relative system state is to 
comprise the relative position between the sprung and unsprung masses 12 
and 24, the matrix C may be described as C=[1 0 -1 0], so that y.sup.e 
(t)=x.sub.1.sup.3 -x.sub.2.sup.e. 
The Luenberger matrix L is generally solved for by determining a stable 
point for matrix [A-LC], with its poles placed anywhere on the left hand 
plane of the real-imaginary coordinate system provided that the pair (A, 
C) is observable. Those skilled in the art of state estimation can easily 
implement the Luenberger matrix with the limitations set forth above. 
The first three terms of the model (AX.sup.3 +Bu+L(y(t)-y.sup.e (t))) are a 
linear estimation of the system state. However, because of the difficulty 
of measuring the absolute displacement of the suspension system, the 
nonlinear mount, the system uncertainties, and the unknown road 
disturbances, the linear equation alone cannot converge the estimated 
system state to the actual system state. To ensure accurate estimations of 
X.sup.e', a signum function, S(y(t), y.sup.e (t)), is added. S(y(t), 
y.sup.e (t)) compensates for road disturbance, system uncertainties, 
non-linearities in the system, if any, and errors in the estimation model. 
The signum function is defined as: S(y(t), y.sup.e (t))=-P.sup.-1 C.sup.T 
(y(t)-y.sup.e (t)).sigma./.vertline..vertline.y(t)-y.sup.e 
(t).vertline..vertline., where C.sup.T is the transpose of matrix C, P is 
the solution of the Lyapunov equation [A-LC].sup.T P+P[A-LC]=-Q (Q being 
any positive definite matrix), and .sigma. is determined from the modified 
matching condition described below. 
Normally, the system would have zero error if the matching condition: 
EQU g=P.sup.-1 C.sup.T- g, 
is satisfied. In the above equation g is the sum of the effect of the road 
disturbance and nonlinear mount on the system, e.g., g .TM.ER +f(X, t), 
where ER is the affect of road disturbance on the system and f(X, t) is 
the affect of the nonlinear mount 18 (FIG. 1) and parameter uncertainties 
on the system. The above matching condition cannot be satisfied due to the 
nature of the problem. However, if instead of converging the estimated 
system state X.sup.e to the actual state X, the estimation is converged 
within a circle defining an acceptable error deviation from the actual 
state, e.g., circle with radius 
.vertline..vertline..DELTA.AX.vertline..vertline., the matching condition 
can be satisfied. .DELTA.A is determined to allow for the parameter 
uncertainties of the system model and errors of the estimated states. With 
.DELTA.A considered in the model, the Luenberger matrix, L, is solved for 
so that the matrix [A-.DELTA.A-LC] is stable. 
To achieve the error limit, define P.sub.2 as the solution of the equation: 
EQU [A-.DELTA.A-LC].sup.T P.sub.2 +P.sub.2 [A-.DELTA.A-LC]=-Q, 
and adjust Q until the new matching condition: 
EQU g=P.sub.2.sup.-1 C.sup.T- g, 
is satisfied. This is easily accomplished by one skilled in the art. Once 
the new matching condition is satisfied, .sigma. is defined such that: 
EQU .sigma..gtoreq.MAX.vertline..vertline.g.vertline..vertline.. 
Referring to FIG. 4a, the state estimation by the observer 194 can be 
easily understood. The road disturbance on line 30 and the actuator force 
on line 182 affect the quarter car suspension system, represented by block 
180, such that an actual relative system state, y(t), on line 184 is 
developed. At block 186, the estimated relative system state, y.sup.e (t), 
is compared to the actual relative system state, and an error signal, 
e(t)=y(t)-y.sup.e (t), on line 188 is developed. The error signal on line 
188 is multiplied by the Luenberger matrix L at box 192 and the result is 
added with the rest of the estimation model in block 194. The error signal 
on line 188 is also input into the nonlinear function box 204 where the 
nonlinear signum function S(y(t), y.sup.e (t)) is determined and added 
with the rest of the estimation model in block 194. 
A signal representative of the actuator force command, u.sub.s, from the 
controller 200 is input into block 194 through line 182 (optional). The 
system actuator force, u, is determined at block 194 through one of a 
variety of different means. The actuator force, u, may be determined in 
relation to a signal such as on line I in FIG. 3. Alternatively, the 
actuator force, u, may be determined from a three dimensional look-up 
table with reference to y(t) and the controller command, u.sub.s, 
described below. In the active case, actuator force, u, may be determined 
in relation to current i.sub.m through resistor 394 (FIG. 12). In block 
194, the estimations X.sup.e' and y.sup.e (t) are determined as described 
above and output on lines 198 and 190, respectively. 
Block 200 is a modified Lyapunov controller and represents one aspect of 
this invention. The modified Lyapunov controller 200 controls the actuator 
force (line 182) of the quarter car system in response to the estimated 
state X.sup.e on line 198 in a manner to drive the state to a reference 
condition. 
