This paper considers output tracking for a one-dimensional wave equation with general disturbance which includes both internal nonlinear uncertainty and external disturbance. The performance output is non-collocated to the control. The disturbance is estimated by an essentially extended state observer from active disturbance rejection control and the difficulty caused by the non-collocated configuration of control and output is overcome by a proper trajectory planning. An output feedback law is proposed to make the tracking error be convergent to zero exponentially as time goes to infinity. At the same time, all states of the closed-loop system are shown to be uniformly bounded. Numerical simulation is also presented to validate the theoretical results.

本文考虑具有一般干扰的一维波动方程的输出跟踪，其中包括内部非线性不确定性和外部干扰。性能输出未与控件并置。干扰由活动干扰抑制控制的基本扩展状态观察者估计，并且通过适当的轨迹规划可以克服由控制和输出的非并置配置引起的困难。提出了一种输出反馈定律，以使跟踪误差随着时间达到无穷大而指数级收敛至零。同时，闭环系统的所有状态均显示为均匀有界。还进行了数值模拟以验证理论结果。