Model-based temperature control of heated plates

Many modern thermal processing systems involve temperature control of heated plates, where the plate can be a single wafer, heated by an array of tungsten halogen lamps from one or both sides, or thicker carriers or susceptors on which one or more wafers are placed, heated by radiation from hot filaments. The plate's temperature is typically measured using pyrometers. These types of systems can be accurately described by a mathematical model of the physics. However, some of the system properties vary over time and/or from wafer-to-wafer and cannot be predicted in practice, although their range of values may be known. In many cases, the plate's temperature is controlled using a proportional-integral-derivative (PID) controller, which may not be able to meet the desired temperature tracking performance (e.g. settling time, overshoot, repeatability) over a broad range of operating conditions. In this paper, an alternative model-based control approach is discussed that can achieve good performance for a wide range of operating conditions. In our approach, the mathematical system model is directly incorporated into the feedback controller. Simulation studies show that this approach yields significantly better performance and exhibits a much smaller sensitivity to system properties variation than a gain-scheduled PID controller.