PID control design for a class of second-order nonlinear systems based on extended Takagi-Sugeno fuzzy models

In this paper we mainly focus on the design of updated laws for the coefficients in PID controllers for a class of second-order nonlinear systems. Fuzzy logic systems have the advantages in approximating nonlinear uncertain functions, furthermore, the consequent of a Takagi-Sugeno (TS, for short) fuzzy model contains the linear combination of the base functions with input signals which makes it feasible to introduce TS fuzzy logic system (TSFLS, for short) to compose the PID controller. In this paper we attempt to realize the aforementioned idea by designing a PID controller based on extended TS fuzzy models, with sliding mode and adaptive control methods, such design makes up for the general lack of conventional PID controllers design in some degree.