Performance Output Tracking For Several Types Of Heat Equations Subject To Boundary Control With Uncertain Disturbance

Distributed parameter systems are the control systems with infinite dimensions,and generally described by partial differential equations,integral equations,functional differen-tial equations,differential integral equations or some abstract differential equations defined in Banach or Hilbert space.Recently,The study of partial differential control system with the external disturbance becomes internationally hotspot and difficulties research in the dis-tributed parameter systems control field.The current research mainly adopts the methods of the variable structure sliding mode control and the active disturbance rejection control to designed the feedback control to offset or suppress the disturbance.Finally,let the state of closed-loop system near zero.However,in the practical problem,we are usually interested in how to set the controller based on the output feedback,so that the output of the system is tracking the non-zero reference signal.Such research is very important in robot application.Our main idea is to design a state reference system determined completely by the measured output and reference signal,then designed the output feedback control to make the closed-loop system is well-posed.At the same time,three control objectives are achieved:1)the performance output is tracking the reference signal;2)all the internal-loops are bounded;3)the closed-loop is stable when the disturbance and reference signal are disconnected.This paper will focus on performance output tracking for infinite dimensional system with the general bounded external disturbance and several kinds of heat equations are detailed analyzed.The overall structure of this paper is as follows:In Chapter 1,the background and significance of this paper,the research status at home and abroad of the related content are presented.Besides,some necessary basic knowledge are illustrate,include the Linear operator semigroup theory,Riesz basic,C0-semigroup theory etc.necessary research tools.In Chapter 2,we study performance output tracking for heat equation with the external boundary disturbance.In order to study the performance output tracking of the system,a reference signal is given,firstly design the state observer according to the reference signal,then studies the error system of observation system and the original state system,next controller is design to stabilize the error system and prove the closed-loop system is bounded,thereby prove that the performance output is tracking the given reference signal.In Chapter 3,the performance output signal of heat equation with boundary disturbance is improved,that is,using the form of integral to track the reference signal.For the perfor-mance output tracking of parabolic system,we studied equation in the state space L2(0,1),the output of the integral form is more meaningful than the output of the form of point.So we designed a system controller based on the output of the integral form,thus performance output with the form of integral is tracking the given reference signal asymptotically.In Chapter 4,we study performance output tracking for one-dimensional heat equation with the unmatched disturbance.Unlike the first chapter,the disturbance of this chapter is unmatched,that is to say,disturbance at the one end and the control at the other end,so the disturbance cannot be offset by control directly.Hence we designed the estimator to estimate disturbance,different from the common methods,we use the infinite dimensional system to estimate disturbance in this chapter,such that the exponential convergence of the performance output tracking can be obtained.