Finite-Dimensional Observer-Based Model Predictive Controller for Heat Equation in Silicon Single Crystal Growth Process with Time Delay

The growth process of the Czochralski (CZ) sili-con single crystal (SSC) involves complex phase changes and interactions between multiple fields. Heat, as the fundamental driving force of crystal growth, plays a crucial role in SSC. The growth process of CZ SSC involves complex phase changes and interactions between multiple fields, resulting in large time delays in temperature control. This paper introduces a finite-dimensional control approach founded on the low-dimensional discreteness of output feedback. The spectral decomposition method is used to establish a Luenberger-type observer for a one-dimensional heat conduction distributed parameter system. Only measurable spatiotemporal outputs are used to design a feasible controller, which solves the problems of system instability caused by output time lag during crystal growth. The final experiment verifies the feasibility of the control design.