Dynamic Compensation For Infinite-dimensional Systems With Non-collocated Configurations

In this thesis,we study stabilization and output tracking for infinite-dimensional systems with non-collocated configurations.The research content is mainly divided into four-part:When the actuator/sensor is installed in a plant indirectly,the dynamics that connect the control plant and the actuator/sensor are referred to as actuator/sensor dynamics.In this indirect case,one has to compensate the actuator/sensor dynamics in the controller or observer design.In order to solve the non-collocated problems of this type,this thesis first con-siders an abstract actuator dynamics compensation problem,and the controller is designed based on the solution of the Sylvester operator equation.As an application,the Euler-Bernoulli beam dynamic compensation problem for an ODE(Ordinary Dif-ferential Equation)system is considered.One end of the Euler-Bernoulli beam acts on the ODE system,and the other free end of the beam is the control input port.Based on the above method,the corresponding controller is designed,and the well-posedness and exponential stability of the closed-loop system are proved by the semi group method and Lyapunov functional method.As the second example,we discuss a case in which an infinite-dimensional system is controlled by a finite-dimensional system:the dynamic compensation of the ODE actuator for an unstable heat system.As a dual problem of actuator dynamics compensation,this thesis studies the sensor dynamics compensation problems in system observation.As an application of the method,the dynamic compensation of the Euler-Bernoulli beam sensor for the ODE system is also considered.The ODE system acts on one free end of the Euler-Bernoulli beam,and the other end of the beam is the output port.The corresponding observer is designed to observe the whole cascade system.As a second application,the dynamic compensation of the ODE sensor for unstable heat system is also studied.In order to solve the non-collocated problem of measurement and control in sta-bilization for infinite dimensional systems,this thesis proposes an infinite dimensional dynamic compensator to exponentially stabilize an unstable wave system with vari-able coefficients.The wave is controlled at one end and has an unstable boundary condition and sensors at the opposite end.Based on the Backstepping method,a new output feedback controller is designed to stabilize the system exponentially.Based on separation principle,the well-posedness and exponential stability of the closed-loop system are proved by employing the semigroup theories and Lyapunov functional method.In order to solve the non-collocated problem in output tracking for infinite di-mensional systems,this thesis considers output tracking for a wave equation where the disturbance and output are non-collocated with the control end.Based on the idea of estimation/elimination,a new method based on trajectory planning is pro-posed to design the corresponding error-based feedback controller.The result shows that the error feedback controller can track the reference signal exponentially.As an application,this thesis discusses the case when the disturbance and the reference trajectory are harmonic signals.Some numerical simulations are presented to validate the effectiveness of the proposed control strategy.