Adaptive Backstepping Sliding Mode Control of Uncertain Semi-Strict Nonlinear Systems and Application to Permanent Magnet Synchronous Motor

A disturbance observer(DOB)based-backstepping sliding mode control scheme is discussed for a class of semi-strict nonlinear system with unknown parameters and mismatched uncertainty.Firstly,adaptive technique and DOB are respectively applied to tackle the unknown parameters and mismatched uncertainty,where the DOB can effectively alleviate the chattering problem of sliding mode control(SMC).Then,exponential sliding mode surface is proposed to improve the convergence rate of the sliding mode state.The‘explosion of complexity’problem inherent in conventional backstepping control is overcome by designing the novel first-order filter.The stability of the closed-loop system is analyzed in the framework of Lyapunov stability theory,in which the tracking error converges to an arbitrarily small neighborhood around zero(ASNZ).At last,two examples are given to illustrate the effectiveness of the proposed control strategy.