The typical Lyapunov controller is a two state min-max controller. However, 
the modified Lyapunov controller of this invention has the following 
control function: 
##EQU4## 
where .epsilon..sub.d is the dead zone limit set to correspond to sensor 
noise and the allowable estimation error (if any), .epsilon. is the 
boundary layer limit set greater than .epsilon..sub.d to ensure smooth 
transition between minimum and maximum actuator force (thereby eliminating 
chatter), and .rho. is the maximum available force at a given rattle space 
velocity. When the controller output, u.sub.s, is zero, the actuator 
force, u, is the minimum damping of the system and may be zero or may 
follow a rattle space velocity dependent curve. When u.sub.s is (B.sup.T 
PX.sup.e).rho./.vertline..vertline.B.sup.T PX.sup.e .vertline..vertline., 
the actuator force u is the maximum actuator force of the system (in the 
semi-active case the maximum actuator force is a damping force and may be 
dependent upon rattle space velocity). When u.sub.s is ((B.sup.T PX.sup.e 
-.vertline..vertline.B.sup.T PX.sup.e .vertline..vertline..epsilon..sub.d 
/B.sup.T PX.sup.e) .rho./(.epsilon.-.epsilon..sub.d), the actuator force u 
is ((B.sup.T PX.sup.e -.epsilon..sub.d /)/(.epsilon.-.epsilon..sub. d) 
percent between the minimum actuator force and maximum actuator force for 
the particular rattle space velocity. 
The output of the controller is shown in FIG. 5. The dead band, between 
-.epsilon..sub.d and .epsilon..sub.d on the B.sup.T PX.sup.e axis, 
represents minimum possible damping and eliminates detrimental effects of 
noise and estimation error on the system. .vertline..vertline.B.sup.T 
PX.sup.e .vertline..vertline. can be referred to as the magnitude of the 
system state. The transfer regions between -.epsilon. and -.epsilon..sub.d 
and between .epsilon. and .epsilon..sub.d on the B.sup.T PX.sup.e axis 
prevent chatter in the suspension system. The regions below -.epsilon. and 
above .epsilon. provide maximum available actuator force on the suspension 
system. 
In implementation of this invention in a semi-active system, the controller 
200 is stable as long as matrix A is stable because the force, u, is 
always a damping force. In implementation of this invention in an active 
system, the control parameter must be chosen correctly to maintain a 
stable system. Stability in the dead band is achieved as long as matrix A 
is stable. The transfer regions are stable as long as a matrix 
(A-.rho.BB.sup.T P/(.epsilon.-.epsilon..sub.d)) is stable. If the above 
two stabilities are met, then the maximum actuator force regions are 
stable. The required stability tests are easily achieved by one of 
ordinary skill in the art. 
In implementing this invention with actuator 22a in FIGS. 2a and 3, the 
microcomputer 174 executes a control routine which estimates the system 
state and calculates the desired actuator command u.sub.s. The signal on 
line PWM is pulse width modulated, preferably at a frequency of about 2 
kHz, to provide the desired damping force. For example, if 
.vertline..vertline.B.sup.T PX.sup.e 
.vertline..vertline..ltoreq..epsilon..sub.d, then the duty cycle of the 
signal on line PWM is zero, resulting in zero power dissipation through 
resistor 46. If .vertline..vertline.B.sup.T PX.sup.e 
.vertline..vertline..gtoreq..epsilon., then the duty cycle of the signal 
on line PWM is 100 percent, resulting in maximum dissipation of power in 
resistor 46. If .epsilon..sub.d &lt;.vertline..vertline.B.sup.T PX.sup.e 
.vertline..vertline.&lt;.epsilon., then the duty cycle on line PWM is 
(.vertline..vertline.B.sup.T PX.sup.e 
.vertline..vertline.-.epsilon..sub.d)/(.epsilon.-.epsilon..sub.d). As an 
optional feature, a measure of the actual damping force may be provided to 
the microcomputer through the signal on line I and may be used by the 
microcomputer in calculating the estimations at block 194. In actual 
practice, there may be some inherent damping in actuator 22a due to 
friction. This inherent damping may be either accounted for in the 
controller in relation to rattle space velocity or may be lumped in with 
the system error for purposes of this invention. 
The flow diagram of FIG. 6a is one example of a computer implementation of 
this invention. The program starts at block 240 and initializes the system 
at block 242 (startup only). During initialization, the computer assigns 
zeros as the standard initial values to the estimated system states, 
X.sup.e (k-1) and y.sup.e (k-1), which are discrete representations of 
X.sup.e and y.sup.e (t) with k being the current time event and k-1 being 
the previous time event. Block 242 also assigns an initial value to the 
damping force signal, u.sub.s (k-1). At block 243, the controller receives 
the sensor input containing signals representative of the relative system 
state y(k-1) and, at block 244, the error between the actual and measured 
relative system states, y(k-1)-y.sup.e (k-1), is computed. At block 246 
the nonlinear term S(y(k-1), y.sup.e (k-1)) is computed and at block 248 
the Luenberger term is computed. At block 250, the damping force, 
u(u.sub.s (k-1), X.sup.e (k-1)), is determined from a three dimensional 
look-up table in response to u.sub.s (k-1) and X.sup.e (k-1) (or X(k-1) if 
the measured relative system state includes relative velocity). 
