一种基于指数趋近律的非线性系统变结构轨迹跟踪控制新方法

针对多输入多输出二阶不确定非线性机械系统中轨迹跟踪控制的问题,提出一种新的基于指数趋近律的滑模变结构控制方法,用于提高系统的平稳性和快速性。在滑模变结构控制器设计过程中采用一种新的指数趋近律以改进闭环系统的暂态和稳态响应性能,使系统跟踪误差收敛速度加快,特别是减少轨迹跟踪误差到达滑模面的时间,同时提高了系统轨迹跟踪过程的平稳性。通过采用边界层方法消除滑模控制输入抖振问题,避免控制过程中执行器的频繁切换,进一步提高所提出滑模控制器在实际系统中的实用性。基于李雅普诺夫稳定性理论证明了闭环系统的稳定性和跟踪误差的收敛性。数值仿真验证了所提出的控制方法的有效性。

A Novel Exponential Reaching Law-Based Variable Structure Trajectory Tracking Control Method for Nonlinear Systems

Aiming at the problem of trajectory tracking control in uncertain multi-input multi-output second-order nonlinear mechanical systems,a new sliding mode variable structure control method based on exponential reaching law is proposed to improve the smoothness and speed of the system.A new exponential reaching law is used in the design process of the sliding mode variable structure controller to improve the transient and steady-state response performance of the closed-loop system so that the convergence speed of the system tracking error is accelerated,and the trajectory tracking process is smoother,especially the time for the trajectory tracking error to reach the sliding mode surface is reduced,and the smoothness of the system trajectory tracking process is improved.Pacticability of the proposed sliding mode controller in practical systems is further improved by adopting the boundary layer method to avoid the frequent switch of the actuator and alleviate the chattering problem of the sliding mode control input.Based on Lyapunov stability theory,the stability of the closed-loop system and the convergence of tracking error is proved.Numerical simulation verify the effectiveness of the proposed control method.