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Foto: LDM

Foto: LDM

Foto: @AdobeStock/Gorodenkoff

Foto: © AdobeStock/Gorodenkoff

Foto: @ Fraunhofer IOSB-INA

Foto: © AdobeStock/Gorodenkoff

Foto: @ Fraunhofer IEM

Foto: @ Heinz Nixdorf Institut

Foto: @ Heinz Nixdorf Institut

Foto: @ Heinz Nixdorf Institut

Foto: @AdobeStock/Gorodenkoff

Dr.-Ing. Julia Timmermann

Dr.-Ing. Julia Timmermann

Regelungstechnik und Mechatronik / Heinz Nixdorf Institut

Wissenschaftliche Mitarbeiterin

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Autonomous Golf Putting with Data-Driven and Physics-Based Methods

A. Junker, N. Fittkau, J. Timmermann, A. Trächtler, in: 2022 Sixth IEEE International Conference on Robotic Computing (IRC), IEEE, 2023

Estimating States and Model Uncertainties Jointly by a Sparsity Promoting UKF

R. Götte, J. Timmermann, in: 12th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2022), 2023, pp. 85-90

State estimation when only a partial model of a considered system is available remains a major challenge in many engineering fields. This work proposes a joint, square-root unscented Kalman filter to estimate states and model uncertainties simultaneously by linear combinations of physics-motivated library functions. Using a sparsity promoting approach, a selection of those linear combinations is chosen and thus an interpretable model can be extracted. Results indicate a small estimation error compared to a traditional square-root unscented Kalman filter and exhibit the enhancement of physically meaningful models.

Approximating a Laplacian Prior for Joint State and Model Estimation within an UKF

R. Götte, J. Timmermann, in: Accepted for IFAC World Congress 2023, 2023

Low-quality models that miss relevant dynamics lead to major challenges in modelbased state estimation. We address this issue by simultaneously estimating the system’s states and its model inaccuracies by a square root unscented Kalman filter (SRUKF). Concretely, we augment the state with the parameter vector of a linear combination containing suitable functions that approximate the lacking dynamics. Presuming that only a few dynamical terms are relevant, the parameter vector is claimed to be sparse. In Bayesian setting, properties like sparsity are expressed by a prior distribution. One common choice for sparsity is a Laplace distribution. However, due to disadvantages of a Laplacian prior in regards to the SRUKF, the regularized horseshoe distribution, a Gaussian that approximately features sparsity, is applied instead. Results exhibit small estimation errors with model improvements detected by an automated model reduction technique.


Autonomes Putten mittels datengetriebener und physikbasierter Methoden

A. Junker, N. Fittkau, J. Timmermann, A. Trächtler, in: Proceedings - 32. Workshop Computational Intelligence: Berlin, 1. - 2. Dezember 2022, 2022, pp. 119-124

Data-Driven Models for Control Engineering Applications Using the Koopman Operator

A. Junker, J. Timmermann, A. Trächtler, in: 2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC 2022), 2022, pp. 1-9

Within this work, we investigate how data-driven numerical approximation methods of the Koopman operator can be used in practical control engineering applications. We refer to the method Extended Dynamic Mode Decomposition (EDMD), which approximates a nonlinear dynamical system as a linear model. This makes the method ideal for control engineering applications, because a linear system description is often assumed for this purpose. Using academic examples, we simulatively analyze the prediction performance of the learned EDMD models and show how relevant system properties like stability, controllability, and observability are reflected by the EDMD model, which is a critical requirement for a successful control design process. Subsequently, we present our experimental results on a mechatronic test bench and evaluate the applicability to the control engineering design process. As a result, the investigated methods are suitable as a low-effort alternative for the design steps of model building and adaptation in the classical model-based controller design method.

