Hybrid fuzzy control of the inverted pendulum via vertical forces

In this article, we look at the excellent effect of vertical force as regards the stabilization of the inverted pendulum (IP) and demonstrate how the fuzzy control design methodology can be used to construct a hybrid fuzzy control system that incorporates PD control into a Takagi–Sugeno fuzzy control structure for stabilizing the IP via a vertical force. By gaining an intuitive understanding of the dynamics of the IP, the IP state space is fuzzily divided into six regions. In each region, a PD controller is designed to satisfy the stability conditions obtained by Lyapunov’s direct and indirect methods. It shows that the proposed hybrid fuzzy control scheme provides a more flexible and intuitive way to stabilize the IP via a vertical force. © 2005 Wiley Periodicals, Inc.