Trajectory Planning Approach to Output Tracking for a 1-D Wave Equation

In this article, we propose a trajectory planning approach to deal with various of the noncollocated configurations of output tracking through a one-dimensional wave equation. We mainly consider two noncollocated configurations: the performance output is noncollocated to the control input and the disturbance is noncollocated to the measurement output. By proper trajectory planning, the noncollocated configurations can be converted into the collocated ones so that the conventional method can be applied. An error-based feedback is proposed to realize the output tracking. Finally, as an application, the output tracking with general harmonic disturbance and reference signal are exemplified. Numerical simulation shows that the proposed approach is very effective.