At block 252, the estimated system state X.sup.e (k), which is a discrete 
representation of X.sup.e', is computed by a discrete representation of 
the above described computations: 
EQU X.sup.e (k)=A.sub.d X.sup.3 (k-1)+B.sub.d u(k-1)+L.sub.d (y(k-1)-y.sup.e 
(k-1))+S.sub.d (y(k-1), y.sup.e (k-1)), 
where: 
##EQU5## 
and where .tau. is the time period between successive estimations of 
X.sup.e (k) and e is the natural log function. At block 249, y.sup.e (k) 
is computed, at block 251, y.sup.e (k-1) is set equal to y.sup.e (k) and 
at block 251, X.sup.e (k-1) is set equal to X.sup.e (k) and y.sup.e (k-1) 
is set equal to y.sup.e (k). At block 254, the computer computes B.sup.T 
PX.sup.e (k). At block 253, the computer computes the product of the force 
computed at block 250 and B.sup.T PX.sup.e (k), and if the result is not 
greater than zero, u.sub.s is set equal to zero at block 256. This test 
determines if the present force (u(k-1) which may be found, for example, 
from a look-up table as a function of commanded force and system state, 
e.g., u(k-1)=u(u.sub.s (k-1), X.sup.e (k-1))) is of proper direction, 
ensuring that the system operates only in the first and third quadrants as 
shown in FIG. 5 and is important because operation in the second and 
fourth quadrants could cause the system to become unstable or yield 
undesirable results; the product u(k-1)B.sup.T PX.sup.e (k) is a signal 
indicating proper present actuator force direction if it is positive, and 
improper present actuator force direction if it is negative. (Note that in 
the case of a fully active suspension system, the calculated force at 
block 250 is of even greater importance, because, since active systems at 
times supply energy to the actuator, there is an even greater chance of 
system instability if operated in the second and fourth quadrants of FIG. 
5.) 
Block 255 compares .vertline..vertline.B.sup.T PX.sup.e 
(k).vertline..vertline. to .epsilon..sub.d. Block 256 sets u.sub.s to zero 
if .vertline..vertline.B.sup.T PX.sup.e (k).vertline..vertline. was less 
than or equal to .epsilon..sub.d at block 255. If 
.vertline..vertline.B.sup.T PX.sup.e (k).vertline..vertline. was not less 
than or equal to ed at block 255, then block 257 determines if 
.vertline..vertline.B.sup.T PX.sup.e (k).vertline..vertline. is between 
.epsilon..sub.d and .epsilon., if so, then block 258 computes u.sub.s as: 
EQU (B.sup.T PX.sup.e (k)-.vertline..vertline.B.sup.T PX.sup.e 
(k).vertline..vertline..epsilon..sub.d /B.sup.T PX.sup.e (k)) 
.rho./(.epsilon.-.epsilon..sub.d). 
If .vertline..vertline.B.sup.T PX.sup.e (k).vertline..vertline. was not 
between .epsilon..sub.d and .epsilon. at block 257, then block 259 sets 
u.sub.s to command maximum possible actuator force. Block 260 outputs the 
command u.sub.s and returns to block 243 to repeat the loop. 
Implementation of the control method and apparatus of this invention into a 
suspension system of the type described with reference to FIG. 1 results 
in a decrease in the magnitude of sprung mass displacement and velocity 
over the amount of sprung mass displacement and velocity in a passive 
suspension system. Sprung mass accelerations are also reduced. In the case 
of implementation of this invention into an active suspension, attitude 
control of the vehicle body is improved. The amount of improvement will 
vary from implementation to implementation. 
The control structure including the observer 195 shown in FIG. 4b 
represents the preferred implementation of this invention. This observer 
is also shown in related copending patent application Ser. No. 07/702,875. 
Referring to FIG. 4b, an estimated relative system state, y.sup.e (t), on 
line 190 is summed with the actual relative system state, y(t), on line 
184, to develop an error signal on line 188 as in FIG. 4a. As in the 
system of FIG. 4a, the error signal on line 188 is multiplied by a 
Luenberger matrix at block 192, and the result input into the alternative 
observer, represented by block 195. The nonlinear term of the model is 
computed at block 204 as set forth below. 
The observer 195 estimates the state of the quarter car suspension system 
according to the model: 
EQU X.sup.e' =AX.sup.e +Bu+L(y(t) -y(t).sub.e)+N.PHI.(y(t)-y.sup.e (t)), 
where the term, .PHI.(y(t)-y.sup.e (t)) (referred to below as 
.PHI.(.multidot.)), is a saturation function and provides a stable 
nonlinear element to the model that guarantees that state estimations 
progress in the direction of a stable sliding surface, y(t)-y.sup.e (t)=0, 
on an X, X' stability plot. 
To further clarify the nonlinear function, assume the worst case (normal 
operation) road disturbance and other uncertainty effects on the 
suspension system can be represented by a term Ed, where d=1 for the worst 
case. One skilled in the art can easily determine E. Since, for the worst 
case d=1, for any given normal driving condition, 
.vertline.d.vertline..ltoreq.1. If N is set equal to E.gamma., where 
.vertline..gamma..vertline..gtoreq.1, then a stable nonlinear function, 
.PHI.(y(t)-y.sup.e (t)), can be set up as follows: 
##EQU6## 
where .epsilon..sub.o defines an error limit around the sliding surface 
y(t)-y.sup.e (t)=0 within which the system is linearly stable and outside 
of which the system is non-linearly stable. To ensure nonlinear stability, 
all real parts of a function H.sub.1 (j.omega.) must lie to the right of 
-1/Gon a real/imaginary plot, where: 
EQU H.sub.1 (j.omega.)=C(j.omega.I-A+LC).sup.-1 N, and 
EQU G=(1+1/.gamma.)/.epsilon..sub.o. 
