A novel sliding mode nonlinear proportional-integral control scheme for controlling chaos

摘要

A novel sliding mode nonlinear proportional-integral control (SMNPIC) scheme is proposed for driving a class of time-variant chaotic systems with uncertainty to arbitrarily desired trajectory with high accuracy. The SMNPIC differs from the previous sliding mode techniques in the sense that a nonlinear proportional-integral action of sliding function is involved in control law, so that both the steady-state error and the high-frequency chattering are reduced, and meanwhile, robustness and fastness are guaranteed. In addition, the proposed SMNPIC actually acts as a class of nonlinear proportional-integral-differential (PID) controller, in which the tracking error and its derivatives up to (n-1)th order as well as the integral of tracking error are considered, so that more useful information than traditional PID can be implemented and better dynamic and static characteristics can obtained. Its good performance for chaotic control is illustrated through a Duffing-Holmes system with uncertainty.