In this paper, we introduce a novel method to formally represent elements of control engineering knowledge in a suitable data structure. To this end, we first briefly review existing representation methods (RDF, OWL, Wikidata, ORKG). Based on this, we introduce our own approach: The Python-based imperative representation of knowledge (PyIRK) and its application to formulate the Ontology of Control Systems Engineering (OCSE). One of its main features is the possibility to represent the actual content of definitions and theorems as nodes and edges of a knowledge graph, which is demonstrated by selected theorems from Lyapunov’s theory. While the approach is still experimental, the current result already allows the application of methods of automated quality assurance and a SPARQL-based semantic search mechanism. The feature set of the framework is demonstrated by various examples. The paper concludes with a discussion of the limitations and directions for further development.

This paper is motivated by three main assumptions: (1) The currently dominant forms of knowledge representation (natural language text, formulas, graphics) are suboptimal to facilitate knowledge transfer between control engineering sub-fields and into potential application domains. (2) Formal knowledge representation (in general) is a promising supplementary approach, but (3) the established technologies so far have failed to be significantly adopted for formal representation of control engineering knowledge. Thus, after briefly reviewing existing representation methods, we introduce our own approach: The Python based imperative representation of knowledge (PyIRK) and its application to formulate the Ontology of Control Systems Engineering (OCSE). One of its main features is the possibility to represent the actual content of definitions and theorems as nodes and edges of a knowledge graph, which is demonstrated by selected elements from Lyapunov theory. While the approach is still experimental, the formalization already allows to apply methods of automated quality assurance and a semantic search mechanism. The current feature set of the framework is demonstrated on various examples before directions for further developments are discussed.

As the amount of volatile, renewable energy sources in power distribution networks is increasing, the stability analysis of the latter is a vital aspect for network operators. Within the STABEEL project, the authors develop rules on how to parameterize the reactive power control of distributed energy resources to increase the performance while guaranteeing voltage stability. The work focuses on distribution networks with a high penetration of distributed energy resources equipped with Q(V)- characteristics. This contribution is based on the stability assessment of previous work and introduces a new approach utilizing the Circle Criterion. Herein, distributed energy resources can be modeled as detailed control loops or as approximations, derived from technical guidelines. In addition, the wavelet transform is applied to RMS time series simulations to obtain a more realistic, less conservative reference. With the aim of extending existing technical guidelines, the stability assessment methods are applied to various distribution networks.

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.

Zusammenfassung Das VGF-Verfahren ist ein moderner Prozess zur Züchtung von Einkristallen, der Grundlage für nahezu alle elektronischen Anwendungen. Die sukzessive Erstarrung der Schmelze zum Einkristall wird dabei durch geeignete Ansteuerung der als Aktoren in der Anlage zur Verfügung stehenden Heizer realisiert. Dieses Regelungsproblem ist Gegenstand des Beitrags, wobei der Schwerpunkt auf einer anschaulichen und einführenden Darstellung der Thematik und weniger den mathematischen Details liegt. Basierend auf einem Modell des Kristallzüchtungsprozesses, das partielle Differentialgleichungen für die Wärmediffusion in Schmelze und Kristall beinhaltet und aufgrund der Übergangsbedingung an der Phasengrenze als zweiphasiges Stefan-Problem bezeichnet wird, werden zwei Entwürfe von Folgereglern vorgestellt. Ein flachheitsbasierter Ansatz nutzt eine endlichdimensionale Approximation des Modells, während eine mittels Backstepping entworfene Zustandsrückführung unendlichdimensional ist. Beide Regler werden in umfangreichen Simulationsstudien validiert und miteinander verglichen.

One of the foundations of a resilient power system is a reliable grid security assessment. Hereby, the distance of an actual grid operating point to the limits of the surrounding safe operating area can be improved by optimizing reactive power operating points. However, when choosing a voltage-dependent reactive power provision, the so-called Q(U)-control, converter interactions of decentralized energy resources have to be considered. This paper is focused on the evaluation of Q(U)-characteristics with respect to variable grid topologies (N-1 cases) and operating cases. In the first part, a stability criterion from preliminary work is revisited. Herein, based on a discrete-time model of the Q(U)-control, filter time constants and slopes of the individual distributed eneregy ressources can be assessed regarding the overall system stability. The method is extended to consider relevant grid states resulting from the combination of topology perturbations and operating cases. The second part of the paper deals with the application of the criterion considering these versatile grid states. Strategies for selecting a sufficient number of relevant grid states are discussed. The filter constant of a plant control system is then introduced as an evaluation variable and grid states are compared on the basis of it. Finally, the application to benchmark grids of the medium and high voltage level is discussed.

