State Estimation and Servo-control of Distributed Parameter Systems

Abstract

The dynamics of many chemical and mechanical processes are influenced by both temporal and spatial factors and these processes are called distributed parameter systems (DPS). Moreover, their mathematical models are given by partial differential equations (PDE) and they belong to infinite-dimensional systems. Due to the existence of the spatial variable in the mathematic model, the state estimation and control of the distributed parameter systems are interesting and challenging. The focus of this thesis is to develop the optimal state estimation method and servo-control (output regulation) methods in the optimal and internal-model framework. To address the control problems for finite and infinite dimensional systems, the full state information is usually necessary. In this thesis, an optimal state estimation method is developed for spectral distributed parameter systems to account for full state estimation problems with state constraints due to physical limitations. In particular, a modal decomposition technique is applied to reduce the order of the considered dissipative systems that are assumed to satisfy the decomposition assumption. With the full state information of the control systems, the proposed servo-control approaches in this thesis are able to implement. In this thesis, two types of servo-control (output regulation) are considered: Internal Model Control (IMC) and Optimal control. In fact, the servo-control includes two aspects: stabilization and reference signal tracking. In the aspect of the stabilization, an operator Riccati equation approach and a weak variational optimal method are developed for the first order hyperbolic PDE systems in this thesis. For the aspect of the reference trajectory tracking, novel output feedback and error feedback regulators are developed to deal with the distributed and/or boundary tracking control problems for general distributed parameter systems. Finally, the servo-control problems for the countercurrent heat exchanger, the plug flow reactor and the solar-thermal district heating system are addressed in the application part of this thesis. In particular, for the countercurrent heat exchanger, the proposed output regulation approach is applied; for the plug flow reactor, the proposed weak variational optimal stabilization and the output regulation method are combined and applied; and for the solar-thermal district heating system, the receding horizon optimal control and the output regulation approach are implemented to solve the energy maximization and the reference tracking problems.