Control of a highly non-linear multi-variable thermal processing furnace

Tuning a controller´s parameters can sometimes be a very complex and challenging task. Many methods have been used through the years to try and overcome this difficult challenge. In this paper we investigate the linear quadratic regulator (LQR) as a method for giving robust control for the non-linear multiple input multiple output system discussed in this paper. The system is a thermal processing furnace used to anneal 150 mm wafer batches in the 250degC to 450degC range in high vacuum. A plant model was developed which is a hybrid of a physical-law heat-transfer model and measurement data based model of the system. Numerical optimization was used to minimize the difference between measured data and model predicted outputs. Then, multiple linearized models were obtained. LQR was applied to one such model. It achieved the required specifications over the specified temperature range. The important specifications in this application are rise time, steady state accuracy and overshoot which are critical to the process.