The VGF method is a modern process for the growth of single crystals, the basis for almost all electronic applications. The gradual solidification of the melt into a single crystal is realized by suitably controlling the heaters that serve as actuators in the plant. The resulting control problem is the subject of this article that aims at an illustrative introductory presentation of the topic, with mathematical details taking a background role. Based on a model of the crystal growth process that is referred to as a Stefan problem and involves partial differential equations for the heat diffusion in the crystal and melt as well as a condition at the phase boundary, two designs of tracking controllers are presented. A flatness-based approach uses a finite-dimensional approximation of the model, while the state feedback resulting from a backstepping design is infinite-dimensional. Both controllers are validated and compared to one another in simulation studies.

As the number of distributed energy resources in today’s energy distribution grids is growing, measures must be taken to keep the voltage magnitudes in the grid within the operational limits. One prevalent way of doing this is to use voltage dependent reactive power provisioning, so-called Q(V )-control, where a Q(V )-characteristic with a certain slope prescribes how much reactive power is used to stabilise the node voltage. However, due to their interconnection by the power grid, the combined Q(V )-controls of several plants may become unstable. The first part of this paper revisits an existing stability criterion from the literature, based on a discrete-time model of Q(V)-control but limited to radial topologies, in order to assess how steep the slopes can be chosen. In the second part, this criterion is extended to grids with arbitrary topologies by introducing a more general grid model which explicitly takes the current operating point of the grid into account. Furthermore, an optimisation-based procedure is presented to exploit this new criterion for the direct maximisation of the slopes of the Q(V)-characteristics while guaranteeing stability of the system. Finally, both criteria are compared by applying them on selected benchmark grids.

Zusammenfassung Die Grundlage eines resilienten Energieversorgungssystems bildet u. a. eine zuverlässige Netzsicherheitsbewertung. Der Abstand des aktuellen Netzbetriebspunktes zu den Grenzen des ihn umgebenden sicheren Betriebsbereiches kann hierbei durch die Optimierung von Blindleistungsarbeitspunkten verbessert werden. Bei der Wahl einer spannungsabhängigen Blindleistungsbereitstellung, der sogenannten Q ( U )-Regelung, müssen Umrichterinteraktionen von dezentralen Energieanlagen berücksichtigt werden. Dieser Beitrag widmet sich der Bewertung von Q ( U )-Charakteristiken in Hinblick auf veränderliche Netztopologien (N-1-Fälle) und Betriebsfälle. Im ersten Teil wird ein Stabilitätskriterium aus Vorarbeiten aufgegriffen, das auf einem zeitdiskreten Modell der Q ( U )-Regelung beruht, um zu beurteilen, wie Anstiege und Filterzeitkonstanten der einzelnen Energieanlagen gewählt werden können. Das Verfahren wird um die Berücksichtigung relevanter Netzzustände erweitert, die sich aus der Kombination von Topologiestörungen und Betriebsfällen ergeben. Der zweite Teil des Beitrages widmet sich der Applikation des Kriteriums unter Berücksichtigung dieser vielseitigen Netzzustände. Dabei werden Strategien zur Auswahl einer hinreichenden Anzahl an Netzzuständen hinsichtlich ihrer Kritikalität diskutiert. Als Bewertungsgröße wird dann die Filterkonstante einer Anlagenregelung eingeführt und die Kritikalität der Netzzustände anhand dieser verglichen. Abschließend erfolgt die Anwendung auf Benchmarknetze der Mittel- und Hochspannungsebene.

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.

In this contribution, tracking control designs using output feedback are presented for a two-phase Stefan problem (SP) arising in the modeling of the vertical gradient freeze process. The two-phase SP, consisting of two coupled free boundary problems, is a vital part of many crystal growth processes due to the temporally varying spatial extent of the solid and liquid domains during growth. After discussing the special needs of the process, collocated and flatness-based state feedback designs are carried out. The quality of the provided approximations and the performance and robustness against parameter uncertainties of the open- and closed-loop control setups are analyzed in several simulations.

Zusammenfassung Die Stabilität eines elektrischen Energieübertragungssystems ist eine der wichtigsten Eigenschaften, die dessen Betreiber garantieren muss, insbesondere angesichts des wachsenden Anteils von dezentral eingespeisten, volatilen Energieträgern wie Solar und Wind am Gesamtmix. Aus diesem Grund werden im Rahmen des STABEEL-Projekts Methoden untersucht, wie – durch spezielle Formen der Blindleistungsbereitstellung von Erzeugern – Netze zukunftssicher, effizient und gleichzeitig stabil betrieben werden können. Um dieses Ziel zu erreichen, stellt dieser Beitrag die Weiterentwicklung eines Modellierungsansatzes vor, der Zustandsraummodelle von Verteilnetzen für die nachgelagerten Stabilitätsbetrachtungen liefert. Nach der Zusammenfassung grundlegender Konzepte geht dieser Artikel dabei auf die Modellierung von Leistungslasten und blindleistungsgeregelten Generatoren ein. Im Anschluss daran wird deren Funktionalität anhand der Simulation eines Beispielnetzes überprüft.