To ensure linear stability within the boundary layer defined by 
.vertline..vertline.y(t)-y.sup.e (t).vertline..vertline.&lt;.epsilon..sub.o, 
the following matrix must be stable: 
EQU [A-(L+N/.epsilon..sub.o)C]. 
To optimize the system, assume a high .gamma. and a low .epsilon..sub.o, 
and adjust .epsilon..sub.o until the system is stable. If the system 
cannot be stabilized, lower .gamma. and again adjust .epsilon..sub.o. In 
general, a smaller .epsilon..sub.o corresponds to a smaller allowable 
error. Repeat the adjustment of .gamma. and .epsilon..sub.o until an 
optimum stable system is found. It is preferable to find several stable 
combinations of .gamma. and .epsilon..sub.o and to pick the system which 
yields the smallest estimation errors. 
With the above information, one skilled in the art can easily implement the 
nonlinear term N.PHI.(.multidot.) to achieve a stable system. During 
normal driving conditions, the resulting control system is linearly stable 
and the estimated system state can converge to the actual system state 
(zero error condition). During driving conditions such as a wheel hitting 
a large pothole or a large rock, the control system is non-linearly stable 
and progresses to a state where it is linearly stable. 
The output of the observer 195, on line 198, is input into the modified 
Lyapunov controller 200. The modified Lyapunov controller 200 determines 
the desired damping command, u.sub.s, in response to the estimated state 
on line 198 as described above. 
The flow diagram of FIG. 6b represents one example of a computer 
implementation of the controller of FIG. 4b. Blocks 240 through 244 are as 
described above with reference to FIG. 6a. Block 300 compares 
y(k-1)-y.sup.e (k-1) to .epsilon..sub.o. If y(k-1)-y.sup.e (k-1) is 
greater than or equal to .epsilon..sub.o, then block 302 sets 
.PHI.(.multidot.)=1. If y(k-1)-y.sup.e (k-1) is less than .epsilon..sub.o, 
then block 304 compares y(k-1)-y.sup.e (k-1) to -.epsilon..sub.o. If 
y(k-1)-y.sup.e (k-1) is less than or equal to -.epsilon..sub.o, then block 
306 sets .PHI.(.multidot.) equal to -1. If y(k-1)-y.sup.e (k-1) is between 
-.epsilon..sub.o and .epsilon..sub.o, then block 308 sets 
.PHI.(.multidot.) equal to (y(k-1)-y.sup.e (k- 1))/.epsilon..sub.o. The 
Luenberger term is computed at block 309 and force, u(u.sub.s (k-1), 
X.sup.e (k-1)), is computed at block 310 as described above with reference 
to FIG. 6a. Block 312 computes X.sup.e (k), discretely, as follows: 
EQU X.sup.e (k)=A.sub.d X.sup.e (k-1)+B.sub.d u(k-1)+L.sub.d (y(k-1)-y.sup.e 
(k-1))+N.sub.d .PHI.(y(k-1)-y.sup.e (k-1)), 
where: 
##EQU7## 
The computer then performs the rest of the control routine as described 
with reference to FIG. 6a, starting at block 249. 
For best mode purposes, a system of integrating four quarter car 
semi-active suspension systems of this invention into one vehicle is set 
forth below. This integrated system is the subject of related copending 
patent application Ser. No. 07/702,874. 
When using this invention in a vehicle, it is important to note that the 
present state of each quarter car suspension system and the road input are 
not the only factors that operate on each suspension system. The suspended 
mass of a vehicle is a semi-rigid body and the motion of each portion of 
the suspended mass generally affects the other portions of the suspended 
mass. The semi-rigid body motions of primary concern in a vehicle are 
heave, pitch and roll. Heave can be adequately controlled by four quarter 
car controllers described above. However, for improved control of pitch 
and roll, it may be desirable to take into account the semi-rigid nature 
of the entire sprung mass of the vehicle. 
Referring to FIG. 7, the integrated semi-active suspension system includes 
four quarter car suspensions 180 including variable force actuators. 
Signals indicative of the relative system state (rattle space velocity or 
relative position between the sprung and unsprung masses) of each quarter 
car suspension are provided to the controller 231 through lines 230. 
Signals representative of forward acceleration and lateral acceleration 
are provided to the controller 231 through lines 224 and 226, 
respectively, from transducers in a package 220 located at the vehicle 
center of gravity. Alternatively, package 220 may be offset from the 
center of gravity of the vehicle with the offset taken into account to 
compute the forward and lateral acceleration of the vehicle. These 
computations are easily implemented by one skilled in the art. Although 
pitch and roll and yaw rate may be taken into consideration, they are not 
considered necessary because a significant portion of vehicle pitch and 
roll deviations result from forward and lateral accelerations of the 
vehicle body and yaw rate is not significantly affected in a semi-active 
suspension system. Therefore, for the sake of simplicity, it is preferable 
that only forward and lateral acceleration be taken into account. 
One alternative implementation for determining forward and lateral 
acceleration is to have signals indicative of steering wheel angle and 
vehicle speed on lines 222 and 235 from a rotary (RVDT) sensor (or 
equivalent) on the steering column and the vehicle speedometer signal (not 
shown) input into the controller 231. The controller 231 can determine 
forward acceleration through differentiation of the vehicle speed signal. 
