Projective Control Design for Multi-Zone Crystal Growth Furnace

This paper addresses the problem of controlling the temperature profile inside a multi-Zone crystal growth furnace. A minimal discrete-time state-space model of the furnace is determined by Least Squares identification of a Multi Input / Multi-Output (MIMO) input-output model. An integral control structure for the discrete-time model is derived to allow reference tracking, and a state-feedback control is designed for the system by solving a Discrete Linear Quadratic Regulator (DLQR) problem with a suitably chosen cost. This state-feedback controller serves as a reference for designing an output-feedback controller through the projective control approach. The resulting projective controller has structure similar to a MIMO Proportional-plus-Integral controller. The projective controller is used to control a simulated and an actual furnace. The resulting control system achieves the necessary control objective; i.e., it maintains the required temperature with no steady-state error and a reasonable transient behavior inspite of the uncertainties associated with the identified model.