Optimal LQ-Feedback regulation of a nonisothermal plug flow reactor model by spectral factorization
(2007) IEEE Transactions on Automatic Control — Vol. 52, n° 7, p. 1179-1193 (2007)
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- Abstract
- The linear-quadratic (LQ) optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional Hilbert state space description. First the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied: it is shown that it is exponentially stable and (approximately) reachable. Next the general concept of LQ-feedback is introduced., It turns out that any LQ-feedback is optimal from the input-output viewpoint and stabilizing. For the plug flow reactor linearized model, a state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation (MRDE) in the space variable. Thanks to the reachability property, the computed LQ-feedback is actually the optimal one. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed. A criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed-loop system. Moreover, under the same criterion, it is shown that the control law designed previously is optimal along the nonlinear closed-loop model with respect to some cost criterion. The results are illustrated by some numerical simulations.
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Aksikas, I., Winkin, J., & Dochain, D. (2007). Optimal LQ-Feedback regulation of a nonisothermal plug flow reactor model by spectral factorization. IEEE Transactions on Automatic Control, 52(7), 1179-1193. https://doi.org/10.1109/TAC.2007.900823 (Original work published 2007)