Boundary optimal (LQ) control of coupled hyperbolic PDEs and ODEs

Authors:
Amir Alizadeh Moghadam;Ilyasse Aksikas;Stevan Dubljevic;J. Fraser Forbes
Affiliations:
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada and Department of Mathematics, Statistics and Physics, Qatar University, Doha, Qatar;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada
Venue:
Automatica (Journal of IFAC)
Year:
2013

Citing 5
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Brief paper: LQ control design of a class of hyperbolic PDE systems: Application to fixed-bed reactor

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Abstract

This contribution addresses the development of a linear quadratic (LQ) regulator for a set of hyperbolic PDEs coupled with a set of ODEs through the boundary. The approach is based on an infinite-dimensional Hilbert state-space description of the system and the well-known operator Riccati equation (ORE). In order to solve the optimal control problem, the ORE is converted to a set of matrix Riccati equations. The feedback operator is found by solving the resulting matrix Riccati equations. The performance of the designed control policy is assessed by applying it to a system of interconnected continuous stirred tank reactor (CSTR) and a plug flow reactor (PFR) through a numerical simulation.