Controller design for hybrid systems using simultaneous D-stabilisation and its application to anti-lock braking systems (ABS)

摘要

In recent years hybrid systems have been widely studied. Many controller design approaches are based on a state space plant model and use full state feedback to satisfy certain stability conditions, for example, the existence of a common Lyapunov function. Pole assignment and LMI-based controller design techniques have also been used. A new controller design method, called simultaneous D-stabilisation and strong simultaneous D-stabilisation, is developed, which can deal with the multiple plant requirement resulting from hybrid systems. Both the simultaneous stabilisation problem (SSP) and strong simultaneous stabilisation problem (SSSP) with the simplest Hurwitz stability requirement are open problems in the control community. In this paper, the new synthesis approach developed is extended to the general D-stability requirement rather than simply the Hurwitz-stability requirement. The advantages of this approach include 1) the desired D-stability region can be of any form and be connected or disjoint. This leads to a unified treatment of continuous and discrete systems, and consequently encompasses the Hurwitz and Schur stability regions as special cases; 2) the size of the family of plants may be finite and more than three, which is the upper bound with the available approaches; 3) both the SSPs and the SSSPS can be dealt with in a unified way, although an SSSP is more complicated than an SSP; 4) the traditional PID-controller tuning problem can be treated within this general framework. The SSP approach is then applied to the synthesis of a robust controller for a typical application in the automotive industry, controller design for anti-lock braking systems (ABS). The controller robustly assigns the closed-loop poles for every plant from different tyre friction models in a prescribed D region. Simulation results with the DaimlerChrysler test vehicle for ABS will also be presented.