Stable and optimal fuzzy control of a laboratory Antilock Braking System

This paper discusse four new Takagi-Sugeno fuzzy controllers (T-S FCs) for the longitudinal slip control of an Antilock Braking System laboratory equipment. Two discrete-time dynamic Takagi-Sugeno fuzzy models of the controlled plant are derived based on the parameters in the consequents of the rules using the domains of the input variables, and doing the local linearization of the plant model. The original T-S FCs are designed by parallel distributed compensation to obtain the state feedback gain matrices in the consequents of the rules. Two T-S FCs are tuned by imposing relaxed stability conditions to the fuzzy control systems (FCSs) and the other two T-S FCs are tuned by the linear-quadratic regulator approach applied to each rule. Linear matrix inequalities are solved to guarantee the global stability of the FCSs. Real-time experimental results validate the original T-S FCs and design approaches.