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LQ control design of a class of hyperbolic PDE systems: application to fixed-bed reactor. (English) Zbl 1166.49033
Summary: A general linear controller design method for a class of hyperbolic linear Partial Differential Equation (PDE) systems is presented. This is achieved by using an infinite-dimensional Hilbert state-space description with infinite-dimensional (distributed) input and output. A state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation in the space variable. The proposed method is applied to a fixed-bed chemical reactor control problem, where one elementary reaction takes place. An optimal controller is designed for linearized fixed-bed reactor model, it is applied to the original nonlinear model and the resulting closed-loop stability is analyzed. Numerical simulations are performed to show the performance of the designed controller.

MSC:
49N10 Linear-quadratic optimal control problems
35L40 First-order hyperbolic systems
93C20 Control/observation systems governed by partial differential equations
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