arXiv subjects

Stefan Ecklebe

Publications and source records attributed to Stefan Ecklebe.

5 recordsLinked to original sources

arXiv2026

On the controller form for linear hyperbolic MIMO systems with dynamic boundary conditions

This contribution develops an algebraic approach to obtain a controller form for a class of linear hyperbolic MIMO systems, bidirectionally coupled with a linear ODE system at the unactuated boundary. After a short summary of established controller forms for SISO and MIMO ODE as well as SISO hyperbolic PDE systems, it is shown that the approach to state a controller form for SISO systems cannot easily be transferred to the MIMO case as it already fails for a very simple example. Next, a generalised hyperbolic controller form with different variants is proposed and a new flatness-based scheme to compute said form is presented. Therein, the system is treated in an algebraic setting where quasipolynomials are used to express the predictions and delays in the system. The proposed algorithm is then applied to the motivating example.

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arXiv2023

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

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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arXiv2022

Analysis of Voltage Stability in Terms of Interactions of Q(U)-Characteristic Control in Distribution Grids

As the amount of volatile, renewable energy sources in power distribution grids is increasing, the stability of the latter is a vital aspect for grid operators. Within the STABEEL project, the authors develop rules on how to parametrize the reactive power control of distributed energy resources to increase the performance while guaranteeing stability. The work focuses on distribution grids with a high penetration of distributed energy resources equipped with Q(U)-characteristic. This contribution is based on the stability assessment of previous work and introduces a new approach utilizing the circle criterion. With the aim of extending existing technical guidelines, stability assessment methods are applied to various distribution grids - including those from the SimBench project. Herein, distributed energy resources can be modelled as detailed control loops or as approximations, derived from technical guidelines.

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arXiv2020

Control of the Vertical Gradient Freeze crystal growth process via backstepping

This contribution presents a backstepping-based state feedback design for the tracking control of a two-phase Stefan problem which is encountered in the Vertical Gradient Freeze crystal growth process. A two-phase Stefan problem consists of two coupled free boundary problems and is a vital part of many crystal growth processes due to the time-varying extent of crystal and melt during growth. In addition, a different approach for the numerical approximation of the backstepping transformations kernel is presented.

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arXiv2019

Towards model based control of the Vertical Gradient Freeze crystal growth process

In this contribution tracking control designs using output feedback are presented for a two-phase Stefan problem arising in the modeling of the Vertical Gradient Freeze process. The two-phase Stefan problem, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated as well as flatness-based state feedback designs are carried out. To render the setup complete, an observer design is performed, using a flatness-based approximation of the original distributed parameter system. The quality of the provided approximations as well as the performance of the open and closed loop control setups is analysed in several simulations.

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