Anti-skid Device

Abstract

An anti-skid device for maintaining the slip factor of the wheels of a running vehicle constant is additionally provided with a second order phase-lead element whose constants are set to the optimum value with regard to the acceleration and deceleration vibration phenomena of the wheels under controlled conditions which characterize the dynamic characteristics of the anti-skid device, whereby an improved overall control performance of the system is ensured.

Description

The present invention relates to an anti-skid device for vehicles.

With the conventional anti-skid devices for vehicles designed to maintain the slip factor of the wheels at a predetermined value, as road conditions change during a journey, the maximum value .mu.bo of the braking coefficient .mu.b between the road surface and the tires governing the loop transfer function characteristics of the control system as well as the slip factor .sigma.o of that time were caused to change so that when constructing the device, it was necessary to design such that the desired value .sigma.c of the slip factor and the gain K of the control system would be altered automatically or manually to set them all over again.

While this required accurate information relating to the pattern of a .sigma.-.mu.b characteristic curve characterizing the tire-road surface characteristics, it was not an easy matter to obtain such information through any simple means. Thus, the conventional anti-skid devices with a constant slip factor where defective in that they lacked adaptability to new or changed road surfaces, since it was necessary to sequentially derive and reset to the new desired values .sigma.c or the optimum values of the gain K as the road surfaces changed.

The present invention proposes a method which eliminates the aforesaid defect and provides an improved control performance by additionally providing an anti-skid device with a simple control element.

According to the present invention, even though the desired value .sigma.c of the slip factor and the gain K of the control system are maintained constant, the result of a control is fully sufficient to meet any road surface changes so that there is no need to alter the desired value .sigma.c of the slip factor and the gain K of the control system, while at the same time an excellent control performance is achieved, since the amplitude of repetitive vibrations of the wheel acceleration and deceleration is small, resulting in a short stopping distance and good riding comfortability.

Other objects, features and advantages will be readily apparent from the following detailed descriptions of a preferred embodiment of the present invention taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a slip factor-braking friction coefficient characteristic curves;

FIG. 2 is a block diagram of a conventional anti-skid device for maintaining the wheel slip factor constant;

FIG. 3 is a block diagram equivalent to the block diagram of a conventional anti-skid device for maintaining the wheel slip factor constant;

FIG. 4 is a diagram for explaining the open-loop transfer characteristics of a block diagram equivalent to the conventional anti-skid device for maintaining the wheel slip factor constant;

FIG. 5 is a block diagram of an anti-skid device according to the present invention; and

FIGS. 6, 7, 8, and 9 are diagrams showing the tests results.

Referring now to FIG. 1, there is illustrated by way of example a slip factor .sigma.-braking friction coefficient .mu.b characteristic curve in which a solid curve is the characteristic curve on a non-slippery road surface such as a dry asphalt road surface and a one-dot chain curve is a characteristic curve on the slippery road surface such as a frozen road surface. In the figure, .sigma.o is the slip factor when the braking friction coefficient assumes the maximum value .mu.bo, .sigma.c is the desired value of the control system and .mu.bc is the braking friction coefficient when the slip factor is .sigma.c. FIG. 2 illustrates by way of example a block diagram of a conventional anti-skid device designed to maintain the wheel slip factor constant, and symbols P, V, and Vw in the figure represent the braking pressure, vehicle speed and wheel peripheral speed, respectively.

Referring to the construction of the device shown in FIG. 2, a slip factor setting means consists of a scale-factor element which produces (1 - .sigma.c/100).sup.. V through the multiplication of the vehicle speed V by a constant (1 - .sigma.c/100), an adder 1 is a comparator which compares the slip factor setting element output (1 - .sigma.c/100.sup.. V V and the wheel peripheral speed Vw, an electro-hydraulic servo is a pressure control circuit which employs a pressure potentiometer to feed back the braking pressure converted into an electrical signal to an adder 2 so as to provide a stable braking force proportional to the output of an integrator, and the integrator is a control element which is combined with the pressure control circuit to form a driving element having integral characteristic of the first order.

Next, the operation of the system of FIG. 2 will be outlined. In this system, if the output .delta. of the adder 1, i.e., (1 - .sigma.c/100) V-Vw is positive, the output of the integrator becomes a braking pressure increasing signal and it becomes a braking pressure reducing signal when the output is negative. Thus, the wheel peripheral speed is controlled by the braking pressure increasing and decreasing operations of the electro-hydraulic servo which follow up such signals one after another, so that there is finally achieved (1 - .sigma.c/100).sup.. V-Vw = 0, that is, the slip factor .sigma. of the wheel converges to .sigma.c.

