Distributed Output Bounded Bilinear Tracking Control of a Parabolic Trough Solar Collector

This paper deals with the problem of constrained bilinear control of a parabolic trough solar collector (PTSC) in the infinite-dimensional setting. The PTSC is modeled by a 1<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup>-order hyperbolic PDE, and the objective is to drive the tube's outlet temperature to track a desired profile. The fluid's velocity is the manipulated variable, and that leads to a bilinear control problem. In addition, due to physical and technical considerations, control constraints are imposed. First, based on Lyapunov's stability theory, we design a distributed state-feedback controller that guarantees point-wise exponential stabilization of the tracking error. Then, since only boundary measurements are available, we develop an observer-based controller that stabilizes the tracking error asymptotically. Simulation results attest to the performance of the proposed control method.