Infinite-Dimensional LQ Control for Combined Lumped and Distributed Parameter Systems

Amir Alizadeh Moghadam
2013
Transport-reaction processes are extensively present in chemical engineering practice. Typically, these processes involve phase equilibria and/or are combined with well-mixed processes. Examples include counter-current two-phase contactors, interconnected CSTR-PFR systems and distillation columns. These processes belong to the class of distributed parameter systems and their mathematical description involves combinations of partial differential equations (PDEs) , ordinary differential equations
more » ... ferential equations (ODEs) and algebraic equations. The commonly used techniques for controlling such distributed parameter systems involve approximation of the PDEs with a set of ODEs and applying standard control methods for lumped parameter systems. It is recognized that such approximate methods may result in significant errors in the analysis and control synthesis for distributed parameter systems. Therefore, the accurate analysis and control synthesis for these systems require the development of methods based on the infinite-dimensional control system theories. The thesis focuses on the development of infinite-dimensional linear quadratic (LQ) control for distributed parameter systems described by combinations of hyperbolic PDEs, ODEs and algebraic equations. In order to solve the optimal control problem, the dynamical properties of the systems considered, including C 0 -semigroup generation, exponential stabilizability and exponential detectability, are explored. These properties provide guarantees of the existence and uniqueness of the solution to the optimal control problem. The technique used to design the LQ controller is based on solving an operator Riccati equation (ORE). This is achieved through finding the equivalent matrix Riccati equation, which can be solved numerically by using proposed algorithms. Several numerical simulation studies, including an interconnected CSTR-PFR process, a continuous countercurrent adsorption process of two interacting components in a moving-bed adsorber and a catalytic distillation process, are performed to demonstrate the theoretical results. L 2 (a, b) n Hilbert space of measurable integrable real-valued functions [a, b] → R n L ∞ (a, b) Space of bounded measurable real-valued functions [a, b] → R n L ∞ (a, b) n×n Space of bounded measurable real-valued functions [a, b] → R n×n
doi:10.7939/r30420 fatcat:wyly7z2khndeff72imyvxfhs6e