Learning Data-Driven PCHD Models for Control Engineering Applications

A. Junker, J. Timmermann, A. Trächtler, in: 14th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, 2022, pp. 389-394

The design of control engineering applications usually requires a model that accurately represents the dynamics of the real system. In addition to classical physical modeling, powerful data-driven approaches are increasingly used. However, the resulting models are not necessarily in a form that is advantageous for controller design. In the control engineering domain, it is highly beneficial if the system dynamics is given in PCHD form (Port-Controlled Hamiltonian Systems with Dissipation) because globally stable control laws can be easily realized while physical interpretability is guaranteed. In this work, we exploit the advantages of both strategies and present a new framework to obtain nonlinear high accurate system models in a data-driven way that are directly in PCHD form. We demonstrate the success of our method by model-based application on an academic example, as well as experimentally on a test bed.

Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering

R. Götte, J. Timmermann, in: 2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC), 2022, pp. 67-76

In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems. Likewise, purely data-driven methods often do not generalise well enough and may violate physical laws. Recently Physics-Guided Neural Networks (PGNN) and physics-inspired loss functions separately have shown promising results to conquer these drawbacks. In this contribution we extend existing methods towards the identification of non-autonomous systems and propose a combined approach PGNN-L, which uses a PGNN and a physics-inspired loss term (-L) to successfully identify the system's dynamics, while maintaining the consistency with physical laws. The proposed method is demonstrated on two real-world nonlinear systems and outperforms existing techniques regarding complexity and reliability.

Batch Constrained Bayesian Optimization for UltrasonicWire Bonding Feed-forward Control Design

M. Hesse, M. Hunstig, J. Timmermann, A. Trächtler, in: Proceedings of the 11th International Conference on Pattern Recognition Applications and Methods (ICPRAM), 2022, pp. 383-394

Ultrasonic wire bonding is a solid-state joining process used to form electrical interconnections in micro and power electronics and batteries. A high frequency oscillation causes a metallurgical bond deformation in the contact area. Due to the numerous physical influencing factors, it is very difficult to accurately capture this process in a model. Therefore, our goal is to determine a suitable feed-forward control strategy for the bonding process even without detailed model knowledge. We propose the use of batch constrained Bayesian optimization for the control design. Hence, Bayesian optimization is precisely adapted to the application of bonding: the constraint is used to check one quality feature of the process and the use of batches leads to more efficient experiments. Our approach is suitable to determine a feed-forward control for the bonding process that provides very high quality bonds without using a physical model. We also show that the quality of the Bayesian optimization based control outperforms random search as well as manual search by a user. Using a simple prior knowledge model derived from data further improves the quality of the connection. The Bayesian optimization approach offers the possibility to perform a sensitivity analysis of the control parameters, which allows to evaluate the influence of each control parameter on the bond quality. In summary, Bayesian optimization applied to the bonding process provides an excellent opportunity to develop a feedforward control without full modeling of the underlying physical processes.

Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems

O. Schön, R. Götte, J. Timmermann, in: 14th IFAC Workshop on Adaptive and Learning Control Systems (ALCOS 2022), 2022, pp. 19-24

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose a physics-guided hybrid approach for modeling non-autonomous systems under control. Starting from a traditional physics-based model, this is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy yielding physically plausible models. While purely data-driven methods fail to produce satisfying results, experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.


Intelligente Steuerungen und Regelungen

C. Lüke, J. Timmermann, J.H. Kessler, A. Trächtler, in: Steigerung der Intelligenz mechatronischer Systeme, Springer Vieweg, 2018, pp. 153-192

A Reinforcement Learning Strategy for the Swing-Up of the Double Pendulum on a Cart

M. Hesse, J. Timmermann, E. Hüllermeier, A. Trächtler, Procedia Manufacturing (2018), 24, pp. 15 - 20

The effective control design of a dynamical system traditionally relies on a high level of system understanding, usually expressed in terms of an exact physical model. In contrast to this, reinforcement learning adopts a data-driven approach and constructs an optimal control strategy by interacting with the underlying system. To keep the wear of real-world systems as low as possible, the learning process should be short. In our research, we used the state-of-the-art reinforcement learning method PILCO to design a feedback control strategy for the swing-up of the double pendulum on a cart with remarkably few test iterations at the test bench. PILCO stands for “probabilistic inference for learning control” and requires only few expert knowledge for learning. To achieve the swing-up of a double pendulum on a cart to its upper unstable equilibrium position, we introduce additional state restrictions to PILCO, so that the limited cart distance can be taken into account. Thanks to these measures, we were able to learn the swing up at the real test bench for the first time and in only 27 learning iterations.


