Brake control apparatus for automotive vehicle that includes feedfoward/feedback mixing device

In an electric control apparatus for a hydraulic brake control system of a vehicle, a feedback control portion is provided to produce a feedback control pulse signal indicative of a difference between a target slip ratio and an actual slip ratio. A feedforward control portion is provided to successively convert the target slip ratio in relation to a required braking force, a hydraulic braking pressure and an amount of hydraulic braking fluid, in sequence, and to convert the amount of hydraulic braking fluid into a feedforward control pulse signal. A pulse mixing circuit is connected to control portions to mix the control pulse signals for producing a mixed control pulse signal as a distinct control pulse signal. A driving circuit is connected to the pulse mixing circuit to control a hydraulic braking pressure applied to each wheel of the vehicle in accordance with the control pulse signal, regardless of the extent to which a brake pedal of the vehicle is depressed.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a brake control apparatus for automotive 
vehicles for normalizing abnormal behavior of the vehicle such as spin, 
drift out or the like. 
2. Description of the Prior Art 
In a conventional brake control apparatus of this kind as disclosed in 
Japanese Patent Laid-open Publication No. 4-257756, a target slip ratio of 
road wheels is determined in accordance with movement condition of the 
vehicle, and an actual slip ratio of the road wheel is detected to produce 
a feedback control signal In accordance with a difference between the 
target slip ratio and the actual slip ratio. The feedback control signal 
is applied to a hydraulic brake control system for control of hydraulic 
braking fluid supplied to each slave cylinder of the road wheels. Thus, 
the hydraulic brake control system is controlled by the feedback control 
signal in such a manner that the actual slip ratio of the road wheel 
becomes identical with the target slip ratio. 
In the conventional brake control apparatus, however, a quick control 
response of the hydraulic brake control system may not be effected under 
such a feedback control as described above, and the hydraulic brake 
control system may not be controlled in accordance with road surface 
conditions. For this reason, it is unable to quickly normalize abnormal 
behavior of the vehicle in a high precision. 
SUMMARY OF THE INVENTION 
It is, therefore, a primary object of the present invention to provide a 
brake control apparatus for automotive vehicles in which a feedforward 
control is adapted to quickly normalize abnormal behavior of the vehicle 
in a high precision. 
According to the present invention, the primary object is accomplished by 
providing an electric control apparatus for a hydraulic brake control 
system of an automotive vehicle, comprising determination means for 
determining a target slip ratio of each road wheel of the vehicle in 
accordance with a movement condition of the vehicle, detection means for 
detecting an actual slip ratio of each road wheel of the vehicle, and 
feedback control means for producing a feedback control signal indicative 
of a difference between the target slip ratio and the actual slip ratio 
and for controlling the hydraulic brake control system in response to the 
feedback control signal so that the actual slip ratio becomes identical 
with the target slip ratio, wherein the electric control apparatus further 
comprises feedforward control means for producing a feedforward control 
signal in accordance with the target slip ratio and mixing means for 
mixing the feedforward control signal with the feedback control signal and 
for controlling the hydraulic brake control system in accordance with the 
mixed control signal. 
According to an aspect of the present invention, the electric control 
apparatus further comprises means for interpolating the feedback control 
signal in accordance with a road surface condition and means for 
interpolating the feedforward control signal in accordance with the road 
surface condition. 
According to another aspect of the present invention, the electric control 
apparatus further comprises means for decreasing a gain of the feedback 
control signal when the target slip ratio or the actual slip ratio is in a 
low value and for increasing the gain of the feedback control signal when 
the target slip ratio or the actual slip ratio is in a high value. 
According to a further aspect of the present invention, the electric 
control apparatus further comprises means for effecting a feedforward 
control of the hydraulic brake control system under control of the 
feedforward control means when the target slip ratio or the actual slip 
ratio is in a low value. 
