T-S Fuzzy Tracking Control Based on H∞ Performance with Output Feedback for Pendulum-Cart System

Abstract

In some practices, not all state variables are available because of limited or noisy measurements. Thus, via output feedback, an observer is used to estimate the unmeasured states. To apply linear controllers to the pendulum-cart system, the Takagi-Sugeno fuzzy model is utilized by linearizing the system in more than one operating point. The effect of disturbances on tracking performance is reduced to the prescribed attenuation level by H∞ performance. The stability of the whole closed-loop system is investigated using the Lyapunov function.  Sufficient conditions are derived in terms of a set of Linear Matrix Inequality (LMI) to obtain the controller and observer gain. Simulation results show that the proposed control method can make the system track the sinusoidal reference signal, maintain stability, and attenuate the effect of disturbances to less than the prescribed attenuation level measured by L2 gain. In the implementation process, an adjustment is needed to move the observer’s pole and speed up the observer’s responses.