Next, the construction and operation of the device of the present invention will be explained hereunder in comparison with the conventional constant slip factor anti-skid device illustrated in FIG. 2.

FIG. 3 illustrates in terms of the transfer functions a block diagram of a constant slip factor anti-skid device equivalent in principle to the device of FIG. 2, with the motion of the wheel being limited within the region 0 .ltoreq. .sigma. < .sigma.o of the slip factor-braking friction coefficient characteristic curve. In the figure, a transfer function K.sub.5 /(1 + T.sub.5 S) is an approximate transfer function when the kinetic characteristic between the wheel and the road surface is evaluated with the input to a vehicle being the braking pressure P and the output being the slip factor .sigma., where K.sub.5 is a gain constant showing the rate of occurrence of slip factor to the braking pressure, T.sub.5 is a time constant which represents the delay between the application of the braking pressure and the occurrence of the slip factor and S is a Laplace's operator. Other transfer function

are approximate transfer functions derived from the other components in FIG. 2, that is, the first one K.sub.1 /S corresponds to the transfer characteristics of the integrator, the second one to that of a power amplifier, a servovalve hydraulic cylinder, a master cylinder and a brake pipe, and the third one to that of the pressure potentiometer in FIG. 2, where K.sub.1, K.sub.3, and K.sub.4 designating their respective gain constants and T.sub.3 designating the time constant.

In this case, the open-loop transfer characteristics of FIG. 3 can be represented by the curves of a gain characteristic G.sub.1 and phase characteristics .PHI..sub.1 in FIG. 4, so that when road surfaces traveled by a vehicle change within the range between a slippery road surface such as a frozen road surface and a non-slippery road surface such as a dry asphalt road surface, the gain characteristic curve represented by the G.sub.1 in FIG. 4 varies within the range G'.sub.1 - G".sub.1, whereas there is no change its phase characteristics.

The curves G'.sub.1 and G".sub.1 are drawn for a case where the value of the .mu.bo changes within the range of 10 times such as between 0.08 and 0.8. Thus, assuming that the braking pressure required to achieve the identical slip factor differs by ten times between a slippery road surface where the .mu.bo = 0.08 and a non-slippery road surface where the .mu.bo = 0.8 and that the difference in gains between G'.sub.1 and G".sub.1 is 20 dB, G'.sub.1 and G".sub.1 are shown representing the gain characteristics of the open-loop transfer characteristics obtained when a braking is effected on a slippery road surface and a non-slippery road surface, respectively. In FIG. 4, the gain is adjusted such that the overshoot of the slip factor will be about 16 percent, that is, a good transient characteristic can be achieved when the vehicle is braked on a non-slippery road surface. As will be seen from the figure, when the gain characteristics change from G".sub.1 to G.sub.1 and then to G'.sub.1 as the road surfaces turn out to be increasingly slippery, the phase margin becomes smaller A"B", AB to A"B", so that if the value of .mu.bo is very small, as is the case on a frozen road surface, the phase margin becomes negative thereby making the system very unstable.

Contrary to the case of FIG. 4, if the loop gain is set such that a good transient characteristic is obtained on a frozen road surface, the response characteristic of a control system is deteriorated as road surfaces become increasingly non-slippery with the result that a longer time is required for the controlled variable .sigma. to reach the desired value .sigma.c and hence a longer distance is required for the vehicle to come to a standstill.

It is now evident from the foregoing that with the construction shown in FIG. 2, it is unavoidably necessary to adjust the gain in a loop transfer path so as to restrain any phenomena of instability or an over-damping phenomena due to changes in road surface conditions.

On the other hand, FIG. 5 illustrates a block diagram of an anti-skid device embodying the present invention which differs from the conventional device of FIG. 2 in that a phase-lead compensating element is additionally connected in parallel with an integrator between the output of an adder 1 and the input of an adder 2.

By establishing the time constant and the gain constant of this phase-lead compensating element constituting a principal part of the present invention in a manner that will be explained hereinafter, the open-loop transfer characteristics shown in FIG. 4 are now represented by curves G'.sub.2, G".sub.2 and .PHI.2 in the figure, so that even if the road surface changes into a slippery one, the phase margin remains always positive thereby reducing the unstable repetitive vibrations of the wheel.