In a practical embodiment of the present invention, it is preferable that 
the feedback control means includes a pulse generator for producing a 
pulse signal the pulse interval of which is reduced In accordance with an 
increase of the feedback control amount, while the feedforward control 
means includes a pulse converter for producing a pulse signal the pulse 
interval of which is reduced in accordance with an increase of variation 
speed of the feedforward amount. In this arrangement, the production 
timing of the pulse signal at the pulse generator is varied by the pulse 
signal from the pulse converter in such a manner that the production 
timing of the former pulse signal does not become identical with the 
production timing of the latter pulse signal.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
In FIG. 1 of the drawings, there are schematically illustrated a hydraulic 
brake control system of an automotive vehicle and a block diagram of an 
electric control apparatus for the hydraulic brake control system. The 
hydraulic brake control system includes a master cylinder 12 arranged to 
be operated by depression of a brake pedal 11. The master cylinder 12 has 
a first port connected to slave cylinders 32, 42 of left and right front 
road wheels through solenoid valves 31, 41 and a second port connected to 
slave cylinders 52, 62 of left and right rear road wheels through a 
proportioning valve 13 and solenoid valves 51, 61. The hydraulic brake 
control system further includes a hydraulic pump 14 arranged to pump out 
hydraulic fluid from a fluid reservoir 15 and to supply the hydraulic 
fluid under pressure to a high pressure line L1. The high pressure line L1 
is provided with an accumulator 16 for accumulating the hydraulic fluid 
under pressure. Disposed between the high pressure line L1 and a low 
pressure line L2 in connection to the fluid reservoir 15 are braking 
pressure control devices 30, 40, 50, 60 for the front and rear road 
wheels. 
The braking pressure control device 30 for the left front road wheel 
includes the solenoid valve 31, the slave cylinder 32, a pressure 
increasing solenoid valve 33 and a pressure reducing solenoid valve 34. 
The pressure increasing solenoid valve 33 is arranged to communicate the 
high pressure line L1 to the slave cylinder 32 when it is retained in a 
first position shown in the figure in a condition where the solenoid valve 
31 has been switched over to a second position from a first position shown 
in the figure. When switched over to a second position from the first 
position, the solenoid valve 33 interrupts the fluid communication between 
the high pressure line L1 and the slave cylinder 32. The pressure reducing 
solenoid valve 34 is arranged to communicate the slave cylinder 32 with 
the low pressure line L2 when it is switched over to a second position 
from a first position shown in the figure in a condition where the 
solenoid valves 31, 33 have been switched over to their second positions. 
When retained in the first position, the solenoid valve 34 interrupts the 
fluid communication between the slave cylinder 32 and the low pressure 
line L2. 
The braking pressure control device 40 for the right front road wheel 
includes the solenoid valve 41, the slave cylinder 42, a pressure 
increasing solenoid valve 43 and a pressure reducing solenoid valve 44 
which are arranged in the same manner as in the braking pressure control 
device 30. Similarly, the braking pressure control device 50 for the left 
rear road wheel includes the solenoid valve 51, the slave cylinder 52, a 
pressure increasing solenoid valve 53 and a pressure reducing solenoid 
valve 54 which are arranged in the same manner as in the braking pressure 
control device 30. The braking pressure control device 60 for the right 
rear road wheel includes the solenoid valve 61, the slave cylinder 62, a 
pressure increasing solenoid valve 63 and a pressure reducing solenoid 
valve 64 which are arranged in the same manner as in the braking pressure 
control device 30. In this embodiment, all the solenoid valves are 
retained in their first positions when they are deenergized and switched 
over from their first positions to their second positions when they are 
energized. 
The electric control apparatus for control of the solenoid valves includes 
a sensor group 71 composed of a plurality of sensors respectively for 
detecting a steering angle .THETA.h of the vehicle steering wheel, a 
longitudinal velocity Ux, a lateral velocity Uy, a longitudinal 
acceleration Gx, a lateral acceleration Gy, a yaw rate Yr, each rotational 
angular speed .omega.fl, .omega.fr, .omega.rl, .omega.rr of the front and 
rear road wheels, a throttle opening degree .THETA.s and operation of the 
brake pedal Br. The sensor group 71 is connected to a condition amount 
calculation portion 72 which is designed to produce an output signal 
indicative of a movement condition amount detected by the sensors and to 
estimate each actual steering angle Stafl, Stafr of the front road wheels, 
a moving speed Us, each wheel speed Usfl, Usfr, Usrl, Usrr of the front 
and rear road wheels, each slip angle .beta.fl, .beta.fr, .beta.rl, 
.beta.rr of the front and rear road wheels, a slip angle .beta.g and a 
road surface frictional coefficient .mu. on a basis of the detected 
movement condition amount for producing an output signal indicative of the 
estimated condition amount. 