For example, forward acceleration, A.sub.f (k), may be determined as 
follows: 
EQU A.sub.f (k)=(v(k)-v(k-2))/(2.DELTA..tau.), 
where v(k) is the current vehicle speed, v(k-2) is the vehicle speed two 
time events previously, and .DELTA..tau. is one time event. Lateral 
acceleration can be determined in the controller from the vehicle speed 
and steering wheel angle through the following model, easily implemented 
by one skilled in the art: 
EQU a.sub.y =v.sup.2 g.delta./(r.sub.s (gL+K.sub.us v.sup.2)) 
where a.sub.y is the lateral acceleration of the vehicle, v is the vehicle 
velocity, g is gravitational acceleration, .delta. is the steering wheel 
angular displacement, r.sub.s is the steering gear ratio, L is the wheel 
base, and K.sub.us is the under-steer coefficient. To reduce noise from 
the vehicle speed signal, v, the signal may be filtered through a low pass 
digital filter before the lateral acceleration is computed. 
In the controller 231, determinations of forward and lateral acceleration 
are used to determine a minimum damping command, correlating to minimum 
damping forces, for the four quarter car suspensions. The greater the 
forward and/or lateral accelerations, the greater the minimum damping 
command. The controller 231 also estimates a state and determines a 
damping command for each quarter car suspension system according to this 
invention. The computer selects between the minimum damping command and 
the individual quarter car damping command for each quarter car system and 
issues a damping command through line 228 corresponding to the command 
which requires greater damping. By controlling the minimum damping as 
described above, deviations in pitch and roll can be minimized, providing 
increased road stability to the vehicle. 
The controller circuitry 231 is shown in more detail in FIG. 8, which may 
be easily implemented by one skilled in the art as shown. The controller 
circuitry 231 includes two eight bit microprocessors 462 and 466 (68CH11s 
may be used for low cost), one computing the individual quarter car 
commands for two quarters of the vehicle, the other computing the 
individual quarter car commands for the other two quarters of the vehicle. 
In the illustration, microprocessor 462 computes the commands for the 
front two suspension and microprocessor 466 computes the commands for the 
rear two suspensions. Each microprocessor 462 and 466 runs the integration 
routine computing the minimum damping command. Dual port RAM 464 is used 
to exchange data between the two microprocessors. Each microprocessor 462 
and 466 is interfaced with a math co-processor chip (456 and 460) to speed 
the computing power of the circuitry. 
Each actuator 22a may contain three hall effect sensors which may be used 
to determine rattle space velocity and/or direction of rattle space 
movement. Block 472 represents the sensors in each quarter of the vehicle, 
and the signal are fed to speed pulse and direction circuitry that 
provides frequency and direction signals. A frequency signal is provided 
for each quarter car by combining the signals from the three hall effect 
sensors from the actuator in that quarter car suspension unit. The 
frequency of the resultant signal for each quarter car represents the 
magnitude of the rattle space velocity of that quarter car suspension and 
is coupled to the microprocessors 462 and 466 through UPP timer chip 468, 
through bus 467. 
The rattle space velocity magnitude signals are received by microprocessor 
462 from chip 468, and the rear velocity signals are provided to processor 
466 through dual port RAM 464. The rattle space velocity directions is 
determined in relation to the order of signals from the hall effect 
sensors in each actuator and are provided directly to the microprocessors 
462 and 466 through buses 463 and 465. 
Although the hall effect sensors may be preferable in certain sensors, they 
are not necessary. Signals on bus 474, representing the relative 
displacement of the sprung and unsprung masses in each suspension unit may 
be fed to the UPP timer chip, and related therethrough to microprocessor 
462, and through microprocessor 462 and dual access RAM 464 to 
microprocessor 466. Rattle space velocity and direction may be estimated 
from the relative displacement information using observer 194 or observer 
195 (FIGS. 4a and 4b). 
A steering wheel angle signal (line 222) is also fed to the UPP timer chip, 
which provides the information for the microprocessors 462 and 466. Sensor 
information such as a door open signal and lateral and longitudinal 
acceleration signals may be fed directly to microprocessor 462 through 
lines 229, 224 and 226. The vehicle velocity signal and break signal may 
be fed directly to microprocessor 466 through lines 484 and 486. 
With the information provided, microprocessor 462 computes the damping 
commands for the front two suspensions and feeds the commands to UPP chip 
468. Microprocessor 466 computes the damping commands for the rear two 
suspensions and feeds the commands to dual port RAM 464, where it is read 
by microprocessor 462 and fed to UPP chip 468. UPP chip 468 outputs pulse 
width modulated commands to each quarter car suspension through lines such 
as line 488, coupled to the PWM driver circuitry 452 for each quarter car 
suspension system. 
Microprocessors 462 and 466, in conjunction with math co-processors 456 and 
460, compute new individual quarter car commands every 2 ms and a new 
minimum damping command every 20 ms. 
If this invention is to be implemented into a fully active system, 
microprocessor 462 outputs force commands for the front suspension to D/A 
converter 454, which outputs a signal used to drive motor control 
circuitry, providing the desired force for the front two suspensions. 
