Non-collocated Control For A Class Of Linear Parabolic Distributed Parameter Systems

In engineering practice,most of the actual physical processes(or systems)have spatial distribution characteristics,which cann't be described by ordinary differen-tial equations,while must be described by partial differential equations accurately.Generally,such systems described by partial differential equations are called dis-tributed parameter systems.Distributed parameter systems are related to both time and space,and have strong practical application backgrounds,such as the vibration problem of spacecraft,temperature control problems in industrial manufacturing,diffusion problems in chemical reaction,and noise problems in life.Parabolic dis-tribution parameter systems are widely used in reaction diffusion problems such as tube-flow,chemical reaction and heat exchange.Parabolic distributed parameter systems have the typical characteristics of distributed parameter systems,so study-ing the parabolic distributed parameter systems has universal significance.The problem of non-collocated control for a class of linear parabolic distributed parameter systems has been studied in this paper.The main contents and achieve-ments are listed as follows:(1)For a class of unstable linear parabolic distributed parameter systems,the static output feedback controller is designed by using the collocated pointwise con-trol and piecewise control respectively,which solves the stability problem of the system under the collocated control.(2)For a class of unstable linear parabolic distributed parameter systems,point-wise measurement and piecewise measurement are adopted to design the Luenberg-er observer to track the state of the system,then the estimation error system is con-structed.The stability of the estimation error system is studied,and the problem that the state of the system is difficult to measure is solved.(3)For a class of unstable linear parabolic distributed parameter system,four forms of non-collocated control such as non-collocated pointwise control and point-wise measurement,non-collocated piecewise control and piecewise measurement,non-collocated piecewise control and pointwise measurement,non-collocated point-wise control and piecewise measurement are adopted.For the non-collocated prob-lem of actuators and sensors,an observer is constructed to observe the collocated state of the system.The Luenberger observer-based dynamic output feedback con-troller is designed,and the stability problem of the system under the non-collocated control is solved.(4)For a class of unstable linear parabolic distributed parameter system with measurement disturbance,non-collocated piecewise control and piecewise mea-surement is adopted to design the H? observer-based dynamic output feedback con-troller,and then the stability problem of the system with measurement disturbance is solved.(5)For the temperature control system of catalytic rod reaction,the spatiotem-poral dynamics model of the catalytic rod temperature is first established.Then the non-collocated control theory and achievements of the linear parabolic distribut-ed parameter system are adopted to solve the temperature control problem of the catalytic-rod reaction and ensure the normal progress of the catalytic reaction.