Abstract
This paper proposes a method to guarantee robust stability for anti-lock braking system (ABS). The objective of ABS is to maintain slip rate at the optimal value in any road condition. The dynamics of ABS depends rationally on uncertain parameters, which are car velocity and friction coefficient between tire and road. We design a method to consider variation of these parameters. Since the friction coefficient cannot be estimated in real time, robust control is applied for any friction coefficient in the prescribed range. On the other hand, the car velocity can be estimated in real time. Gain scheduling control whose scheduling parameter is the car velocity is applied for ABS. Control law is designed to minimize the quadratic cost function, which is model of LQ control. The polytopic representation for the system with uncertain parameters is provided. By using descriptor representation and linear fractional transformation (LFT), we show that the system which is affine with respect to car velocity and friction coefficient can be obtained.Then, the problem is formulated as solving a finite set of Linear Matrix Inequalities(LMI). Finally, the robust stability and the robust performance are guaranteed theoretically. The effectiveness of the proposed method is illustrated by simulation and experiment.