The condition amount calculation portion 72 is connected to a target slip 
ratio calculation portion 73, an abnormal behavior detection portion 74 
and an actual slip ratio calculation portion 75. The target slip ratio 
calculation portion 73 is designed to determine each target slip ratio 
Sfl*, Sfr*. Srl*, Srr* based upon the steering angle .THETA.h, 
longitudinal acceleration Gx, lateral acceleration Gy, throttle opening 
degree .THETA.s, operation of the brake pedal Br, each slip angle 
.beta.fl, .beta.fr, .beta.rl, .beta.rr of the front and rear road wheels, 
and slip angle .beta.g. In this embodiment, the respective target slip 
ratios Sfl*, Sfr*, Srl* Srr* of the front and rear road wheels are defined 
to normalize abnormal behavior of the vehicle and stabilize the travel of 
the vehicle. The calculation method of the target slip ratios Sfl*, Sfr*, 
Srl*, Srr* is described in detail in Japanese Patent Laid-open Publication 
4-257756 discussed in the introductory portion. The abnormal behavior 
detection portion 74 is designed to estimate behavior of the vehicle (a 
synthetic movement condition of the vehicle) based upon the detection 
signals applied thereto from the condition amount calculation portion 72 
thereby to produce an abnormal signal in the occurrence of abnormal 
movement of the vehicle. The actual slip ratio calculation portion 75 is 
designed to execute calculation of the following equations (1) for 
calculating each actual slip ratio Sfl, Sfr, Srl, Srr of the road wheels 
based upon each rotational angular speed .omega.fl, .omega.fr, .omega.rl, 
.omega.rr of the front and rear road wheels, each speed Usfl, Usfr, Usrl, 
Usrr of the front and rear road wheels and each load radius R (a fixed 
value) applied from the condition amount calculation portion 72 
EQU Sfl=(Usfl-R.multidot..omega.fl)/Usfl 
EQU Sfr=(Usfr-R.multidot..omega.fr)/Usfr 
EQU Srl=(Usrl-R.multidot..omega.rl)/Usrl 
EQU Srr=(Usrr-R.multidot..omega.rr)/Usrr (1) 
Electric signals respectively indicative of the target slip ratios Sfl*, 
Sfr*, Srl*, Srr*, abnormal behavior of the vehicle and the actual slip 
ratios Sfl, Sfr, Srl, Srr are applied to the slip ratio control portion 
100. 
When applied with the electric signal indicative of the abnormal behavior 
of the vehicle, the slip ratio control portion 100 acts to control the 
respective solenoid valves of the brake control devices 30, 40, 50, 60 in 
accordance with the actual slip ratios Sfl, Sfr, Srl, Srr and target slip 
ratios Sfl*, Sfr*, Srl*, Srr* in such a manner that the actual slip ratios 
Sfl, Sfr, Srl, Srr become identical with the target slip ratios Sfl*, 
Sfr*, Srl*, Srr*. As shown in FIG. 2, the target slip ratio control 
portion 100 includes a feedback control portion 100A, a feedforward 
control portion 100B and an output portion 100C which are provided for 
each road wheel of the vehicle. Since the feedback control portion 100A, 
feedfoward portion 100B and output portion 100C for each road wheel of the 
vehicle are substantially the same, only the brake control of the left 
front wheel will be described as an example hereinafter, and the target 
slip ratio Sfl* and actual slip ratio Sfl are represented as slip ratios 
S* and S. 
The feedback control portion 100A includes a subtracter 101 for calculating 
a difference between the target slip ratio S* and actual slip ratio S. The 
subtracter 101 is connected to a differential control term calculator 102, 
a proportional control term calculator 103 and an integral control term 
calculator 104 which are connected in parallel to one another for 
realizing a well-known PID feedback control. The calculators 102, 103 and 
104 are arranged to execute calculation of the following equations (2) for 
producing output signals respectively indicative of calculation results 
CALd, CALp, CALi. 
EQU CALd=Kd.multidot.d(S*-S)/dt 
EQU CALp=Kp.multidot.(S*-S) 
EQU CALi=Ki.multidot..intg.(S*-S)dt (2) 
where the coefficients Kd, Kp, Ki each are a predetermined constant. 
The output signals indicative of calculation results CALd, CALp, CALi are 
applied to an adder 105 which acts to calculate a sum of the calculation 
results CALd, CALp, CALi and to apply the calculated sum as a feedback 
control signal Cfb to an interval time converter 106. The interval time 
converter 106 has a characteristic table shown in FIG. 3 and acts to 
convert the feedback control signal Cfb into an interval signal Tfb 
indicative of a pulse duration (a time interval) and to apply the interval 
signal Tfb to a pulse generator 107. The pulse generator 107 includes a 
counter, a comparator and a one-shot circuit which are arranged to produce 
a control pulse signal P1 of a predetermined pulse width at each time 
interval represented by the interval signal Tfb. If the interval signal 
Tfb is positive as shown in FIG. 4, a positive control pulse signal P1 of 
the predetermined width is produced by the comparator and one-shot circuit 
when a time defined by the interval signal Tfb has been measured by the 
counter. If the interval signal Tfb is negative, a negative pulse signal 
P1 of the predetermined width is produced by the comparator and one-shot 
circuit when a time defined by the interval signal Tfb has been measured 
by the counter. Thus, the feedback control portion 100A produces a 
feedback control pulse signal P1 of the predetermined width the time 
interval of which is inversely proportional to an absolute value of a 
difference S*-S between the target slip ratio S* and actual slip ratio S 
and the sign of which corresponds with a positive or negative sign of the 
difference S*-S. 
