Design and implementation of a robust fuzzy controller for a rotary inverted pendulum using the Takagi-Sugeno descriptor representation

The rotary inverted pendulum (RIP) is an under-actuated mechanical system. Because of its nonlinear behavior, the RIP is widely used as a benchmark in control theory to illustrate and validate new ideas in nonlinear and linear control. This paper presents a robust Takagi-Sugeno (T-S) fuzzy descriptor approach for designing a stabilizing controller for the RIP with real-time implementation. It is shown in this paper how the modeling of the physical system on descriptor T-S form with a reduced number of rules possible can lead to a simplified controller that is practically implementable. Relaxed linear matrix inequality-based stability conditions for the non quadratic case are given. Experimental results illustrate the effectiveness of the proposed approach.