Tracking Problem For Coupled One-Dimensional Wave Equations

Output regulation is a classical problem in control theory,which has been of great interest to researchers.This kind of problem has been applied more and more widely in practice.In this thesis,the tracking problem of coupled partial differential wave system is studied.The whole thesis includes four chapters.In the first chapter,we introduce the background and development of coupled partial differential tracking problem at home and abroad,and present the relevant preliminary definitions and lemmas.In the second chapter,we consider the following coupled system(?)where t and x stand for time and space variable,v*(x,t)represents the displacement of string in position x at time t,q>0 is the internal parameter of the couple strings,U(t)control input,yc(t)control output,and di(t),i=1,2,3 disturbances.This system describes the vibration behavior of series strings with internal coupling.We suppose that the disturbances di(t),i=1,2,3,and the given reference signal yref(t)are generated by the following exosystem:(?)We will use the backstepping method to design the controller so that the regulated output signal yc can track the reference signal yref asymptotically,i.e.lim t??(yc(t)-yref(t))=0.In the third chapter,we consider the following coupled partial differential sys-tems (?),where-U(t)is the input(control),ym(t)the measured output,yc the regulated output signal,d(t)represents the general disturbance,k>0 is a damping constant.In this chapter,we consider performance output tracking for coupled wave equations with general external unmatched disturbance.An observer is designed first to estimate the state and disturbance simultaneously.Then we construct a servo system determined completely by the measured output and the reference signal which in turn gives a dynamics of reference signal.In the following,an output feedback controller is designed based on this observer and servo system.It is shown that the closed-loop system is well-posed and the performance output is tracking the reference signal.Finally,we present some numerical results to illustrate the effectiveness of the controller.Chapter four concludes this thesis and presents some research works in the future.