As shown in FIG. 2, the feedforward control portion 100B has a braking 
force calculation circuit 111 which is applied with electric signals 
respectively indicative of the target slip ratio S*, the road surface 
coefficient .mu., the tire slip angle .beta. identical with the foregoing 
slip angle .beta.fl and a contact load Fz for determining a braking force 
Fx necessary for the left front road wheel. The braking force calculation 
circuit 111 includes a calculator and a four dimensional table 
representing a relationship of variables S*, .mu..multidot.Fz, .mu., 
.beta., Fx as shown in FIG. 5(A) or 5(B). The braking force calculation 
circuit 111 calculates a multiplied value .mu..multidot.Fz of the road 
surface frictional coefficient .mu. and the contact load Fz and refers to 
the four dimensional table to calculate a braking force Fx based upon the 
multiplied value .mu..multidot.Fz, target slip ratio S* and tire slip 
angle .beta.. The braking force calculation circuit 111 further 
interpolates the braking force to determine a final braking force Fx. 
Although in this embodiment the four dimensional table has been adapted to 
determine the braking force Fx, a neural network calculation may be 
adapted to determine the braking force Fx on a basis of the variables S*, 
.mu..multidot.Fz, .mu. and .beta.. 
A subtracter 112 is connected to the braking force calculation circuit 111 
to be applied with an electric signal indicative of the braking force Fx, 
and a loss factor calculator 113 is connected to the condition amount 
calculation portion 72 to be applied with an electric signal indicative of 
the rotation angle speed .omega. identical with the foregoing wheel 
rotation angle speed .omega.fl. The loss factor calculator 113 is arranged 
to execute calculation of the following equation (3) for calculating a 
loss factor .DELTA.Fx caused by a rotational moment of the road wheels. 
EQU .DELTA.Fx=(I/R).multidot.d.omega./dt (3) 
where I is a rotational moment of inertia, and R is a dynamic loaded 
radius. In this instance, the rotational moment of inertia I and dynamic 
loaded radius R each are preliminarily determined as a constant. 
When applied with electric signals respectively indicative of the braking 
force Fx and the loss factor .DELTA.Fx, the subtracter 112 subtracts the 
loss factor .DELTA.Fx from the braking force Fx. A first converter 114 is 
connected to the subtracter 112 to be applied with an electric signal 
indicative of the braking force Fx compensated by the subtraction. The 
first converter 114 is designed to multiply the braking force Fx by a 
coefficient Kfp for calculation of a required hydraulic braking pressure 
Pb, the coefficient representing a ratio of a hydraulic braking pressure 
relative to a braking force. A second converter 115 is connected to the 
first converter 114 to be applied with an electric signal indicative of 
the required hydraulic braking pressure Pb. The second converter 115 has a 
table representing a relationship between the required hydraulic braking 
pressure Pb and an amount of hydraulic fluid V necessary for effecting the 
required hydraulic braking pressure Pb. (see FIG. 6) Based on the table of 
FIG. 6, the second converter 115 calculates an amount of hydraulic fluid V 
necessary for the required hydraulic braking pressure Pb. A pulse 
converter 116 is connected to the second converter 115 to be applied with 
an electric signal indicative of the calculated amount of hydraulic fluid 
V. The pulse converter 116 includes a comparator and a pulse generator. As 
shown in FIG. 7, the pulse generator of the pulse converter 116 produces a 
feedfoward control pulse signal P2 of a predetermined width when the 
comparator detected the fact that the calculated amount of hydraulic fluid 
V exceeded reference values V1 and V2. In this instance, the pulse 
generator produces a positive control pulse signal P2 therefrom when the 
amount of hydraulic fluid is increased and produces a negative control 
pulse signal P2 therefrom when the amount of hydraulic fluid is decreased. 
Although in FIG. 7 only the two reference values V1 and V2 have been 
adapted, a number of reference values are adapted in actual practice of 
the present invention. 
