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 the least squares identification of a multi-input/multi-output (MIMO) 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 a 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 in spite of the uncertainties associated with the identified model