Likewise, microprocessor 466 outputs force commands for the rear 
suspension to D/A converter 458, which outputs a signal used to drive 
motor control circuitry for the rear two suspensions. 
When this invention is implemented into an integrated vehicle system, 
various other factors should be taken into account. For example, when 
persons get into and out of the vehicle and when cargo is loaded to and 
unloaded from the vehicle, the sprung mass of the vehicle changes and the 
at-rest state of each quarter car suspension system changes (e.g., the 
distance between the sprung and unsprung masses when the vehicle is at 
rest changes). If only the relative velocity of the sprung and unsprung 
masses are measured, then the system automatically resets the at rest 
state with changes of vehicle load. If the relative position of each 
sprung and unsprung mass is measured, a line 229 can be implemented to 
receive a vehicle door signal indicating when a door has been opened and 
closed. An easy implementation for this line is to wire it into the dome 
light circuit in the vehicle. When the computer senses that a door has 
just been closed, it reinitializes the suspension system control, to set 
the new at-rest state of each quarter car suspension system as the 
reference state. A similar feature may also be implemented with a signal 
detecting opening and closing of a vehicle trunk, or cargo bed. 
Although the sprung mass of the vehicle changes as passengers and cargo of 
the vehicle change, the controller of this invention can robustly control 
the suspension system without changing the model parameters at every 
change in the sprung mass. However, if an LVDT position sensor is used to 
measure the relative distance between the sprung and unsprung mass 12 and 
24 (FIG. 1), then new at rest state can be used to determine the amount of 
mass in the vehicle, e.g., the greater the at rest distance between the 
sprung and unsprung masses, the smaller the sprung mass. The model 
parameters of matrices A and B can be adjusted accordingly. Although 
altering the matrices A and B may be desirable in certain implementations, 
it is not necessary. 
If the computer detects a failure of the suspension control, e.g., zero 
current on line I (see FIG. 3) when the damper is commanded to have full 
damping, then a signal is sent through line 234 to an instrument panel 
warning light (not shown) to notify the vehicle operator. 
Another optional feature that may be implemented with this invention is to 
command full damping at vehicle acceleration from a rest position to 
compensate for possible delays in receiving the speed signal that occur in 
some systems. This command can be triggered by change in throttle 
position, gear shift to drive, vehicle door closing, or any parameter 
which indicates the vehicle might launch. Once the speed signal is sensed, 
damping is controlled as described above. A signal from the break pedal 
can be used to indicate vehicle breaking without computational delays. 
The flow diagram in FIG. 9 is one example of a computer implementation of 
the vehicle integration routine. The routine starts at block 270 and 
initializes at block 272, including determining the at rest state of each 
quarter car suspension. Sensor data is received at block 274 and block 276 
determines if the system needs to be reinitialized, e.g., if a door was 
just opened or closed. At block 278, each of the quarter car commands, 
u.sub.s, is determined as described above, e.g., with reference to FIGS. 
6a and/or 6b. At block 280, forward and lateral acceleration are computed 
if necessary, e.g., if the center of gravity package is offset or if the 
vehicle speed and steering angle are used to determine forward and lateral 
acceleration. 
Blocks 282 and 284 determine if forward or lateral acceleration is above a 
first threshold, e.g., 0.5G, if so, the minimum damping command is set at 
block 286 to 100% of the maximum damping available. Blocks 288 and 292 
compare forward and lateral acceleration to a second threshold, which is 
less than the first threshold, e.g., 0.3G. If the forward or lateral 
acceleration is greater than the second threshold, but wasn't greater than 
the first threshold, then the minimum damping is set at block 290 to, for 
example, 50% of the maximum available damping. If neither the forward nor 
lateral accelerations is greater than the first or second thresholds, then 
the damping command for each quarter car 180 is set, at block 294, equal 
to the command u.sub.s determined for that quarter car in accordance with 
this invention. 
With the above implementation, this invention is used to improve the 
driving performance of a vehicle based, not only on the individual state 
of each quarter car suspension, but on the effect of the whole suspended 
body of the vehicle. 
The above descriptions are example implementations of this invention using 
the electromechanical machine of actuator 22a. This invention is not 
limited to the use of electromechanical actuators but may be used to 
control any variable force suspension system which is controllable between 
at least two force states, as described above. A sample alternative 
actuator is a hydraulic shock with an adjustable flow control valve. For 
purposes of this discussion, hydraulic shock absorbers with adjustable 
flow control valves can be classified into two categories: continuously 
variable hydraulic shock absorbers and shock absorbers variable between 
discrete states, e.g., minimum and maximum damping. This invention can be 
successfully implemented with either type of hydraulic shock absorber, but 
use with continuously variable shock absorbers is preferred. 
An example of a continuously variable hydraulic shock absorber is 
designated by reference numeral 22b in FIG. 2b. Shock absorber 22b is 
described in detail in U.S. Pat. No. 4,902,034 to Maguran et al., assigned 
to the assignee of this invention, and hereby incorporated into this 
specification by reference. Certain portions of Maguran et al. are also 
set forth below. 