Nonlinear Model Predictive Control with Discrete Mechanics and Optimal Control

K. Xu, J. Timmermann, A. Trächtler, in: Proc. Advanced Intelligent Mechatronics (AIM), IEEE, 2017

Swing-up of the moving double pendulum on a cart with simulation based LQR-Trees

K. Xu, J. Timmermann, A. Trächtler, in: Proc. 20th IFAC World Congress, 2017


Control strategies on stable manifolds for energyefficient swing-ups of double pendula

K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, A. Trächtler, International Journal of Control (2014), DOI: 10.1080/00207179.2014.893450, pp. 1-20

Optimale Steuerung und Mehrzieloptimierung von dynamischen Systemen untersucht am Beispiel des Mehrfachpendels

J. Timmermann, 2014

In dieser Arbeit wird gezeigt, wie optimale Trajektorien für ein unteraktuiertes mechanisches System - das Doppel- bzw. Dreifachpendel auf einem Wagen - mittels optimaler Steuerung bestimmt werden können. Dabei werden neuartige mathematische Methoden verwendet und deren Vorteile in der Anwendung aufgezeigt. Es werden sowohl die theoretischen Ergebnisse analysiert als auch die praktische Umsetzung in Simulationen und am Prüfstand untersucht. Das Manöver, welches hier hauptsächlich betrachtet wird, ist der Aufschwung des Pendels aus der stabilen unteren Ruhelage in die instabile obere Ruhelage. Dabei werden mit Hilfe von Methoden der Mehrzieloptimierung viele Varianten von Lösungen berechnet, die die zwei gegenläufigen Zielgrößen Dauer des Manövers und Steueraufwand unterschiedlich stark berücksichtigen. So ist es möglich eine komplexe Bibliothek von optimalen Lösungen zu erhalten und diese weitergehend bezüglich des Gesamtsystemverhaltens zu analysieren. Ein weiterer Ansatz ist die Entwicklung von Strategien für eine optimale Steuerung auf Mannigfaltigkeiten, die besondere dynamische Strukturen des Pendelsystems für einen optimalen Aufschwung nutzen. Auf der stabilen Mannigfaltigkeit kann sich das dynamische System kostenlos in die Ruhelage bewegen. Dies ist somit ein besonderer physikalisch motivierter Ansatz, um optimale Manöver zu finden.


Optimal Control on Stable Manifolds for a Double Pendulum

K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, M. Dellnitz, A. Trächtler, in: Proceedings in Applied Mathematics and Mechanics, 2012, pp. 723-724


Iterative learning of Stochastic Disturbance Profiles Using Bayesian Networks

D. Bielawny, M. Krüger, P. Reinold, J. Timmermann, A. Trächtler, in: 9th International Conference on Industrial Informatics (INDIN), 2011

Optimale Steuerung durch DMOC mit Anwendungen am Doppelpendel

J. Timmermann, Vortrag beim 45. Regelungstechnischen Kolloquium in Boppard (2011)

Discrete Mechanics and Optimal Control and its Application to a Double Pendulum on a Cart

J. Timmermann, S. Khatab, S. Ober-Blöbaum, A. Trächtler, in: 18th IFAC World Congress 2011, 2011


Optimal Control for a Pitcher's Motion Modeled as Constrained Mechanical System

S. Ober-Blöbaum, J. Timmermann, in: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Contro, ASME International Design Engineering Technical Conferences , ASME, 2009

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