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ABSTRACTWe present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class and utilizes condensed forms which often arise in applications and reveal the solution behaviour of a system. Provided that the original system has such a form, our method produces reduced-order models (ROMs) of minimal dimension, which tangentially interpolate the original model’s transfer function and are guaranteed to be again in pH-DAE form. This allows the ROM to be safely coupled with other dynamical systems when modelling large system networks, which is useful, for instance, in electric circuit simulation.

In the last decades, the application of automatic control techniques in freeform bending processes was limited to the motion control of the bending die, i.e., the workpiece itself was not considered inside the closed-loop control system. In a previous work, a simple preliminary model for the workpiece was used as a foundation for developing a closed-loop system for freeform bending that includes both the geometry and the mechanical properties of the semi-finished product. However, this approach did not consider the fact that the same geometry can be reached by either over- or underbending the tube. In this work, the previously developed system model is extended to include this physical property of the system.

In motion planning for autonomous racing, the challenge arises in planning smooth trajectories close to the handling limits of the vehicle with a sufficient planning horizon. Graph-based trajectory planning methods can find the global discrete-optimal solution, but they suffer from the curse of dimensionality. Therefore, to achieve low computation times despite a long planning horizon, coarse discretization and simple edges that are efficient to generate must be used. However, the resulting rough trajectories cannot reach the handling limits of the vehicle and are also difficult to track by the controller, which can lead to unstable driving behavior. In this paper, we show that the initial edges connecting the vehicle’s estimated state with the actual graph are crucial for vehicle stability and race performance. We therefore propose a sampling-based approach that relies on jerk-optimal curves to generate these initial edges. The concept is introduced using a layer-based graph, but it can be applied to other graph structures as well. We describe the integration of the curves within the graph and the required adaptation to racing scenarios. Our approach enables stable driving at the handling limits and fully autonomous operation on the race track. While simulations show the comparison of our concept with an alternative approach based on uniform acceleration, we also present experimental results of a dynamic overtake with speeds up to 74 m/s on a full-size vehicle.

Autonomous racing has increasingly become a research subject as it provides insights into dynamic, high-speed situations. One crucial aspect of handling these situations, especially in the presence of dynamic obstacles, is the generation of a collision-free trajectory that represents a safe behavior and is also competitive in the case of racing. We propose a local planning approach that generates such trajectories for a racing car on an oval race track by searching a spatiotemporal graph. A considerable challenge of search-based methods in a spatiotemporal domain is the curse of dimensionality. Therefore, we propose how a previously presented graph structure that is based on intervals instead of discrete values can be searched more efficiently without losing optimality by using a uniform-cost search strategy. We extend the search method to make it anytime-capable so that it can provide a suboptimal trajectory even if the search has to be terminated early. The graph-based planning approach allows us to apply a flexible cost function so that our approach can operate fully autonomously on an oval race track, including the pit lane. We present a cost function for oval racing and explain how the terms contribute to the desired behaviors. This is supported by results with a full-scale prototype.

The superordinate goal of this study is to develop a closed-loop control for a property-controlled freeform bending process based on the prediction of the residual stresses and further mechanical properties by a soft sensor. Therefore, it is hypothesized that different combinations of freeform bending process parameters lead to matching geometry pairs with different residual stresses that can be influenced by the bending die position. A novel correlation between the bending die position, residual stresses and hardness provides the basis for the soft sensor and for closed-loop control design.This paper focuses on freeform bending with movable die, for which a novel bending strategy is developed that results in a set geometry while also providing various residual stress states in the tube. A numerical simulation model for freeform bending with movable die successfully models the variation in degrees of freedom of the machine and provides high qualitative and quantitative results regarding the identification of geometry and residual stresses. Real freeform bent validation experiments and HV 10 Vickers hardness measurements were carried out. HV 10 Vickers hardness tests were identified as a suitable parameter for preliminary system identification and validation, hence making it an appropriate parameter for soft sensor development.

The primary goal of this study is the formulation of a soft sensor that predicts industrially relevant mechanical properties for freeform bending. This serves as the foundation of a closed-loop property control. It is hypothesized that by inline measurement of hardness, predictions regarding residual hoop stresses, local strength and strain level can be achieved. A novel hardness-based correlation scheme is introduced, which is implemented into an extended Kalman filter (EKF) and allows an inline prediction of local strength, residual hoop stresses and plasticity. Furthermore, the ultrasonic contact impedance (UCI) method is validated as a suitable inline measuring solution.

In this contribution, we develop a feedback controller in the form of a parametric function for a mobile inverted pendulum. The control both stabilizes the system and drives it to target positions with target orientations. A design of the controller based only on a cost function is difficult for this task, which is why we choose to train the controller using imitation learning on optimized trajectories. In contrast to popular approaches like policy gradient methods, this approach allows us to shape the behavior of the system by including equality constraints. When transferring the parametric controller from simulation to the real mobile inverted pendulum, the control performance is degraded due to the reality gap. A robust control design can reduce the degradation. However, for the framework of imitation learning on optimized trajectories, methods that explicitly consider robustness do not yet exist to the knowledge of the authors. We tackle this research gap by presenting a method to design a robust controller in the form of a recurrent neural network, to improve the transferability of the trained controller to the real system. As a last step, we make the behavior of the parametric controller adjustable to allow for the fine tuning of the behavior of the real system. We design the controller for our system and show in the application that the recurrent neural network has increased performance compared to a static neural network without robustness considerations.