Algorithm for reducing the number of constraints of POD-based predictive controllers

This paper introduces an algorithm for reducing the number of temperature constraints of a POD-based predictive controller for a non-isothermal tubular reactor. Apart from keeping the process operating around some nominal conditions, the control system has to maintain the temperature inside the reactor below a certain limit in order to avoid undesirable side reactions. The controller uses a reduced order model of the process, which is derived by means of the proper orthogonal decomposition (POD) and Galerkin projection techniques. The use of a reduced order model is necessary due to the high dimensionality of the discretized system used to approximate the partial differential equations (PDEs) that model the reactor. Although a big order reduction can be obtained with the POD technique, this technique does not reduce the number of temperature constraints which is typically very large. The algorithm proposed in this paper reduces dramatically the number of temperature constraints, and consequently the memory needed for storing them and the time required for solving the optimization of the predictive controller.