This paper considers the active control of the microstructure evolution in a thin film of copper by regulating the temperature distribution using a heater array. A nonlinear finite element model based on heat conduction is used to analyze the system dynamics. As in traditional heat treatment of metal, the control objective is specified as a desired temperature profile. In addition, to avoid excessive temperature gradient which could cause microstructure defects, the temperature gradient in the transient phase should also be minimized. The overall system is a multi-input/multi-output control system. We verify numerically that the system is open loop stable and locally strictly passive. Hence a passive feedback control law would ensure local closed loop stability. The feedback gain is motivated from consensus control, with a graph structure chosen to restrict the temperature spread in the transient phase. With the selected feedback structure, repeated simulation is needed to optimize the feedback gain. To reduce the computation time, we apply the proper orthogonal decomposition technique to obtain a reduced order model, which is then used for the gain optimization process. We demonstrated about 30% computation time reduction in each iteration. We present simulation results comparing fully decentralized independent proportional-integral control, decentralized control augmented by consensus feedback, and consensus feedback together with inverse problem feedforward control. In all cases, close setpoint regulation is achieved, with the consensus control resulting in much smaller temperature gradients in the transient phase.
American Control Conference (ACC), Chicago, 2015.