The output portion 100c includes a pulse mixing circuit 121 arranged to be 
applied with the feedback control pulse signal P1 from the feedback 
control portion 100A and the feedforward control pulse signal P2 from the 
feedforward control portion 100B. The pulse mixing circuit 121 is designed 
to logically mix the control pulse signals P1 and P2 for producing a 
control pulse signal P3 as follows: 
1) When applied with either one of the control pulse signals P1 and P2, the 
pulse mixing circuit 121 produces the applied control pulse signal as the 
control pulse signal P3 at times t1, t4 shown in FIG. 8. 
2) When applied with both the control pulse signals P1 and P2 at an 
identical sign, the pulse mixing circuit 121 produces a sum of the control 
pulse signals P1, P2 as the control pulse signal P3 at times t2, t5 shown 
in FIG. 8. 
3) When applied with both the control pulse signals P1 and P2 at a 
different sign, the pulse mixing circuit 121 produces a difference of the 
control pulse signals P1, P2 as the control pulse signal P3 at times t3, 
t6 shown in FIG. 8. 
The pulse mixing circuit 121 is connected to a driving circuit 122 which is 
arranged to energize the solenoid valves 31 in response to an electric 
signal indicative of an abnormal behavior of the vehicle applied from the 
abnormal behavior detection portion 74 and to energize or deenergize the 
solenoid valves 33, 34 when applied with the control pulse signal P3 in a 
condition where the solenoid valve 31 is being energized. If the control 
pulse signal P3 does not occur in a condition where the solenoid valve 31 
is being energized, the driving circuit 122 energizes the solenoid valve 
33 to switch over the same from the first position to the second position 
and deenergizes the solenoid valve 34 to retain the same in the first 
position. When applied with the positive control pulse signal P3 from the 
pulse mixing circuit 121, the driving circuit 122 deenergizes both the 
solenoid valves 33, 34 to retain them in their first positions. When 
applied with the negative control pulse signal P3, the driving circuit 122 
energizes both the solenoid valves 33, 34 to switch over them from their 
first positions to their second positions. If the signal indicative of 
abnormal behavior of the vehicle does not occur, the driving circuit 122 
deenergizes all the solenoid valves 31, 33, 34 to retain them in their 
first positions as shown in the figure. 
Hereinafter, operation of the embodiment will be described in detail. 
Assuming that the brake pedal 11 has been depressed by a driver during 
travel of the vehicle, the master cylinder 12 is operated to produce 
hydraulic braking pressure. If in this instance the behavior of the 
vehicle is normal, all the solenoid valves are retained in their first 
positions as shown in the figure. Thus, the hydraulic braking pressure is 
applied to the slave cylinders 32, 42 through the solenoid valves 31, 41 
and applied to the slave cylinders 52, 62 through the proportioning valve 
14 and solenoid valves 51, 61. As a result, the road wheels are applied 
with a braking force in accordance with depression of the brake pedal to 
brake the vehicle. 
In the occurrence of abnormal behavior of the vehicle, the abnormal 
behavior detection portion 74 detects the abnormal behavior of the vehicle 
and applies an electric abnormal signal indicative of the abnormal 
behavior to the slip ratio control portion 100. In the slip ratio control 
portion 100, the driving circuit 122 energizes the solenoid valves 31, 41, 
51, 61 in response to the abnormal signal to switch over them from their 
first positions to their second positions. Thus, the slave cylinders 32, 
42, 52, 62 are disconnected from the master cylinder 12 and applied with 
hydraulic fluid under pressures from the high pressure line L1 under 
control of the solenoid valves 33, 34; 43, 44; 53, 54; 63, 64. 
Under such a condition as described above, the slip ratio control portion 
100 is applied with electric signals respectively indicative of a target 
slip ratio S* and actual slip ratio S from the target slip ratio 
calculation portion 73 and actual slip ratio calculation portion 75. In 
this instance, the slip ratio control portion 100 applies a feedback 
control pulse signal P1 indicative of a difference S* -S of the slip 
ratios S* and S as a control pulse signal P3 to the driving circuit 122 
through the pulse mixing circuit 121. If the difference S* -S is positive, 
the control pulse signal P3 is applied as a plurality of positive pulses 
of the predetermined width, and each interval time (duration) of the 
positive pulses becomes short in accordance with increase of an absolute 
value of the difference S* -S. Thus, the driving circuit 122 acts to 
retain the solenoid valves 33, 34 in their first positions in the 
occurrence of the positive control pulse signal P3. 
If there is not any positive control pulse signal P3, the driving circuit 
122 acts to switch over the solenoid valve 33 from the first position to 
the second position and to retain the solenoid valve 34 in the first 
position. This causes the hydraulic braking pressure in the slave cylinder 
32 to increase in proportion to the absolute value of the difference S* 
-S. If the difference S* -S is negative, the control pulse signal P3 is 
applied as a plurality of negative pulses of the predetermined width, and 
each interval time (duration) of the negative pulses becomes short in 
accordance with increase of an absolute value of the difference S* -S. 
