Experimental validation of LMI approaches for robust control design of a spatially three-dimensional heat transfer process

In this paper, two alternative control procedures are compared for a spatially three-dimensional distributed heating system. In both cases, the system model is derived as a finite volume representation that assumes a piecewise homogeneous distribution of the temperature in each finite volume element. The parameterization of both control strategies is performed by using linear matrix inequalities in combination with a polytopic model for uncertain system parameters. The basic difference between both implementations is that either parameter-independent or parameter-dependent candidates for Lyapunov functions are assumed in the derivation of the control laws. It is shown experimentally that both approaches lead to an accurate tracking of smooth temperature trajectories. However, the parameter-dependent approach is less conservative and, in such a way, leads to a smaller amplification of measurement noise in an observer-based closed-loop control structure.