Such unstable repetitive vibrations of the wheels include vibrations attributable to the motion of the wheels entering into the range .sigma. > .sigma.o of the .sigma.-.mu.b characteristic curve as is commonly known, in addition to the aforesaid vibrations caused by variations in the value of .mu.bo. Explanation will be made hereunder of the case .sigma.c> .sigma.o where the wheel motion comes into the range .sigma. > .sigma.o without fail.

In the case of the system shown in FIG. 2, if it is set that .sigma.c > .sigma.o, the deceleration of the wheels when the slip factor .sigma. reaches the desired value .sigma.c will be very large as compared with the obtained at .sigma. > .sigma.o, so that even if the braking pressure is reduced at this instance, the wheels will not be accelerated immediately but it will be only after the lapse of a certain time that the acceleration starts to take place. In other words, the controlled variable .sigma. inevitably exceeds the desired value .sigma.c with the result that there inevitably take place vibrations of the wheel acceleration and deceleration which prevent stable control of the wheels. According to the method of the present invention, stable control of wheels is possible even in such a state. The reason for this will be explained hereunder.

Consider the various desired values of a control system assuming that the road surface travelled by a vehicle is not subject to any temporary change. Since the desired value of the wheel slip factor is .sigma.c, the desired value of the vehicle deceleration may be given as .mu.bc .sup.. g, the desired value of the wheel deceleration as (1- .sigma.c) .mu.bc .sup.. g, and the desired value T.sub.BC of the wheel braking torque (proportional to the braking pressure) may be approximately expressed as T.sub.BC = .mu.bc {R.sup.. W - (I/R) (1-.sigma.c).sup.. g },

where g is the acceleration by gravity; R is the radius of a wheel; W is the longitudinal load imposed on the wheel; and I is the moment of inertia of the wheel. T.sub.BC represents a value which causes a slip factor .sigma.c.sub.1 within the region .sigma. < .sigma.o, so that in order that the wheel slip factor may be .sigma.c, it is necessary to first apply to the wheel a braking torque having a value larger than T.sub.BC so as to cause the motion of the wheel to fall within the region .sigma. > .sigma. c and then to reduce the braking torque to the level of T.sub.BC. Therefore, considering this fact in connection with the characteristics of the wheel motion by which once the wheel motion has entered into the region .sigma. > .sigma.c, even under the condition of .sigma. < .sigma.c, the reduction of braking pressure at any finite rate cannot cause the wheel peripheral speed to immediately turn towards the direction of its recovery, but it proceeds towards locking the wheel (Regarding .sigma., it is the direction towards the desired value), it is evident that the braking pressure reducing operation must be initiated before the slip factor .sigma. reaches the desired value .sigma.c in order that the braking pressure and the slip factor may reach their respective desired values in an ideal manner.

According to the method of the present invention, a second order phase-lead element is indirectly provided by the composite circuit of an integrator and a phase-lead element of FIG. 5, so that the aforesaid pressure reducing operation is made possible by virtue of the predictive property of this element.

Next, a method of designing the characteristics of the second order phase-lead element constituting the principal part of the present invention, will hereinafter be explained in detail.

The acceleration and deceleration repetitive vibrations of the wheel under control represent a phenomenon characterizing the dynamic characteristics of a control system, and thus the method of determining the constant of a compensating element with regard to such wheel vibrations constitutes a characteristic feature of the present invention.

The transfer function Gc(S) of the second order phase-lead element is given by the resultant transfer function of the transfer function K.sub.1 /S of the integrator and the transfer function K.sub.2 (1 + T.sub.2 S)/(1 + .alpha. T.sub.2 S) of the phase-lead compensating element and it may be expressed by the following equation: ##SPC1##

.zeta..sub.n = damping factor

.omega.n = natural angular frequency

T.sub.2 = the time constant of the phase-lead compensating element

K.sub.2 = the gain constant of the phase-lead compensating element

.alpha. = constant

The technique for setting the values of .omega..sub.n and .zeta. in Gc(S) constitutes an important feature of the present invention and the values of K.sub.2, T.sub.2, and .alpha. which concretely determine the values of .omega..sub.n and .zeta. may be established by a technique which will hereinafter be explained. It is assumed that the value of K.sub.1 is predetermined so that it has a value large enough to provide the control system with a sufficiently fast response characteristic on a non-slippery road surface.

In other words, the value of T.sub.2 is set to fall within the limits between (1/4 .pi.) to (5/2 .pi.) times the period T.sub.o of the acceleration and deceleration repetitive vibrations of the wheels under the controlled condition and the value of .alpha. is set to fall within the range between 0.1 and 0.4, while the value of K.sub.2 is set so that, when K.sub.2, T.sub.2, and .alpha. are substituted into the equations (1) and (2), .omega..sub.n and .zeta. take such values which satisfy the relations 2 .pi./T.sub.o .gtoreq. .omega..sub.n .gtoreq. 2 .pi./5T.sub.o and 0.1 .ltoreq. .zeta. .ltoreq. 1, respectively.

