Optimal LQ-Feedback Regulation of a Nonisothermal Plug Flow Reactor Model by Spectral Factorization

Optimal LQ-feedback control for a class of first-order hyperbolic distributed parameter systems

“…[9]). This alternative method was successfully applied to a nonisothermal plug flow reactor in [4,5].…”

“…In [4,5], the Linear-Quadratic (LQ) problem is studied for a nonisothermal plug flow reactor model that represents a particular process described by first-order hyperbolic PDE's. In this paper, the LQ-optimal control problem is studied for a more general class of first-order hyperbolic PDE models by using a nonlinear infinitedimensional Hilbert state-space description.…”

Model Approximation and Simulations of a Class of Nonlinear Propagation Bioprocesses

“…An alternative to these classical numerical methods is the development of some techniques for the projection of the PDEs onto a low dimensional subspace. In accordance to these techniques, the original PDEs are transformed into a set of ordinary differential equations (ODEs) known as reduced order model (Aksikas et al, 2007;Americano da Costa Filho et al, 2009;Bouaziz & Dochain, 1993;Christofides, 2001;Dochain et al, 1992;Hoo & Zheng, 2001;Petre et al, 2007;Shvarstman et al, 2000). As a result, the first objective of this chapter is to provide the mathematical tools, which are used for most of numerical methods, for solving PDEs and, on this basis, to give a brief outline of the most commonly employed techniques.…”

“…Also, the controllability and observability properties would depend on the number of discretization points as well as its location and may lead to a poor control quality (Christofides, 2001). Due to these disadvantages, new methods based on spectral decomposition techniques, which take into account the spatially distributed nature of these systems, have developed (Aksikas et al, 2007;Shi et al, 2006). This approach uses the Galerkin method so as to approximate the system by a low-dimensional set of ODEs to design the controller (Aksikas et al, 2007;Shvarstman et al, 2000).…”

“…Due to these disadvantages, new methods based on spectral decomposition techniques, which take into account the spatially distributed nature of these systems, have developed (Aksikas et al, 2007;Shi et al, 2006). This approach uses the Galerkin method so as to approximate the system by a low-dimensional set of ODEs to design the controller (Aksikas et al, 2007;Shvarstman et al, 2000). In (Americano da Costa Filho et al, 2009) this approach is used in combination with the Lyapunov's direct method to derive stabilizing controllers applied in the case of chemical processes that are carried out in tubular reactors.…”