Thus, the driving circuit 122 acts to switch over both the solenoid valves 
33, 34 from their first positions to their second positions in the 
occurrence of the negative control pulse signal P3. If there is not any 
negative control pulse signal P3, the driving circuit 122 acts to switch 
over the solenoid valve 33 from the first position to the second position 
and to retain the solenoid valve 34 in the first position. This causes the 
hydraulic braking pressure in the slave cylinder 32 to decrease at a speed 
proportional to the absolute value of the difference S* -S. As a result, 
the slip ratio of the left front road wheel is controlled to converge into 
the target slip ratio S*. 
Simultaneously, the feedforward control portion 100B applies a feedforward 
control pulse signal P2 to the pulse mixing circuit 121 in accordance with 
the target slip ratio S*. In this instance, an amount of hydraulic fluid V 
corresponding with the target ratio S* is calculated. If the calculated 
amount of hydraulic fluid V increases, the control pulse signal P2 is 
produced as a plurality of positive pulses of the predetermined width, and 
each interval time (duration) of the positive pulses becomes short in 
accordance with the increasing speed of the amount of hydraulic fluid V. 
If the calculated amount of hydraulic fluid decreases, the control pulse 
signal P2 is produced as a plurality of negative pulses of the 
predetermined width, and each interval time (duration) of the negative 
pulses becomes short in accordance with the decreasing speed of the amount 
of hydraulic fluid. The feedforward control pulse signal P2 is mixed with 
the feedback control pulse signal P1 at the pulse mixing circuit 121. 
If the feedforward control pulse signal P2 is not overlapped with the 
feedback control pulse signal P1 at the pulse mixing circuit 121, the 
feedforward control pulse signal P2 is applied to the driving circuit 122. 
If the feedforward control pulse signal P2 is overlapped with the feedback 
control pulse signal P1 at an identical sign, a time width of the 
overlapped portion is added to the pulse width of the control pulse signal 
P1 or P2, and a control pulse signal P3 of the added pulse width is 
applied to the driving circuit 122. If the feedforward control pulse 
signal P2 is overlapped with the feedback control pulse signal P1 at a 
different sign, the control pulse signal P1 or P2 is applied as the 
control pulse signal P3 to the driving circuit 122. When applied with the 
control pulse signal P3, the driving circuit 122 energizes or deenergizes 
the solenoid valves 33, 34 as described above. As a result, the hydraulic 
pressure in the slave cylinder 32 is regulated by the feedback control 
and/or the feedforward control. In addition, the hydraulic pressure in the 
other slave cylinders is controlled substantially in the same manner as in 
the slave cylinder 32. 
Since in this embodiment the feedforward control is added to the feedback 
control to converge each actual slip ratio S of the road wheels into the 
target slip ratio S*, the abnormal behavior of the vehicle can be quickly 
normalized in a high precision. 
In actual practices of the present invention, the above embodiment may be 
modified as described below. 
a) First Modification: 
In a first modification of the embodiment, the differential control term 
calculator 102, proportional control term calculator 103 and integral 
control term calculator 104 are modified as shown in FIG. 9. In this 
modification, there is provided a coefficient table circuit 130 which is 
arranged to memorize a three dimensional map representing coefficients Kp, 
Kd, Ki in relation to the detected road surface frictional coefficient 
.mu., a predetermined contact load Fz and a tire slip angle as shown in 
FIG. 10. In addition, the coefficient table circuit 130 includes a 
multiplexer for multiplying the road surface frictional coefficient .mu. 
by the contact load Fz and an interpolator for interpolating an output of 
the table circuit. The coefficients Kp, Kd, Ki from the coefficient table 
circuit 130 are applied to multiplexers 102a, 103a and 104a. The 
multiplexer 102a is arranged to multiply the coefficient Kd by a 
differentiated value d(S* -S)/dt of a difference between the target slip 
ratio S* and actual slip ratio S calculated at the differentiator 102b and 
to apply the multiplied value to an adder 105. The multiplexer 103a 
multiplies the difference S* -S by the coefficient Kp and applies the 
multiplied value to the adder 105. The multiplexer 104a multiplies an 
integrated value (S* -S)dt of the difference S* -S calculated at the 
multiplexer 104b by the coefficient Ki and applies the multiplied value to 
the adder 105. 
