Robust fuzzy control of mechanical systems

This paper considers the problem of controlling a mechanical system described by Euler-Lagrange equations to follow a desired trajectory in the presence of uncertainties. A fuzzy logic system (FLS) is used to approximate the unknown dynamics of the system. Based on the a priori information, the premise part of the FLS as well as a nominal weight matrix are designed first and are fixed. A compensation signal to the weight matrix error is designed based on Lyapunov analysis. To further reduce the tracking error due to the function reconstruction error, a second compensation signal is also synthesized. By running two estimators online for weight matrix error bound and function reconstruction error bound, the implementation of the proposed controller needs no a priori information on these bounds. Exponential tracking to a desired trajectory up to a uniformly ultimately bounded error is achieved with the proposed control. The effectiveness of this control is demonstrated through simulation and experiment results. These results also show that by incorporating a priori informations about the system, the fuzzy logic control can result good tracking behavior using a few fuzzy IF- THEN rules.