  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.
