Nonlinear Wheel Slip Control Design

Up to now, for the case of actuators with continuous dynamics, we have discussed how to design braking controllers based on linearised models of the braking dynamics of interest.

In this chapter, we discuss a nonlinear approach to wheel slip control design, namely a Lyapunov-based dynamic feedback control law. For an introduction to the control approach employed in this chapter, the reader is referred to Appendix A.

As a matter of fact, the braking dynamics are nonlinear due to the tyre–road interaction model; as such, the proposed approach allows us to take these nonlinearities directly into account and to consider their effects on the control algorithm. Further, the proposed control strategy is grounded on theoretical tools which allow us analyse its characteristics and to highlight its advantages with respect to the linear approaches.

Specifically, the nonlinear slip controller discussed in this chapter relies on a nonlinear dynamic feedback control law, based on wheel slip and wheel speed measurements, which guarantees bounded control action and thus copes with input constraints. The main advantage of the proposed controller with respect to a wheel slip controller based on a linearised model of the braking dynamics is that the closed-loop system properties allows one to detect if the current operating condition is such that the chosen wheel slip set-point determines a closed-loop equilibrium point which is beyond the peak of the tyre–road friction curve, thereby enabling us to adapt the set-point and yielding a significant enhancement of both performance and safety. This is a special feature of the proposed control law, which in general is not offered by other active braking control systems unless they are complemented with tyre–road friction estimators.