Fuzzy hierarchical swing-up and sliding position controller for the inverted pendulum–cart system

In this paper, a fuzzy hierarchical swing-up and sliding position controller is proposed for the swing-up and position controls of an inverted pendulum–cart system. The proposed fuzzy hierarchical swing-up and sliding position controller includes a fuzzy switching controller, a fuzzy swing-up controller, and a twin-fuzzy-sliding-position controller. The fuzzy switching controller is designed to smoothly switch between the swing-up and position controls. With the inverted pendulum–cart system decomposed into a pendulum subsystem and a cart subsystem, fuzzy sliding position controllers are presented to robustly balance the pendulum and cart at the desired positions. The sliding mode and stability of the fuzzy sliding position control systems are guaranteed. Moreover, an adaptive mechanism is provided to on-line adjust the parameters in the fuzzy sliding position controllers. Simulation results are included to illustrate the effectiveness of the proposed fuzzy hierarchical swing-up and sliding position controller.