PID controller tuning by frequency loop-shaping: Application to diffusion furnace temperature control

A frequency loop-shaping technique for tuning proportional-integral-derivative controllers is applied to temperature control of a three-zone industrial diffusion furnace used in semiconductor manufacturing. In this tuning method the controller parameters are tuned so as to minimize the difference between the actual and a target loop transfer function, in an L infinity sense. The problem is formulated in the frequency domain as a convex optimization which can be solved numerically in a reliable way. This method, combined with a system identification step, has produced very satisfactory controllers for the furnace temperature control application.