In actual practice, those results which satisfy the aforesaid conditions may be automatically obtained, if a phase-lead compensating element with T.sub.2 .apprxeq. (T.sub.o /2 .pi.) and .alpha.=0.25 is additionally disposed at the position shown in FIG. 5 and the value of K.sub.2 is then gradually increased from zero until it is set to a value at which the vibration of the wheels is minimum.

FIGS. 6 through 9 illustrate the test results, with FIGS. 6 and 7 showing the results of the running tests conducted on a non-slippery road surface and FIGS. 8 and 9 showing the results obtained on a slippery road surface. These graphs illustrate the results of comparative tests conducted before and after the present invention was utilized to accomplish an improved performance. In the figures, the abscissae are a common time axis (T.sub.sec) and the ordinates represent the braking pressure (P Kg/cm.sup.2), wheel peripheral speed V (Km/H) and the vehicle speed V(Km/H), respectively. Further, in the graphs showing the vehicle speed V, V.sub.l is an imaginery curve showing the decelerating performance of the vehicle speed V obtained when wheels are locked; in one of the graphs shown in FIG. 6 which represents the wheel peripheral speed V , T.sub.o is the period of acceleration and deceleration repetitive vibrations of the wheels; and in those graphs of FIGS. 7 and 9 which represent the wheel peripheral speed V , V and (1 - .sigma.c/100).sup.. V respectively represent the vehicle speed curve and the same curve multiplied by (1 - .sigma.c/100), which are simultaneously shown in the graphs representing the wheel peripheral speed.

Here, it is assumed that of the four wheels of the vehicle, only the two rear ones are subjected to control and no braking pressure is applied to the two front wheels, while the desired value .sigma.c of the slip factor is set to 20 percent, the gain constant K.sub.1 of the integrator is set to 19.2 (volt/sec/volt), and the values of the gain constant K.sub.2 of the phase-lead compensating element, the time constant T.sub.2 and .alpha. are set to 5.78 (volt/volt), 0.1 (sec) and 0.25, respectively.

As will be seen from a comparison between the braking pressure P and the wheel peripheral speed V with respect to those portions marked with .DELTA. and .quadrature. in FIGS. 7 and 9 showing the results obtained when the present invention was incorporated, before the value of the wheel peripheral speed V reaches (1 - .sigma.c).sup.. V, there has already been initiated an operation reducing the braking pressure P at the portions marked with .DELTA. and an operation increasing the braking pressure P at the portions marked with .quadrature.. In other words, the predictive performances of increasing and decreasing operations of the braking pressure constituting an important feature of the present invention is remarkably manifested.

Accordingly, from the above comparison made between the results of the tests conducted with and without the utilization of the present invention, it is now evident that the utilization of the present invention is effective in that an improved control performance is achieved by virtue of the fact that the control performance is not greatly influenced by road surface changes even if the desired value .sigma.c of the slip factor and the gain K of a control system are maintained constant, and hence a shorter stopping distance, a lower vibration level of the wheels during the braking operation and a comfortable ride can always be ensured.

Claims

What is claimed is:

1. An anti-skid device for vehicles comprising: a first adder for comparing a value obtained by multiplying, through a slip factor setting means, the output of a vehicle speed detecting means by a coefficient smaller than unity and the output of a wheel peripheral speed detector; a second adder for comparing the output of a parallel combination of an integrator and a phase-lead compensating element, which are connected to the output terminal of said first adder, and the output proportional to the wheel braking pressure; and an electro-hydraulic driving element connected to the output terminal of said second adder and controlled by the output of said second adder to produce a wheel braking pressure to effect a predictive control so as to maintain the slip factor of the wheels constant.

2. An anti-skid device for vehicles according to claim 1 wherein the parallel combination of said integrator and said phase-lead compensating element is a phase-lead compensating element of the second order which is represented by the resultant transfer function:

of the transfer function (K.sub.1 /S) of the integrator element and the transfer function K.sub.2 (1 + T.sub.2 S)/1 + .alpha.T.sub.2 S) of the phase-lead compensating element.

3. An anti-skid device for vehicles according to claim 1 wherein the parallel combination of said integrator and said phase-lead compensating element constitutes a vibration minimizing means of the wheels in motion.