Adaptive Control Strategies in Heat Transfer Problems with Parameter Uncertainties Based on a Projective Approach

Control problems for distributed heating systems described by parabolic partial differential equations are considered in this paper. This type of mathematical model is also a common description for other distributed parameter systems involving diffusion as well as heat and mass transfer. The goal of the paper is to develop an adaptive strategy including online parameter identification for efficient control of heat transfer systems. The developed strategy is based on the method of integrodifferential relations, a projective approach, and a suitable finite element technique. An adaptive control algorithm with predictive estimates of the desired output trajectories is proposed and its specific features are discussed. We use the parameters, geometry, and actuation principles of a real test setup available at the University of Rostock for the numerical simulation and verification. The test setup consists of a metallic rod equipped with a finite number of Peltier elements which are used as distributed control inputs allowing for active cooling and heating. A validation of the control laws derived in this contribution is performed taking into account the explicit local and integral error estimates resulting directly from the method of integrodifferential relations.