Method for determining an optimal slip value

A method for determining an optimal slip value .lambda. at at least one wheel of a vehicle for regulating braking force, using signals (V.sub.R *;

• V.sub.F) at least approximated to the wheel speed V.sub.R and the vehicle speed V.sub.F, characterized in that the method comprises during driving, varying the slip value .lambda. by varying the braking pressure P.sub.B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V.sub.R *(K), V.sub.F *(K), P.sub.B *(K) and F.sub.A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value .lambda. into a function V.sub.R (K+1)=f with unknown estimated coefficients .alpha..sub.n, solving the resultant equation system and ascertaining the coefficients .alpha..sub.n, ascertaining coefficients .alpha..sub.n which are coefficients of a generalized description of a .mu. slip curve .mu.=f(V.sub.R, V.sub.F) from the coefficients .alpha..sub.n, and ascertaining a location of the optimal slip value .lambda..sub.opt by use of the ascertained instantaneous course of the .mu. slip curve, where p.sub.B (K) is the braking pressure, F.sub.A (K) is the tire/road contact force and K is an increment counter, which defines the measurement and calculation instances which are located at intervals of .DELTA.T from one another, and obtaining function V.sub.R (K+1) by the following expression:
• ##EQU40## where .alpha..sub.1 -.alpha..sub.5 are the constants .alpha..sub.n that are to be ascertained, R is the radius of the wheel, IR is its moment of inertia and C is a constant (e.g., 0.98).

A method for determining an optimal slip value .lambda. at at least one wheel of a vehicle for regulating braking force, using signals (V.sub.R *;

• V.sub.F) at least approximated to the wheel speed V.sub.R and the vehicle speed V.sub.F, characterized in that the method comprises during driving, varying the slip value .lambda. by varying the braking pressure P.sub.B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V.sub.R *(K), V.sub.F *(K), P.sub.B *(K) and F.sub.A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value .lambda. into a function V.sub.R (K+1)=f with unknown estimated coefficients .alpha..sub.n, solving the resultant equation system and ascertaining the coefficients .alpha..sub.n, ascertaining coefficients .alpha..sub.n which are coefficients of a generalized description of a .mu. slip curve .mu.=f(V.sub.R, V.sub.F) from the coefficients .alpha..sub.n, and ascertaining a location of the optimal slip value .lambda..sub.opt by use of the ascertained instantaneous course of the .mu. slip curve, where p.sub.B (K) is the braking pressure, F.sub.A (K) is the tire/road contact force and K is an increment counter, which defines the measurement and calculation instances which are located at intervals of .DELTA.T from one another, and the parameters .alpha..sub.n of the function V.sub.R (K+1) are obtained from the expression
• V.sub.R (K+1)=V.sub.R (K+1)+.nu.(K)
• by minimizing the sum of the square of the error ##EQU41## where V.sub.R (K+1) is a measured value, V.sub.R (K+1) is an estimated value and .nu.(K) is an approximation error, and the noisy measured values V.sub.R, V.sub.F, F.sub.A and P.sub.B are ascertained by means of a Kalman filter.

A method for determining an optimal slip value .lambda. at at least one wheel of a vehicle for regulating braking force, using signals (V.sub.R *;

• V.sub.F) at least approximated to the wheel speed V.sub.R and the vehicle speed V.sub.F, characterized in that the method comprises during driving, varying the slip value .lambda. by varying the braking pressure P.sub.B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V.sub.R *(K), V.sub.F *(K), P.sub.B *(K) and F.sub.A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip values .lambda. into a function V.sub.R (K+1)=f with unknown estimated coefficients .alpha..sub.n, solving the resultant equation system and ascertaining the coefficients .alpha..sub.n, ascertaining coefficients .alpha..sub.n which are coefficients of a generalized description of a .mu. slip curve .mu.=f(V.sub.R, V.sub.F) from the coefficients .alpha..sub.n, and ascertaining a location of the optimal slip value .lambda..sub.opt by use of the ascertained instantaneous course of the .mu. slip curve, where p.sub.B (K) is the braking pressure, F.sub.A (K) is the tire/road contact force and K is an increment counter, which defines the measurement and calculation instances which are located at intervals of .DELTA.T from one another, and the parameters .alpha..sub.n of the function V.sub.R (K+1) are obtained from the expression
• V.sub.R (K+1)=V.sub.R (K+1)+.nu.(K)
• by minimizing the sum of the square of the error ##EQU42## where V.sub.R (K+1) is a measured value, V.sub.R (K+1) is an estimated value and .nu.(K) is an approximation error, and the values V.sub.F, F.sub.A and P.sub.B are estimated from the measured value for V.sub.R or from the estimated measured value V.sub.R, at least partially by means of a Kalman filter.