Braking Control Systems Design: Actuators with Discrete Dynamics

As discussed in the previous chapters, the design of automatic braking control systems is highly dependent on the braking system characteristics and actuator performance. This chapter addresses the problem of designing an ABS controller based on a hydraulic actuator system with on/off dynamics, which is capable of providing only three control actions: namely, one can only

increase

,

hold

and

decrease

the brake pressure.

Clearly, the control objectives must be traded off with the braking system capabilities. Accordingly, the aim of the control system will be that of maintaining the wheel slip around acceptable values, thus avoiding wheel locking, abandoning the goal of regulating it around a constant single value as was done in the preceding chapter for the case of a braking system with continuous dynamics.

To solve this problem, we will design a switching controller that yields closed-loop dynamics that converge to an asymptotically stable limit cycle.

For this control system, we provide necessary conditions for the limit cycle existence, which come from a detailed analysis of the state plane trajectories of the resulting braking dynamics. Further, the limit cycle stability properties are formally proved

via

a Poincaré map analysis (the interested reader may refer to Section A.2.2 for an introduction to the analysis tools used in this chapter).