With the modification, the coefficients Kp, Kd, Ki of a PID interpolation 
in the feedback control can be varied in accordance with a road surface 
condition. Thus, the feedback control is stabilized even if the road 
condition has changed. 
b) Second Modification: 
In a second modification of the embodiment, the differential control term 
calculator 102, proportional control term calculator 103 and integral 
control term calculator 104 are modified as shown in FIG. 11. In this 
modification, there is provided a gain table circuit 140 which is arranged 
to memorize a two dimensional map representing a feedback gain .alpha. in 
relation to an actual slip ratio S as shown in FIG. 12. The gain table 
circuit 140 includes an interpolator for interpolation of data read out 
from the two dimensional table as well as in the braking force calculation 
circuit 111. Multiplexers 141, 142, 143 are connected to the gain table 
circuit 140 to be applied with the interpolated gain .alpha. therefrom. 
The multiplexers 141, 142, 143 are connected to a coefficient table 
circuit 144 to multiply coefficients Kp, Kd, Ki applied therefrom by the 
interpolated gain .alpha.. Multiplexers 102a, 103a, 104a are connected to 
the multiplexers 141, 142, 143 to be applied with the multiplied values 
therefrom. Preferably, the coefficient table circuit 144 is arranged to 
produce the coefficients Kp, Kd, Ki in accordance with the road surface 
frictional coefficient .mu., contact load Fz and slip angle .beta. as in 
the first modification. Alternatively, the coefficient table circuit 144 
may be arranged to produce the coefficients Kp, Kd, Ki each as a 
predetermined value as in the above embodiment. 
With the second modification, the gain .alpha. is determined as a small 
value in a small region of the actual slip ratio S where the braking force 
for the feedforward control linearly changes. Thus, in a lower linear 
region of the actual slip ratio S, mainly the feedforward control is 
effected without any interference with the feedback control to quickly 
control each slip ratio of the road wheels to the target slip ratio S*. In 
a higher non-linear region of the actual slip ratio S, mainly the feedback 
control is effected to control each slip ratio of the road wheels to the 
target slip ratio S* in a stable condition. 
Although in the second modification the multiplexers 141-143 have been 
adapted to multiply the gain .alpha. from the gain table circuit 140 by 
the coefficients Kp, Kd, Ki from the coefficient table circuit 144, the 
gain .alpha. may be multiplied by the output of the multiplexers 102a, 
103a, 104a or the adder 105. Although in the second modification, the gain 
.alpha. has been determined on a basis of the actual slip ratio S, the 
gain .alpha. may be determined in accordance with the target slip ratio 
S*. 
c) Third Modification: 
In a third modification of the above embodiment, the interval time 
converter 106 and pulse generator 107 are partly modified as shown in FIG. 
13. In this modification, there is provided an on-time table circuit 150 
which is arranged to memorize a three dimensional map representing a 
pulse-on time (pulse width) Tpul in relation to the detected road surface 
frictional coefficient .mu., the predetermined contact load Fz and the 
slip angle .beta. as shown in FIG. 14. In addition, the on-time table 
circuit 150 includes a calculator for multiplying the road surface 
frictional coefficient .mu. by the contact load Fz and an interpolator for 
interpolation of an output of the table circuit 150. A multiplexer 151 and 
a pulse generator 152 are connected to the on-time table circuit 150 to be 
applied with a pulse signal indicative of a pulse-on time Tpul therefrom. 
The multiplexer 151 multiplies an interval time Tfb applied from the 
interval time converter 106 by the pulse-on time Tpul and applies the 
multiplied value to the pulse generator 152. When applied with the 
multiplied value from the multiplexer 151, the pulse generator 152 
produces a control pulse signal P1 for feedback control in accordance with 
an interval time (pulse frequency) and pulse-on time Tpul defined by the 
compensated interval time Tfb. 
In the third modification, the interval time and the pulse-on time of the 
control pulse signal P1 for the feedback are controlled in accordance with 
a road surface condition. Thus, in the case that the hydraulic braking 
pressure in the slave cylinders 32, 42, 52, 62 can be increased under a 
good condition of the road surface or cannot be increased under a bad 
condition of the road surface, a dynamic range of the braking pressure 
under the feedback control can be varied in accordance with a condition of 
the road. 
d) Fourth Modification: 
In a fourth modification of the above embodiment, the pulse converter 116 
is modified as shown in FIG. 15. In this modification, there is provided a 
reference value width table circuit 160 arranged to memorize a three 
dimensional map representing a reference value width VLSB in relation to 
the detected road surface frictional coefficient .mu., the predetermined 
contact load Fz and tire slip angle .beta. as shown in FIG. 16. The 
reference value width table circuit 160 is designed as in the on-time 
table circuit 150 of the third modification to interpolate an output value 
of the table circuit 160 in accordance with a multiplied value of the road 
surface frictional coefficient .mu. and contact load Fz and the slip angle 
.beta.. A pulse converter 116a is connected to the reference value width 
table circuit 160 to be applied with the reference value width VLSB 
therefrom for converting each width among reference values V.sub.1, 
V.sub.2, V.sub.3 for comparison with the amount of hydraulic braking fluid 
V In proportion to the reference value width VLSB as shown in FIG. 17. The 
other function of the pulse converter 116a is substantially the same as 
that in the pulse converter 116. 
