Performance Output Tracking for a One-Dimensional Wave-Heat Cascade System with Unmatched Disturbance

The objective of this paper is to solve the performance output regulation problem for a wave-heat cascade system with unmatched disturbance. Applying the series expansion, the auxiliary trajectory for the cascade system is constructed and the unmatched disturbance is rejected. Meanwhile, the controller and observer only based on error signal are designed, and the performance output regulation problem is solved. Under the control feedback, the performance output can track the reference signal, and the regulation error goes to zero asymptotically. Finally, some numerical simulations are presented for illustration.

[1]  Bao-Zhu Guo,et al.  A New Active Disturbance Rejection Control to Output Feedback Stabilization for a One-Dimensional Anti-Stable Wave Equation With Disturbance , 2017, IEEE Transactions on Automatic Control.

[2]  M. Krstić,et al.  Boundary Control of PDEs , 2008 .

[3]  Seppo Pohjolainen,et al.  Robust controller design for infinite‐dimensional exosystems , 2014 .

[4]  Seppo Pohjolainen,et al.  The Internal Model Principle for Systems with Unbounded Control and Observation , 2014, SIAM J. Control. Optim..

[5]  Shuxia Tang,et al.  Stabilization for a coupled PDE-ODE control system , 2011, J. Frankl. Inst..

[6]  Miroslav Krstic,et al.  Adaptive error feedback regulation problem for 1D wave equation , 2018, International Journal of Robust and Nonlinear Control.

[7]  Miroslav Krstic,et al.  Compensating a string PDE in the actuation or sensing path of an unstable ODE , 2009, 2009 American Control Conference.

[8]  Hongyinping Feng,et al.  Performance output exponential tracking for a wave equation with a general boundary disturbance , 2016, Syst. Control. Lett..

[9]  Bao-Zhu Guo,et al.  The active disturbance rejection control approach to stabilisation of coupled heat and ODE system subject to boundary control matched disturbance , 2015, Int. J. Control.

[10]  M. Krstić.  Boundary Control of PDEs: A Course on Backstepping Designs , 2008 .

[11]  Jun‐min Wang,et al.  Output Tracking for One‐Dimensional Schrödinger Equation subject to Boundary Disturbance , 2018 .

[12]  Joachim Deutscher,et al.  Output regulation for coupled linear parabolic PIDEs , 2019, Autom..

[13]  David S. Gilliam,et al.  The State Feedback Regulator Problem for Regular Linear Systems , 2014, IEEE Transactions on Automatic Control.

[14]  Bao-Zhu Guo,et al.  Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance , 2016, Int. J. Control.

[15]  Seppo Pohjolainen,et al.  Internal Model Theory for Distributed Parameter Systems , 2010, SIAM J. Control. Optim..

[16]  Hua-Cheng Zhou,et al.  Solving the regulator problem for a 1-D Schrödinger equation via backstepping , 2017 .

[17]  Wei Guo,et al.  Performance output tracking for a wave equation subject to unmatched general boundary harmonic disturbance , 2016, Autom..

[18]  Bao-Zhu Guo,et al.  Performance boundary output tracking for one-dimensional heat equation with boundary unmatched disturbance , 2018, Autom..

[19]  Bao-Zhu Guo,et al.  Performance output tracking for one-dimensional wave equation subject to unmatched general disturbance and non-collocated control , 2017, Eur. J. Control.