Optimal control of a distributed solar collector field

The dynamics of a distributed solar collector field can be modelled by a nonlinear hyperbolic partial differential equation (PDE) based on the energy balance. The model-based optimal control of the outlet temperature is studied. One of few ways to influence the outlet temperature is by adjusting the oil pump volumetric flow rate. In this work, an optimal algorithm is developed to minimize the mismatch between the outlet temperature and a desired temperature. The method is based on the adjoint approach for constrained optimization problems with a nonlinear hyperbolic PDE applied as an optimization constraint. In particular, the algorithm simplifies a problem by decomposing it into a two-level optimization problem. Unlike the traditional tracking control such as motion planing, the reference tracking equations in this work do not need state trajectory generation. Finally, the proposed approach is verified to perform well via a computer simulation.