Singular perturbation stability conditions for adaptive control of a solar furnace with actuator dynamics

A solar furnace is a thermodynamic device that concentrates sun radiation in order to achieve high temperatures at a focus, where a sample of the material to be tested is located. This paper address the problem of designing a control architecture for solar furnaces. It is motivated by the use of a solar furnace as an instrument in material science research to perform two types of experimental tests. In first type, samples are tested in high temperature stress cycles. In these experiments it is important to control the temperature profile. The second test type is characterized by imposing a solar radiation flux profile. On both experiment types there are strong nonlinear effects, a significant degree of parametric uncertainty exists and there are disturbances, such as solar radiation fluctuation due to clouds and to sun´s apparent movement. The dominant dynamics is of first order and results from an energy balance performed at the sample. The actuator, consists in a mechanical shutter that reduces the fraction of solar radiation. Although the shutter is much faster than the thermic system, it may severely destabilize the overall controlled system. The contribution of this paper consists in the design of a control architecture for solar furnaces and the application of Singular Perturbation methods in order to derive conditions in the form of bounds for the speed of actuator dynamics so that the closed-loop system is stable.