Low-cost fuzzy control approaches to a class of state feedback-controlled servo systems

This paper offers two low-cost Takagi-Sugeno state feedback fuzzy controllers (T-S SFFCs) dedicated to the position control of a class of servo systems. The process of this class of servo systems is characterized by second-order linear dynamics with an integral component, and a saturation and dead zone input static nonlinearity. A discrete-time dynamic Takagi-Sugeno (T-S) fuzzy model of the process that consists of ten rules is derived. The discrete-time dynamic T-S model merges ten discrete-time linear local models of the process in the rule consequents. The original T-S SFFCs are designed by parallel distributed compensation to obtain the state feedback gain matrices in the rule consequents. One of the T-S SFFCs is designed by pole placement and by imposing relaxed stability conditions to the fuzzy control system (FCS). The other T-S SFFC is designed by the linear-quadratic regulator approach applied to each rule. Linear matrix inequalities are solved to guarantee the global stability of the FCSs. A case study related to the position control of a DC servo system laboratory equipment is included. Real-time experimental results validate the original low-cost T-S SFFCs and their design approaches.