Robust feed-back control of distributed chemical reaction systems

Abstract

There are many distributed processes in the chemical industry as it is the case of tubular reactors in which the parameters or the structure of the reaction terms are only a rough approximation of reality. In order to efficiently control this kind of systems, it is important to take into account this lack of detailed information (robustness). In this work, we make use of the classical theory on the robust nonlinear control for finite dimensional systems and extend it to distributed process systems by taking advantage of the special nature of dissipative systems. In this way, theoretical issues related to the nonlinearity of the diffusion terms and inhomogeneous boundary conditions are handled by means of the Kirchhoff and state transformations, respectively. In addition, and for practical reasons, the problem of controller saturation is considered. The different aspects of the methodology will be illustrated through a number of computational experiments concerning non-isothermal tubular reactors with convection and/or diffusion terms.

A robust multi-model predictive controller for distributed parameter systems

“…Note however that equivalent conclusions can be drawn for the more general case of v ≡ v(ξ) as it is described in [55]. The terms f (z) and p(ξ, t) represent the nonlinear reaction term and the, possibly distributed, control input, respectively.…”

“…As shown in [32,55] a field that obeys equations (1)- (4) is dissipative and therefore bounded in L 2 , provided that the control input field p(ξ, t) is bounded. On the other hand, since f (z) is Lipschitz, it is also bounded and thus belongs to L 2 .…”

“…In what follows some of the function arguments will be omitted for the sake of clarity. We assume that the system is dissipative in the sense of references [56,55]. This implies, among other things, that k in …”

“…3 The basis set has been previously normalized so that The first two terms on the RHS of Eq (B.2) were proved to be non positive in [55], therefore using Eq (5) with µ = 0 leads to:…”

Reducing computational time via order reduction of a class of reaction-diffusion systems

“…This approach avails of the spatial differential operator structure along with the Galerkin method to approximate the system by a lowdimensional set of ODEs [5].…”