Combined run-to-run and delta LQG control: Controller design and application to 12-inch RTP equipment

A constrained iterative learning control (ILC) technique based on a delta-form linear quadratic Gaussian (LQG) technique has been designed for overcoming model error and for numerically stable control of a rapid thermal processing(RTP). The RTP is characterized by very short sampling time and repetition of single batch. The delta form LQG control technique was applied for accurate control in high frequency caused by short sampling time. The designed control technique, ILC, acquired both numerically stable and to overcome model error in combination with the multivariable delta form LQG technique. A structural problem of the equipment or an excessive model error may cause physically unreasonable solution computed by the delta form LQG. For this, Constraints were applied to the ILC solution to be placed on the physically reasonable area. Cubic spline approximation was used as a numerical method to approximate time-varying gain matrices. The method remarkably reduced not only a computation time, but also a data transmission time from computer to DSP board in RTP equipment. In the results of simulation, control performance was improved from batch to batch, and finally reached specification-satisfied wafer's temperature uniformity with physically reasonable lamp powers. The proposed control technique was designed for commercial RTP equipment which has 10 tungsten-halogen lamp groups and 6 pyrometers installed for heating and measure a 12-inch wafer.