Method for determining an optimal slip value

Claim 1

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K, K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients a n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and obtaining function V R (K+1) by the following two expressions: ##EQU34## for s>0.5, where α' 1 and α' 2 and α 1 -α 5 are the coefficients α n that are to be ascertained, R is the radius of the wheel, IR is its moment of inertia, ##EQU35## ε is a tire constant, μ=μ o (1+Aλ.νλ), μ o is the coefficient of friction between the tire and the road, Aλ is a rubber constant and νλ=λ.V F .

Claim 2

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K, K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients a n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and obtaining function V R (K+1) by the following two expressions: ##EQU34## for s>0.5, where α' 1 and α' 2 and α 1 -α 5 are the coefficients α n that are to be ascertained, R is the radius of the wheel, IR is its moment of inertia, ##EQU35## ε is a tire constant, μ=μ o (1+Aλ.νλ), μ o is the coefficient of friction between the tire and the road, Aλ is a rubber constant and νλ=λ.V F .

Claim 12

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and obtaining function V R (K+1) by the following expression: ##EQU40## where α 1 -α 5 are the constants α 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).

Claim 13

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and obtaining function V R (K+1) by the following expression: ##EQU40## where α 1 -α 5 are the constants α 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).

Claim 14

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and the parameters α n of the function V R (K+1) are obtained from the expression V.sub.R (K+1)=V.sub.R (K+1)+ν(K) by minimizing the sum of the square of the error ##EQU41## where V R (K+1) is a measured value, V R (K+1) is an estimated value and ν(K) is an approximation error, and the noisy measured values V R , V F , F A and P B are ascertained by means of a Kalman filter.

Claim 15

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip value λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and the parameters α n of the function V R (K+1) are obtained from the expression V.sub.R (K+1)=V.sub.R (K+1)+ν(K) by minimizing the sum of the square of the error ##EQU41## where V R (K+1) is a measured value, V R (K+1) is an estimated value and ν(K) is an approximation error, and the noisy measured values V R , V F , F A and P B are ascertained by means of a Kalman filter.

Claim 16

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip values λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and the parameters α n of the function V R (K+1) are obtained from the expression V.sub.R (K+1)=V.sub.R (K+1)+ν(K) by minimizing the sum of the square of the error ##EQU42## where V R (K+1) is a measured value, V R (K+1) is an estimated value and ν(K) is an approximation error, and the values V F , F A and P B are estimated from the measured value for V R or from the estimated measured value V R , at least partially by means of a Kalman filter.

Claim 17

A method for determining an optimal slip value λ at at least one wheel of a vehicle for regulating braking force, using signals (V R *; V F ) at least approximated to the wheel speed V R and the vehicle speed V F , characterized in that the method comprises during driving, varying the slip value λ by varying the braking pressure P B and at individual measuring instants (K,K+1 . . . ) and ascertaining signal value combinations V R *(K), V F *(K), P B *(K) and F A *(K), that after inserting a plurality of these ascertained signal value combinations for various values of slip values λ into a function V R (K+1)=f with unknown estimated coefficients α n , solving the resultant equation system and ascertaining the coefficients α n , ascertaining coefficients α n which are coefficients of a generalized description of a μ slip curve μ=f(V R , V F ) from the coefficients α n , and ascertaining a location of the optimal slip value λ opt by use of the ascertained instantaneous course of the μ slip curve, where p B (K) is the braking pressure, F 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 ΔT from one another, and the parameters α n of the function V R (K+1) are obtained from the expression V.sub.R (K+1)=V.sub.R (K+1)+ν(K) by minimizing the sum of the square of the error ##EQU42## where V R (K+1) is a measured value, V R (K+1) is an estimated value and ν(K) is an approximation error, and the values V F , F A and P B are estimated from the measured value for V R or from the estimated measured value V R , at least partially by means of a Kalman filter.