Volume 69, Issue 8 - Special issue: Ausgewählte Beiträge des GMA-Fachausschusses 1.30 / Frank Woittennek, Nicole Gehring

Zusammenfassung In diesem Beitrag wird eine neue algebraische Methode zur Detektion und Identifikation von Parameterfehlern für Roboter vorgestellt. Sie ist unabhängig von auftretenden Störungen und ermöglicht es, zusätzlich zu bestimmen, welche Fehler detektierbar sind. Das Verfahren basiert dabei auf der Rekonstruktion des Residuums als nichtlinearen differentialalgebraischen Ausdruck, der numerisch effizient mithilfe einer polynomialen Approximation ausgewertet wird. Daraus resultiert ein Ansatz für die Fehlerdetektion, -identifikation und -analyse, welcher mit FIR-Filtern, allein auf Basis von messbaren Signalen, effizient realisiert werden kann. Die vorgestellte Methode wird anschließend für einen SCARA-Roboter angewendet und durch eine Simulation validiert.

Mobile robots are enjoying increasing popularity in a number of different automation tasks. Omnidirectional mobile robots especially allow for a very flexible operation. They are able to accelerate in every direction, regardless of their orientation. In this context, we developed our own robot platform for research on said types of robots. It turns out that these mobile robots show interesting behaviour, which commonly used models for omnidirectional mobile robots fail to reproduce. As the exact sources and structures of mismatches are still unknown, non-parametric Gaussian process regression is used to develop a data-based model extension of the robot. A common control task for industrial applications is trajectory tracking, where a robot needs to follow a predefined path, for example in a warehouse, as close as possible in space and time. Appropriate feed-forward solutions for the data-based model are developed and finally leveraged in closed-loop control via nonlinear model predictive control. In real-world experiments, the results are compared to commonly used proportional position-based feedback. This novel contribution builds upon the preliminary work in [7] but, for the first time, includes also closed-loop (trajectory) tracking.

Dynamic models have proven to be helpful for determining the residual water content in combustible biomass. However, these models often require partial differential equations, which render simulations impracticable when several thousand particles need to be considered, such as in the drying of wood chips. Reduced-order models help to overcome this problem. We compare proper orthogonal decomposition (POD) based to balanced truncation based reduced-order models. Both reduced models are lean enough for an application to systems with many particles, but the model based on balanced truncation shows more accurate results.

Discrete-time systems are a common tool in the modeling of processes in many application areas such as digital signal processing and population dynamics. Model reduction is an essential remedy to handle high-fidelity systems in practice. To benefit from the performance gained by using reduced-order models, the computation of these models itself must be done with a reasonable use of resources. In this paper, we consider the case of medium-scale dense discrete-time systems and compare the performance of different numerical methods for the implementation of two basic model reduction techniques. Therefore, we give an overview of the considered model reduction methods and of the techniques used in underlying implementations. The outlined methods are then compared with established implementations in several numerical examples in terms of accuracy and performance.

In air-jet weaving, the braking of inserted weft threads plays a significant role in fabric quality and machine productivity. This contribution presents Model Predictive Control (MPC) which controls the weft tip’s position and velocity with an optimal braking force. The inserted weft thread is firstly modeled as a distributed parameter system. The relation between the braking force and the weft tip’s position is described by a Partial Differential Equation (PDE). By analyzing the PDE with Laplace transform and solving the PDE with a Galerkin method, a state-space model is presented. Subsequently, identification experiments of the constructed yarn brake are performed and the whole model is analyzed as well as reduced using balanced truncation. Based on the system states and input disturbance estimated by a dual Kalman filter, an MPC controls the weft tip’s position and velocity appropriately without any backward movement. Regarding model deviations and simulated measurement errors, the MPC performs robustly.

Stereotactic neurosurgery requires a careful planning of cannulae paths to spare eloquent areas of the brain that, if damaged, will result in loss of essential neurological function such as sensory processing, linguistic ability, vision, or motor function. We present an approach based on modelling, simulation, and optimization to set up a computational assistant tool. Thereby, we focus on the modeling of the brain topology, where we construct ellipsoidal approximations of voxel clouds based on processed MRI data. The outcome is integrated in a path-planning problem either via constraints or by penalization terms in the objective function. The surgical planning problem with obstacle avoidance is solved for different types of stereotactic cannulae using numerical simulations. We illustrate our method with a case study using real MRI data.

Zusammenfassung Es werden verteilt-parametrische Modelle hergeleitet, die das nichtlineare fraktionale Verhalten von Lithium-Ionen-Zellen beschreiben. Die vorgestellten Modelle interpolieren lineare verteilt-parametrische Kleinsignalmodelle, die sich als diffusive Realisierungen fraktionaler Übertragungsfunktionen in den Arbeitspunkten ergeben. Diese Übertragungsfunktionen werden mittels Impedanzspektroskopie parametriert. Zur endlich-dimensionalen Approximation der vorgestellten Modelle werden Krylov-Unterraum-Verfahren und Finite-Elemente-Ansätze genutzt. Diese nichtlinearen konzentriert-parametrischen Modelle werden in Simulationsstudien miteinander verglichen und anhand experimenteller Daten validiert.

Zusammenfassung Diese Arbeit behandelt inverse dynamische Spiele, welche eine Verallgemeinerung des inversen Problems der optimalen Regelung darstellen. Ziel dabei ist die Identifikation von Kostenfunktionen auf Basis von beobachteten optimalen Trajektorien. Die identifizierten Kostenfunktionen können individuelles Verhalten in kooperativen Systemen beschreiben, beispielweise menschliches Verhalten während der haptischen Interaktion mit anderen Menschen oder mit Maschinen.