Uses of differential-algebraic equations for trajectory planning and feedforward control of spatially two-dimensional heat transfer processes

Tracking control design is a common task in many engineering applications, where efficient controllers commonly consist of two components. First, a feedback control law is implemented to guarantee asymptotic stability of the closed-loop system and to meet robustness requirements. Second, a feedforward control signal is usually integrated, which improves the tracking of predefined output trajectories in transient operating phases. The analytic computation of this feedforward signal often becomes complicated or even impossible, if the output variables of the system do not coincide with the system's flat outputs. The situation becomes even worse, if the system is not flat at all, or if nonlinearities are included in the system model, which makes analytic solutions for the state trajectories unavailable in the non-flat case. For these reasons, the differential-algebraic equation solver Daets was used in previous work to solve this task numerically. The current paper describes extensions of the use of Daets in the framework of feedforward control design for non-flat outputs of a spatially two-dimensional heat transfer process with significant parameter uncertainty and actuator constraints. Numerical and experimental results are presented for a suitable test rig at the Chair of Mechatronics at the University of Rostock, where the robust feedback control part is designed using linear matrix inequalities in combination with a polytopic uncertainty model.