一种新颖的滑模非线性比例积分混沌控制方法

一种新颖的滑模非线性比例积分控制方法（SMNPIC）被提出用于高精度驱动一类时变不确定混沌系统到任意期望轨道。SMNPIC区别于以前的滑模控制技术之处在于滑动模的一个非线性比例积分函数被包含在控制率中，因此不仅稳态误差和高频抖振都被减小，同时鲁棒性和快速性也能被保证。此外，SMNPIC实际上能被作为一类非线性PID控制器，不仅仅跟踪误差及其直到n-1阶微分被考虑，而且跟踪误差的积分也被考虑，因此有比传统PID更多的有用信息能被使用，因此更好的动静态特性能被获得。通过不确定Duffing-Holmes系统的仿真实例证实了SMNPIC用于混沌控制能获得好的性能。

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

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.