A Novel Variable Exponential Discrete Time Sliding Mode Reaching Law

A new variable exponential discrete-time sliding mode control (DSMC) reaching law is proposed to suppress the chattering phenomenon and accelerate the reaching speed for the switching function. The variable exponential reaching law consists of two-phase different exponential term. The main effect of the first phase exponential reaching law is to reduce reaching steps. The second phase exponential reaching law can decrease the magnitude of quasi-sliding-mode domain (QSMD). Otherwise, the disturbance term is restrained by second order difference function which can also significantly diminish the range of QSMD. The reaching steps of the reaching law to converge to QSMD are derived from this new reaching law. Meanwhile, the dynamic analysis of the DSMC system based on new reaching law is presented. Finally, the mathematical simulations are conducted to preliminarily verify the results of theoretical analysis.