Interval type-2 fuzzy adaptive tracking control design for PMDC motor with the sector dead-zones

Abstract

This paper deals with the permanent magnet DC motor system with sector dead-zones and external disturbances via interval type-2 fuzzy adaptive tracking control scheme to achieve H∞ tracking performance. The type-2 fuzzy dynamic model is used to approximate the motor dynamics without constructing sector dead-zone inverse, where the parameters of the fuzzy model are obtained both from the fuzzy inference and online update laws. Based on the Lyapunov criterion and Riccati-inequality, the control scheme is derived to stabilize the closed-loop system such that all states of the system are guaranteed to be bounded and H∞ tracking performance is achieved due to uncertainties, dead-zone nonlinearities, and external disturbances. The advantage of the proposed control scheme is that it can better handle the vagueness or uncertainties inherent in linguistic words using fuzzy set membership functions with adaptation capability by linear analytical results instead of estimating non-linear system functions as the system parameters are unknown. Finally, the simulations of the PMDC motor system with sector dead-zone nonlinearities are used to illustrate the effectiveness of the proposed control scheme and the performance comparisons with the three-dimensional autonomous Ro¨ssler system (Wang and Chua, 2008) are used to validate the H∞ tracking performance of the PMDC motor system.