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.