Model Predictive Control of the Vertical Gradient Freeze Crystal Growth Process

Ecklebe, Stefan; Buchwald, Tom; Rüdiger, Patrick; Winkler, Jan

doi:10.1016/j.ifacol.2021.08.548

Cited by 5 publications

(3 citation statements)

References 18 publications

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“…This section briefly revisits a simplified 1D model of a VGF plant (see Ecklebe et al [2021] for the comprehensive form) and specifies the control objective.…”

Section: Modelling and Problem Statementmentioning

confidence: 99%

“…We only focus on the processes inside the crucible, a cross section of which is depicted in Figure 1. Furthermore, deviating from Ecklebe et al [2021] the jacket heaters are assumed to act as active insulation and therefore ignored.…”

Section: Plant Modelmentioning

confidence: 99%

“…An overview of control strategies for Stefan problems can be found in Koga and Krstic [2022]. Specifically, methods include the energy-based designs in Petrus et al [2010]; Koga and Krstic [2020], a flatness-based approach in Ecklebe et al [2021] and the optimal control designs in Kang and Zabaras [1995]; Hinze et al [2009]; Baran et al [2018]; Ecklebe et al [2021]. Considering only a one-phase Stefan problem (OPSP), where the temperature in one phase is assumed to be at melting temperature everywhere, Koga et al [2019] uses a backstepping design (see Krstic and Smyshlyaev [2008], in general) to stabilise a desired fixed position of the phase boundary.…”

Section: Introductionmentioning

confidence: 99%

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Backstepping-based tracking control of the vertical gradient freeze crystal growth process

Ecklebe¹,

Gehring²

2023

Preprint

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The vertical gradient freeze crystal growth process is the main technique for the production of high quality compound semiconductors that are vital for today's electronic applications. A simplified model of this process consists of two 1D diffusion equations with free boundaries for the temperatures in crystal and melt. Both phases are coupled via an ordinary differential equation that describes the evolution of the moving solid/liquid interface. The control of the resulting two-phase Stefan problem is the focus of this contribution. A flatness-based feedforward design is combined with a multi-step backstepping approach to obtain a controller that tracks a reference trajectory for the position of the phase boundary. Specifically, based on some preliminary transformations to map the model into a time-variant PDE-ODE system, consecutive decoupling and backstepping transformations are shown to yield a stable closed loop. The tracking controller is validated in a simulation that considers the actual growth of a Gallium arsenide single crystal.

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“…This section briefly revisits a simplified 1D model of a VGF plant (see Ecklebe et al [2021] for the comprehensive form) and specifies the control objective.…”

Section: Modelling and Problem Statementmentioning

confidence: 99%

Section: Plant Modelmentioning

confidence: 99%