Nonlinear Temperature Regulation of Solar Collectors with a Fast Adaptive Polytopic LPV MPC Formulation

TL;DR

This paper presents an adaptive nonlinear MPC approach for solar collector temperature regulation using LPV modeling, which outperforms traditional linear and robust MPC methods in tracking and disturbance rejection.

Contribution

It introduces a novel LPV-based adaptive MPC formulation with a two-QP scheme for improved nonlinear temperature control in solar collectors.

Findings

The proposed MPC outperforms linear MPC in tracking accuracy.

The method demonstrates superior disturbance rejection.

Computational effort remains feasible for real-time implementation.

Abstract

Temperature control in solar collectors is a nonlinear problem: the dynamics of temperature rise vary according to the oil flowing through the collector and to the temperature gradient along the collector area. In this way, this work investigates the formulation of a Model Predictive Control (MPC) application developed within a Linear Parameter Varying (LPV) formalism, which serves as a model of the solar collector process. The proposed system is an adaptive MPC, developed with terminal set constraints and considering the scheduling polytope of the model. At each instant, two Quadratic Programming (QPs) programs are solved: the first considers a backward horizon of N steps to find a virtual model-process tuning variable that defines the best LTI prediction model, considering the vertices of the polytopic system; then, the second QP uses this LTI model to optimize performances along a forward horizon of N steps. The paper ends with a realistic solar collector simulation results, comparing the proposed MPC to other techniques from the literature (linear MPC and robust tube-MPC). Discussions regarding the results, the design procedure and the computational effort for the three methods are presented. It is shown how the proposed MPC design is able to outrank these other standard methods in terms of reference tracking and disturbance rejection.