Output Tracking for One-Dimensional Wave Equation with Non-Collocated Control and Output Configuration

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.