Rule regulation of fuzzy sliding mode controller design: direct adaptive approach

Abstract

On the basis of sliding mode control (SMC), a fuzzy sliding mode controller (FSMC) synthesized through rule adaptation is proposed in this paper. There are two sets of control rule bases. The first set is utilized to approach the equivalent control of SMC according to the adaptive scheme. Another set is used to attenuate the hitting control of SMC in the sense of heuristic. In particular, instead of several tuning parameters needed in conventional fuzzy adaptive approaches, only one tuning factor is characterized to adapt the control rules. The results show that the rule adaptive FSMC system is stable in the sense of Lyapunov under giving a common Lyapunov function. This direct rule adaptive FSMC is synthesized through the following stages. First, the control rules are constructed according to the concepts of SMC, and the fuzzy sets, whose membership functions are symmetrically covered in the state space, are defined. Then, the derived adaptive law is applied to adjust the given parameter for changing the control rules to meet system dynamic. This FSMC is employed to approximate the equivalent control of SMC under the situations of the mathematical model of controlled system is unknown. Third, the hitting control, which guarantees the stability of control system, is developed. Finally, the hitting control signal is smoothed via the constructed heuristic control rules. We apply this FSMC to control a nonlinear inverted pendulum system for demonstrating the availability of the proposed approach.