Shock absorber 22b comprises a first shock member 70 comprising a rod 72 
with an enlarged diameter piston 90 within a cylinder tube 76 which is 
part of a shock member 88. Piston 90 is sealingly but slidably engaged 
with the inner surface of cylinder tube 76 so as to divide it into a first 
pumping chamber 84 above piston 90 and a second pumping chamber 94 below 
piston 90. Chambers 84 and 94 are filled with an incompressible fluid; and 
piston 90 includes one way check valves 92 which allow fluid flow from 
chamber 94 upward to chamber 84 as piston 90 moves downward but no flow 
from chamber 84 downward to chamber 94 as piston 90 moves upward. 
Shock member 88 further comprises a reservoir tube 74 which surrounds 
cylinder tube 76 coaxially and defines, with cylinder tube 76, a reservoir 
chamber 86, which is partially filled with the incompressible fluid. 
Reservoir chamber 86 extends across the bottom of the unit between a lower 
end cap 100 and which closes reservoir tube 74 and a base valve assembly 
98 which closes cylinder tube 76 and includes a one way check valve 96 
which allows fluid flow from reservoir chamber 86 into chamber 94 but not 
vice versa. An electrically controlled valve 80 allows and controls fluid 
flow from chamber 84 through passage 78, valve 80 and a passage 82 to 
reservoir chamber 86. 
Shock member 70 is attached either to a rubber bushing 18 (FIG. 1) or to 
the sprung mass 12. Shook member 88 is attached to the unsprung mass 24. 
A signal on line 81, either a direct current signal or a pulsed signal 
modulated to affect an average current, controls valve 80, which controls 
the fluid flow, thereby controlling force on the suspension system exerted 
by the shock absorber. A detailed description of the valve 80 is set forth 
in U.S. Pat. No. 4,902,034 and will not be set forth here. The valve 80 
controls fluid flow so that the damping force on the suspension system is 
proportional to the current on line 81, and independent of rattle space 
velocity. This allows for direct control of damping force. If it is 
desired that the suspension system have damping force proportional to 
rattle space velocity, the signal on line 81 may be controlled to vary 
with rattle space velocity so that damping force increases with rattle 
space velocity in the manner of a conventional passive shock absorber. 
Alternatively, valve 80 may be replaced by an adjustable valve in which 
fluid back-pressure is dependent upon rattle space velocity. 
Actuator 22b may be easily implemented with the control schemes of this 
invention shown in FIGS. 4a and 4b. With a hydraulic damper such as 
actuator 22b, inertia can be ignored in the system model. In a model for a 
hydraulic damper, elements of matrix A are as follows: a.sub.1 =-k.sub.s 
/M.sub.s, a.sub.2 =-b.sub.p /M.sub.s, a.sub.3 =k.sub.s /M.sub.s, a.sub.4 
=b.sub.p /M.sub.s, a.sub.5 =ks/M.sub.u, a.sub.6 =b.sub.p /M.sub.u, a.sub.7 
=-(k.sub.s +k.sub.u)/M.sub.u, and a.sub.8 =-b.sub.p /M.sub.u, where 
b.sub.p is the passive damping force on the system, e.g., when the flow 
valves are completely open. The elements of matrix B are as follows: 
b.sub.1 =1/M.sub.s and b.sub.2 =1/M.sub.u. The matrix C is as described 
above. 
If the valve 80 controls damping force independent of rattle space 
velocity, then the damping force control signal u.sub.s as controlled by 
block 200 (FIG. 4) is: 
##EQU8## 
where .rho.' is the maximum damping force, regardless of rattle space 
velocity. In actuality, when the valve 80 is wide open (u.sub.s =0), there 
may be some natural damping caused by the fluid flow which is dependent 
upon rattle space velocity. This damping, however, may be slight and 
nevertheless converges to zero with rattle space velocity. This damping 
may be included in the model, i.e., as b.sub.p or part of b.sub.p. 
If valve 80 is the type in which fluid pressure is dependent upon rattle 
space velocity, then the damping control signal, u.sub.s, and damping 
force, u, follow the same pattern as for actuator 22a (FIG. 2a). 
Implementation of actuator 22b into an integrated vehicle control system is 
similar to the implementation described above with reference to FIG. 7. 
With the hydraulic shock absorber, the preferred implementation of a means 
to measure the relative system state for each quarter car suspension 
system is to use LVDTs because the rotary signals of the electromechanical 
actuator 22a on lines A, B, and C (FIG. 3) are not as readily available. 
Hydraulic dampers which are controllable between only discrete states, 
e.g., between minimum damping and maximum damping, are well known and 
readily available to those skilled in the art. Hydraulic dampers with only 
discrete states exert a damping force in relation to rattle space 
velocity. The higher the rattle space velocity, the greater the damping 
force. Adjustment of the flow control valve between alternate positions 
alters the damping between lower and higher values for a given rattle 
space velocity. 
In implementing this invention with such hydraulic dampers, a slight 
modification to the controller 200 (FIGS. 4a and 4b) needs to be made. 
FIG. 10 shows a graph of typical the minimum and maximum damping force 
characteristics of a two state hydraulic shock absorber, line MIN 
representing the minimum damping force and line MAX representing the 
maximum damping force. Dotted line 320 represents a threshold force, above 
which the damping command signals maximum damping and below which the 
damping command signals minimum damping. 
Implementation to the controller can be easily understood with reference to 
FIG. 11. Threshold levels T and -T, corresponding to the line 320 of FIG. 
