Reliable finite-dimensional models with guaranteed approximation quality for control of distributed parameter systems

A large variety of technical systems is characterized by process variables which do not only depend on time but which also depend on at least one spatial coordinate. Such processes are typically contained in systems for heat and mass transfer as well as in flexible mechanical structures. Mathematical descriptions for such systems are generally given in terms of partial differential equations. To derive control and state estimation approaches which can be evaluated in real time, these infinite-dimensional models are commonly reduced to a finite-dimensional description. In this paper, different strategies are derived which, on the one hand, allow for a derivation of finite-dimensional representations on the basis of the method of integrodifferential relations and, on the other hand, allow for a reliable quantification of the resulting approximation quality. As application scenarios, an energy-optimal heating-up strategy based on Pontryagin´s maximum principle as well as state and disturbance estimation procedures are presented for a one-dimensional heat transfer process.