Finite-time tracking with actuator saturation: application to RTP temperature trajectory following

Precise trajectory following in the presence of actuator saturation constraints is important in performance of many control systems. An approximate finite-time tracking problem is formulated for a multivariable discrete-time linear time-invariant system. The actuator saturation constraints are taken into account explicitly. The problem is set up as a set of linear programming problems using a transfer matrix approach. The approach is applied to temperature profile tracking in rapid thermal processing (RTP) systems. It is known that fast and precise temperature tracking is crucial in performance of RTP systems. The actuator saturation manifests itself in terms of the power driving the lamps. Two rapid thermal processing examples are presented to illustrate the validity of the approach