This contribution presents the application of nonlinear model predictive control to the Vertical Gradient Freeze crystal growth process. Due to the time-varying spatial extent of the crystal and melt during growth, this process is characterised by two coupled free boundary problems that form a so called two-phase Stefan problem which is of nonlinear nature. To apply model predictive control to this process, a simplified, spatially distributed representation of the system is derived and transferred into a spatially lumped form by means of the finite element method. For this model, a nonlinear control problem is formulated, that takes process limitations into account and tries to satisfy different quality objectives by formulating demands on the systems spatiotemproal temperature distribution. This provides the foundation for the presented predictive control design. Finally, the approximated model and the controller are verified for different real-world scenarios that include model errors and parameter uncertainties.

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 seek to develop better rules on how to parametrise the reactive power control of various sources within a distribution grid to increase the performance while guaranteeing stability. As a first step in this direction, this contribution presents a time-domain based modelling approach for a fixed grid frequency that provides the state-space models needed for the following stability analysis. In detail, models for generic grid components are created which are later combined into a dynamic system by using a provided grid topology. Depending on the specific design goal, this process yields different model variants which are evaluated by using a benchmark model.

The aim of this study was to assess the aptitude of the recurrent Long Short-Term Memory (LSTM) neural networks for fast and accurate predictions of process dynamics in vertical-gradient-freeze growth of gallium arsenide crystals (VGF-GaAs) using datasets generated by numerical transient simulations. Real time predictions of the temperatures and solid–liquid interface position in GaAs are crucial for control applications and for process visualization, i.e., for generation of digital twins. In the reported study, an LSTM network was trained on 1950 datasets with 2 external inputs and 6 outputs. Based on network performance criteria and training results, LSTMs showed the very accurate predictions of the VGF-GaAs growth process with median root-mean-square-error (RMSE) values of 2 × 10−3. This deep learning method achieved a superior predictive accuracy and timeliness compared with more traditional Nonlinear AutoRegressive eXogenous (NARX) recurrent networks.

The paper presents a generalization of a data mining method for the extraction of classification rules for classification of sequences of events, which is called discriminant chronicles mining. The generalization is motivated by the objective to extract classification rules from crystal growth data, for which the original method needs to be extended to events with vectors of attributes and to real-valued attributes. The paper elaborates incorporating both extensions into the theoretical fundamentals of the original method, and describes a corresponding modification of a system for discriminant chronicles mining, which has been developed three years ago to implement the original method. Finally, an application of the generalized method, using the modified system for discriminant chronicles mining, to data from the growth of GaAs crystals by vertical gradient freeze method is briefly sketched.

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.

Fast forecasting of process variables during the crystal growth is a critical step in a process development, optimization and control. The common approach based on computational fluid dynamics modeling is accurate, but too slow to deliver results in real time. Here we conducted a feasibility study on the application of dynamic artificial neural networks in the forecasting of VGF-GaAs crystal growth cooling program. Particularly, we studied various Nonlinear-AutoRegressive artificial neural networks with eXogenous inputs (NARX) with 2 external inputs and 6 outputs derived from 500 transient data sets. Data were generated by transient 1D CFD simulation. The first encouraging results are presented and the pros and cons of the application of dynamic artificial neural networks for the fast predictions of VGF process parameters are discussed.

AbstractA novel approach to the efficient numerical approximation and implementation of transformation based state feedback originating from backstepping or flatness based approaches is applied to a flatness based feedback law for the so called heavy rope system. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

This paper presents an approach for the efficient numerical implementation of transformation based state feedback laws for linear distributed parameter systems. The control laws considered may originate from backstepping or flatness-based design methods. They are, therefore, directly based on the underlying distributed parameter systems. In general, they are given as unbounded functionals on the infinite-dimensional state-space. By approximating a carefully chosen bounded part, the implementation of these feedback-operators can be considerably simplified. This is achieved by approximating the state in appropriate finite-dimensional sub-spaces of the state-space. The choice of these sub-spaces as well as the controller implementation are discussed for both, a particular motivating example specific and the general case. For the implementation and validation of the obtained approximated controllers the python-based software toolbox PyInduct is introduced.