Design of a Fuzzy Controller With Fuzzy Swing-Up and Parallel Distributed Pole Assignment Schemes for an Inverted Pendulum and Cart System

In this paper, the inverted pendulum and cart system is effectively approximated by a Takagi-Sugeno (T-S) fuzzy model in a small range of angle near its equilibrium state. According to the proposed (T-S) fuzzy model of the inverted pendulum and cart system, a fuzzy controller designed with the parallel distributed pole assignment scheme is adopted to position the pendulum and cart at the desired states. The nonlinear friction is also considered. Moreover, a fuzzy swing-up controller is developed to swing up the pendulum on a limited rail under the constraints of control actions. Further, the stability of the inverted pendulum and cart system with the fuzzy parallel distributed pole assignment controller is studied. Simulation results are included to indicate the effectiveness and robustness of the proposed fuzzy controller.