Positive Polynomial Constraints for POD-based Model Predictive Controllers

This paper presents an application of positive polynomials to the reduction of the number of temperature constraints of a proper orthogonal decomposition (POD)-based predictive controller for a non-isothermal tubular reactor. The objective of the controller is to maintain the reactor at a desired operating condition in spite of disturbances in the feed flow, while keeping the maximum temperature low enough to avoid the formation of undesired byproducts. The controller is based on a model derived by means of POD, which reduces the high dimensionality of the discretized system used to approximate the partial differential equations that model the reactor. However, POD does not lead to a reduction in the number of temperature constraints which is typically very large. If we use univariate polynomials to approximate part of the basis vectors derived with the POD technique, it is possible to apply the theory of positive polynomials to find good approximations of the temperature constraints by linear matrix inequalities and to get a reduction in their number. This is the approach that is followed in this paper. The simulation results show that the predictive controller presented a good behavior and that it dealt with the temperature constraints very well.