Flatness based trajectory generation for a system with heat-generation term shown for the inductive heating for thixoforming

An important step in processing of Semi Solid Metals(SSM) is the inductive reheating of the raw material. Using conventional technologies the heating process behaviour is unsatisfactory in terms of reproducibility and disturbance rejection. But reproducibility is a stringent requirement for achieving good quality in the forming process that follows the reheating. In industrial application open loop control is often used but the control trajectories are generated by costly experiments. In order to improve the performance of the open loop control problem and to take constrains on the heating behaviour into consideration, this paper presents a flatness based method to calculate a trajectory for the manipulated variable. The parametrization of the solution is determined by using a Taylor-series expansion around the flat output. In this way a trajectory can be calculated which guarantees that the target temperature is reached as fast as possible and at the same time no overheating of the outer regions occurs. First simulation results are shown for the open loop control case.