Material derivative based control of a solar parabolic trough field

This paper considers the temperature control of a concentrating solar power (CSP) parabolic trough system, where sun energy is harvested to produce thermal and electrical energy. In this process, the temperature of the heat transfer fluid depends on the solar power variability and on the solar exposure time and is described by a partial differential equation (PDE). To control the temperature, the speed of the fluid is used as the the manipulated variable. The dynamics of this process is usually represented using a time-varying state space model. The solution of the PDE is interpreted from the material derivative description point of view and is used to formulate an optimal constrained control problem of the state of an infinitesimal volume element, defined by its temperature and its position, with free final time and fix terminal state. The control problem is then extended to the whole fluid inside the pipe, where the state of the fluid is represented by the set of states of infinitesimal volume elements without the need to use a time-varying state space model of the process. From this work, a control law with simple structure is obtained that fulfills the performance objectives.