基于干扰观测器的不确定非线性系统的预定性能控制

Disturbance observer based prescribed performance control of uncertain nonlinear systems

针对一类带有外界干扰及未知参数的严反馈非线性系统,提出新型的预定性能控制策略。首先,设计新型的障碍Lyapunov函数,实现跟踪误差的预定性能;其次,采用自适应律对未知参数进行估计,并构造干扰观测器对系统中的外界干扰进行估计,在此基础上设计反步控制器;为消除传统反步控制的"计算爆炸"问题,设计新型的一阶滤波器对虚拟控制输入的导数进行估计;再次,基于Lyapunov稳定性理论证明闭环系统的稳定性和跟踪误差的预定性能;最后,通过对永磁同步电机控制系统进行仿真验证所设计控制策略的有效性。

In this paper,a new prescribed performance control scheme is proposed for a class of nonlinear strict feedback systems with unknown parameters and external disturbance.Firstly,a novel barrier Lyapunov function is designed to achieve the prescribed performance of tracking error.Secondly,the adaptive law is proposed to tackle the unknown parameters,and the disturbance observer is designed to estimate the external disturbance in the system.In order to avoid the“explosion of terms”problem in traditional backstepping control,a new first-order filter is designed to estimate the time derivative of the virtual control inputs.Furthermore,on the basis of the Lyapunov theory,the stability of the closed-loop system and the prescribed performance of the tracking error are proved.Finally,the effectiveness of the control strategy is verified by the simulation of the permanent magnet synchronous motor system.