A pulse width conversion circuit 162 is connected to the pulse converter 
116a to be applied with the control pulse signal P2 therefrom and 
connected to a pulse width calculation circuit 161 to be applied a pulse 
width Twid therefrom for converting the pulse width of the control pulse 
signal P2 in proportion to the pulse width Twid. The converted pulse width 
is applied as a control pulse signal P2' to the pulse mixing circuit 121 
in the above embodiment. The pulse width calculation circuit 161 is 
applied with electric signals respectively indicative of the hydraulic 
braking pressure Pb and pulse width Twid to execute calculation of the 
following equation (4) for calculating the pulse width Twid when the 
hydraulic braking pressure Pb is increased and to execute calculation of 
the following equation (5) for calculating the pulse width Twid when the 
hydraulic braking pressure Pb is decreased. 
EQU Twid=K.multidot.VLSB.multidot.(P.sub.L1 -Pb).sup.-1/2 (4) 
EQU Twid=K.multidot.VLSB.multidot.(Pd).sup.-1/2 (5) 
In the equations (4) and (5), the character P.sub.L1 represents a hydraulic 
pressure in the high pressure line L1, and the coefficient K represents a 
predetermined constant. 
When the hydraulic braking pressure Pb is increased, the amount of 
hydraulic fluid in the slave cylinder 32 increases in proportion to a 
square root of a difference between the hydraulic pressure in the high 
pressure line L1 and the hydraulic pressure in the slave cylinder 32. When 
the hydraulic braking pressure Pb is decreased, the amount of hydraulic 
fluid in the slave cylinder 32 decreases in proportion to a square root of 
a difference between the hydraulic pressure in the slave cylinder 32 and 
the hydraulic pressure in the low pressure line L2. Thus, the pulse-on 
time for providing a necessary amount of hydraulic fluid in accordance 
with variation of the reference value width VLSB can be calculated by 
calculation of the equations (4) and (5). 
With the fourth modification, the pulse interval and pulse-on time of the 
control pulse signal P2 for the feedforward are controlled in accordance 
with a condition of the road surface. Thus, in the case that the hydraulic 
braking pressure in the slave cylinders 32, 42, 52, 62 can be increased 
under a good condition of the road surface or cannot be increased under a 
bad condition of the road surface, a dynamic range of the hydraulic 
braking pressure under the feedforward control can be varied in accordance 
with a condition of the road surface. 
e) Fifth Modification: 
In a fifth modification of the above embodiment, the pulse generator 107, 
pulse converter 116 and pulse mixing circuit 121 are modified as shown in 
FIG. 18. In this modification, the pulse generator 107 has an internal 
counter which is arranged to be reset in response to the control pulse 
signal P2 applied thereto from the pulse converter 116. The pulse mixing 
circuit 121 is replaced with a pulse mixing circuit 170 which is arranged 
to be applied with the control pulse signals P1 and P2 from the pulse 
converters 107 and 116. When applied with either one of the control pulse 
signals P1, P2, the pulse mixing circuit 170 produces the applied control 
pulse signal as a control pulse signal P3 at times t1, t4 shown in FIG. 
19. 
With the fifth modification, both the control pulse signals P1, P2 are not 
applied to the pulse mixing circuit 170 at the same time since the 
internal counter of pulse generator 107 is reset in response to the 
control pulse signal P2 from the pulse converter 116. Accordingly, both 
the control pulse signals can be mixed at the pulse mixing circuit 170 in 
a simple manner, and the pulse mixing circuit 170 can be provided in a 
simple construction. Since the number of mixed control pulse signals P3 is 
reduced, the changeover frequency of the solenoid valves 33, 34 is 
reduced. This is useful to enhance the durability of the solenoid valves 
33, 34. 
f) Further Modifications: 
Although in the above embodiment and modifications the condition amount 
calculation portion 72, target slip ratio calculation portion 73, abnormal 
behavior detection portion 74, actual slip ratio calculation portion 75 
and slip ratio control portion 100 each have been constructed by a 
hardware, they may be replaced with a software such as an appropriate 
microcomputer for effecting the identical function.