A velocity control of frictional servosystems using an adaptive fuzzy control

Based on the system relative degree, the frictional servosystem is transformed into external and internal parts. By using a feedback linearizing control, the external part becomes a linear dynamic system with uncertainties. A reference model with the desired amplitude and phase properties is given to obtain an error dynamics in the presence of uncertainties. The unmatched uncertainty is also examined. To improve the system performance, an online fuzzy model is employed to model these uncertainties in a compact subset. An updating law with e-modification for the weight of fuzzy model is designed to obtain an effective learning of the uncertainties. Then, an equivalent control using the known part of frictional servosystem and the learning fuzzy model of uncertainties is established to achieve the desired result. The unmodeled dynamics caused by the error of the approximated fuzzy model and estimated weight are tackled by a switching control. In summary, the adaptive fuzzy control includes two parts: a feedback linearizing control with a reference model and an adaptive fuzzy variable structure control. The stability of the overall system is then verified by Lyapunov theory so that the uniformly ultimately bounded tracking is accomplished. Simulations are also presented to verify the usefulness of the proposed control