An Integrodifferential Approach to Adaptive Control Design for Heat Transfer Systems with Uncertainties

Open-loop and closed-loop control problems for distributed parameter systems, described by parabolic partial differential equations, are considered in this contribution. The goal of the study is the development of strategies for control and estimation of states, disturbances, and parameters. These strategies are based on the method of integrodifferential relations, a projection approach, and a suitable finite element technique. A real-time applicable control algorithm is proposed and its specific features are discussed. A verification of the control laws derived in this contribution is performed taking into account explicit error estimates resulting directly from the integrodifferential approach. The parameters, geometry, and actuation principles of a heat transfer system available at the Chair of Mechatronics, University of Rostock, are used for the numerical simulation and experimental validation. 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.