10 and which may be dependent upon rattle space velocity, are located 
between .epsilon..sub.d and .epsilon., and between -.epsilon. and 
-.epsilon..sub.d, respectively. When B.sup.T PX.sup.e (k) is between -T 
and T, minimum damping is commanded. When B.sup.T PX.sup.e (k) is greater 
than T or less than -T, maximum damping is commanded. The two state 
hydraulic shock absorbers can be implemented with this invention into an 
integrated vehicle system of the type described with reference to FIG. 7 
with the above modifications. Three or more state hydraulic shock 
absorbers can be implemented with little modifications, to provide steps 
between minimum and maximum damping. 
The circuit diagrams of FIGS. 12 and 13 illustrate one example of hardware 
useful for implementation of this invention into a quarter car active 
suspension. The functioning of this circuitry is explained in detail in 
U.S. Pat. No. 4,544,868, to Murty, which is assigned to the assignee of 
this invention and incorporated into this specification by reference. 
The actuator 22 is, in this case, a three phase brushless DC motor 
comprising coils 340, 358, and 360 with lines A, B, and C, permanent 
magnet rotor 364 and Hall effect sensors 344, 362, and 366. The Hall 
effect sensors are coupled to the vehicle positive voltage supply, 
V.sub.cc, line 320, through pull-up resistors 324, 326, and 328. Signals 
from the Hall effect sensors 344, 362, and 366 on lines 336, 338, and 330 
are provided to the A.sub.0, A.sub.1, and A.sub.2 address inputs of ROM 
334. 
ROM 334 controls the standard transistor bridge driver circuits 350, which 
drive the transistor bridge circuit comprising transistors 372, 373, 374, 
375, 376, and 377, through lines 348, 349, 353, 354, 356, and 352, 
respectively. The ROM outputs D.sub.0 through D.sub.5 contain the 
brushless motor driving commands stored in memory addresses accessed 
through the address inputs A.sub.0 through A.sub.4. The address inputs 
A.sub.0 -A.sub.4 selectively control the energizing of coils 340, 358, and 
360 of the actuator by selectively engaging bridge transistors 373-377, 
which are connected to the positive side of the vehicle battery 368 and 
coupled to the negative side of the battery 368 through current sensing 
resistor 394. The address inputs A.sub.0 -A.sub.2 indicate the position of 
the rotor 364. Address input A.sub.3, connected to line V.sub.d, controls 
the direction of rotational force desired of the actuator 22. Through the 
signals on address inputs A.sub.0 -A.sub.3, it is known which coils are 
desired to be energized. Line 322, connected to address input A.sub.4, 
contains a pulse width modulated signal that determines when power is to 
be applied to actuator 22. Controlling the duty cycle of the signal on 
line 322 controls the amount of power to be applied to actuator 22. 
Actuator 22 is also a generator which generates power when it is rotated 
but not energized by a command on line 322. When the relative movements of 
the sprung and unsprung masses cause rotational movement of rotor 364, but 
line 322 does not signal for power to be input to the actuator 22, power 
generated through coils 340, 358 and 360 is rectified by diodes 370, 371, 
378, 392, 396, and 398, and charges the vehicle battery 368. 
The PWM circuit 332, shown in detail in FIG. 13, provides the signal on 
line 322 for address input A.sub.4 and is described in detail in U.S. Pat. 
No. 4,544,868. Referring to FIG. 13, a force magnitude command, in terms 
of a voltage signal, is provided on line 410. The signal on line 410 is 
compared to the signal indicative of actuator force on line 346. The 
signal on line 346 acts as feedback indicative of actual actuator force by 
measuring the current, i.sub.m, through resistor 394, which controls the 
voltage on line 346 in proportion to the current i.sub.m. The signal on 
line 346, coupled to the operational amplifier 424 through resistor 430, 
is compared to the signal on line 410. The rest of the PWM circuit 
comprising resistors 412, 414, 416, 420, 432, 438 and 442, capacitor 444, 
diode 440, and operational amplifier 428 provide a PWM signal on line 322 
corresponding to the error between actual actuator force and the desired 
actuator force on line 410. 
In implementation of this invention with the circuitry of FIGS. 11 and 12, 
a microprocessor based controller 321 computes the suspension system state 
as described above with reference to FIGS. 4a and/or FIG. 4b. The 
controller then develops an actuator force command in accordance with this 
invention and applies that command to the actuator control circuitry 
through lines V.sub.d and 410. The signal on line 410 is a voltage signal 
developed by the microcomputer, interfaced through a D/A converter and is 
indicative of the magnitude of the desired actuator force. The signal on 
line V.sub.d is either a one or a zero depending on the desired direction 
of the force to be applied by the actuator 22. For example, the signal on 
line V.sub.d may be zero if u.sub.s /.vertline..vertline.u.sub.s 
.vertline..vertline.=1 and one if u.sub.s /.vertline..vertline.u.sub.s 
.vertline..vertline.=-1. Using the above description, those skilled in the 
art can easily implement this invention to control an active quarter car 
suspension. 
As can be seen through the examples set forth above, the apparatus and 
method of this invention eliminate system chatter and nullify the affect 
of system system noise and state estimation error while providing a 
control responsive to the entire system state, which reduces overall 
sprung mass displacement and improves vehicle attitude control. As is 
apparent to those skilled in the art, the implementations set forth above 
are illustrative examples and are not limiting on this invention, the 
scope of which is set forth below.