A Differential-Algebraic Approach for Robust Control Design and Disturbance Compensation of Finite-Dimensional Models of Heat Transfer Processes

Control design for heat transfer processes usually has to deal with significant uncertainty in parameters of finite-dimensional system models. These finite-dimensional models are used as an approximation for the underlying infinite-dimensional representation of the system dynamics governed by partial differential equations. To obtain control laws that can be evaluated in real time, the infinite-dimensional representation usually has to be replaced by a finite-dimensional one. However, the resulting approximation errors as well as the parameters characterizing heat transfer and heat conduction properties are typically not directly measurable in experiments. Therefore, control strategies have to be derived that are able to cope with the before-mentioned sources of uncertainty. In this paper, a robust combination of feedforward and feedback control laws is derived that guarantees asymptotic stability and accurate trajectory tracking. The robustness of the control structure is obtained by an offline control synthesis by means of linear matrix inequalities for a linear system model with polytopic uncertainty. Moreover, an efficient approach for solving high-dimensional and high-index differential algebraic equations, implemented in DAETS, is employed to numerically compute dynamic feedforward control sequences.