Model predictive control of Czochralski crystal growth process

Abstract

This paper presents a model predictive control (MPC) formulation for the Czochralski (CZ) crystal growth which is given by the discrete finite-dimensional system representation of a class of parabolic partial differential equations (PDEs) with time-varying features. The motivation behind this work is to address the problem of stabilizing, infinite horizon, linear quadratic regulator synthesis for PDEs with time-dependent parameters which affect the dynamics of the underlying system and appear in the state-space representation. The modal decomposition of the PDE facilitates its approximation by a finite-dimensional linear state-space system. A receding horizon regulator is proposed which incorporates the time-dependence of the PDE parameters and numerical simulations are carried out which demonstrate the optimal stabilization of the process under state and input constraints.