Fuzzy swinging-up with sliding mode control for third order cart-inverted pendulum system

Abstract

Cart Inverted Pendulum (CIP) system is a benchmark problem in nonlinear automatic control. In this paper, two third-order differential equations were derived to create a combining model for the cart-pendulum with its DC motor dynamics. Motor voltage was considered the system input in the presented model. The friction between the cart and rail was included in the system equations through a nonlinear friction model. Fuzzy Swinging-up controller was designed to swing the pendulum to the upright position, once reaching the upward position; Sliding Mode Controller (SMC) is activated, to balance the system. In order to verify the performance of the proposed SMC, a Linear Quadratic Regulator Controller (LQRC) was suggested and compared with the proposed SMC. Simulation and experimental results have shown a significant improvement of the proposed SMC over LQRC where, the pendulum angle oscillations were decreased by 80% in the real implementation.