Study on Model Predictive Control to Minimize Movements in Positions Due to Thermal Expansion of Plate with Varying Generation of Heat

Precise temperature control to decrease movements in positions due to thermal expansion of work pieces is required in the manufacturing processes to achieve nanometer-order accuracy. We analytically examined the effect of a method of minimizing movements in positions on a plate with varying generation of noise-heat. Control by monitoring temperature changes caused larger movements in positions than that without control because maximum change in temperature occurred at non-monitoring positions. The best method of minimizing movements in positions due to thermal expansion of a plate with varying generation of noise-heat was model predictive control by the monitoring movements and distributed temperature changes in the control heater according to the effects of the generation of noise-heat. The maximum movement in positions was 6 nm, which was 1/4 times of that without control.