The Method of Integro-Differential Relations for Control of Spatially Two-Dimensional Heat Transfer Processes

The design of control strategies for distributed parameter systems is an important field of current research. To design control laws and state estimation procedures for this class of systems, it is essential to find approximations that represent the system dynamics with good accuracy and simultaneously allow for an evaluation in real time. Moreover, possibilities for the quantification of approximation errors are useful to determine reliable finite-dimensional models which are sufficiently accurate for the control task at hand. Approximation errors result from the replacement of the original system model that is given in terms of partial differential equations by a finite-dimensional system representation. In this paper, the method of integro-differential relations is used for the derivation of a finite-dimensional approximation of a spatially two-dimensional heat transfer process. Simulation results for control and state estimation employing the before-mentioned modeling approach are presented for a test rig that is available at the Chair of Mechatronics at the University of Rostock.