Multi-object tracking filters require a birth density to detect new objects from measurement data. If the initial positions of new objects are unknown, it may be useful to choose an adaptive birth density. In this paper, a circular birth density is proposed, which is placed like a band around the surveillance area. This allows for 360° coverage. The birth density is described in polar coordinates and considers all point-symmetric quantities such as radius, radial velocity and tangential velocity of objects entering the surveillance area. Since it is assumed that these quantities are unknown and may vary between different targets, detected trajectories, and in particular their initial states, are used to estimate the distribution of initial states. The adapted birth density is approximated as a Gaussian mixture, so that it can be used for filters operating on Cartesian coordinates.
One major realm of Condition Based Maintenance is finding features that reflect the current health state of the asset or component under observation. Most of the existing approaches are accompanied with high computational costs during the different feature processing phases making them infeasible in a real-world scenario. In this paper a feature generation method is evaluated compensating for two problems: (1) storing and handling large amounts of data and (2) computational complexity. Both aforementioned problems are existent e.g. when electromagnetic solenoids are artificially aged and health indicators have to be extracted or when multiple identical solenoids have to be monitored. To overcome those problems, Compressed Sensing (CS), a new research field that keeps constantly emerging into new applications, is employed. CS is a data compression technique allowing original signal reconstruction with far fewer samples than Shannon-Nyquist dictates, when some criteria are met. By applying this method to measured solenoid coil current, raw data vectors can be reduced to a way smaller set of samples that yet contain enough information for proper reconstruction. The obtained CS vector is also assumed to contain enough relevant information about solenoid degradation and faults, allowing CS samples to be used as input to fault detection or remaining useful life estimation routines. The paper gives some results demonstrating compression and reconstruction of coil current measurements and outlines the application of CS samples as condition monitoring data by determining deterioration and fault related features. Nevertheless, some unresolved issues regarding information loss during the compression stage, the design of the compression method itself and its influence on diagnostic/prognostic methods exist.
In many industrial applications a workpiece is continuously fed through a heating zone in order to reach a desired temperature to obtain specific material properties. Many examples of such distributed parameter systems exist in heavy industry and also in furniture production such processes can be found. In this paper, a real-time capable model for a heating process with application to industrial furniture production is modeled. As the model is intended to be used in a Model Predictive Control (MPC) application, the main focus is to achieve minimum computational runtime while maintaining a sufficient amount of accuracy. Thus, the governing Partial Differential Equation (PDE) is discretized using finite differences on a grid, specifically tailored to this application. The grid is optimized to yield acceptable accuracy with a minimum number of grid nodes such that a relatively low order model is obtained. Subsequently, an explicit Runge-Kutta ODE (Ordinary Differential Equation) solver of fourth order is compared to the Crank-Nicolson integration scheme presented in Weiss et al. (2022) in terms of runtime and accuracy. Finally, the unknown thermal parameters of the process are estimated using real-world measurement data that was obtained from an experimental setup. The final model yields acceptable accuracy while at the same time shows promising computation time, which enables its use in an MPC controller.
This paper describes an early lumping approach for generating a mathematical model of the heating process of a moving dual-layer substrate. The heat is supplied by convection and nonlinearly distributed over the whole considered spatial extend of the substrate. Using CFD simulations as a reference, two different modelling approaches have been investigated in order to achieve the most suitable model type. It is shown that due to the possibility of using the transition matrix for time discretization, an equivalent circuit model achieves superior results when compared to the Crank-Nicolson method. In order to maintain a constant sampling time for the in-visioned-control strategies, the effect of variable speed is transformed into a system description, where the state vector has constant length but a variable number of non-zero entries. The handling of the variable transport speed during the heating process is considered as the main contribution of this work. The result is a model, suitable for being used in future control strategies.
Modeling a suitable birth density is a challenge when using Bernoulli filters such as the Labeled Multi-Bernoulli (LMB) filter. The birth density of newborn targets is unknown in most applications, but must be given as a prior to the filter. Usually the birth density stays unchanged or is designed based on the measurements from previous time steps.
In this paper, we assume that the true initial state of new objects is normally distributed. The expected value and covariance of the underlying density are unknown parameters. Using the estimated multi-object state of the LMB and the Rauch-Tung-Striebel (RTS) recursion, these parameters are recursively estimated and adapted after a target is detected.
The main contribution of this paper is an algorithm to estimate the parameters of the birth density and its integration into the LMB framework. Monte Carlo simulations are used to evaluate the detection driven adaptive birth density in two scenarios. The approach can also be applied to filters that are able to estimate trajectories.
Observer-based self sensing for digital (on–off) single-coil solenoid valves is investigated. Self sensing refers to the case where merely the driving signals used to energize the actuator (voltage and coil current) are available to obtain estimates of both the position and velocity. A novel observer approach for estimating the position and velocity from the driving signals is presented, where the dynamics of the mechanical subsystem can be neglected in the model. Both the effect of eddy currents and saturation effects are taken into account in the observer model. Practical experimental results are shown and the new method is compared with a full-order sliding mode observer.
This paper presents a modeling approach of an industrial heating process where a stripe-shaped workpiece is heated up to a specific temperature by applying hot air through a nozzle. The workpiece is moving through the heating zone and is considered to be of infinite length. The speed of the substrate is varying over time. The derived model is supposed to be computationally cheap to enable its use in a model-based control setting. We start by formulating the governing PDE and the corresponding boundary conditions. The PDE is then discretized on a spatial grid using finite differences and two different integration schemes, explicit and implicit, are derived. The two models are evaluated in terms of computational effort and accuracy. It turns out that the implicit approach is favorable for the regarded process. We optimize the grid of the model to achieve a low number of grid nodes while maintaining a sufficient amount of accuracy. Finally, the thermodynamical parameters are optimized in order to fit the model's output to real-world data that was obtained by experiments.
A semilinear distributed parameter approach for solenoid valve control including saturation effects
(2015)
In this paper a semilinear parabolic PDE for the control of solenoid valves is presented. The distributed parameter model of the cylinder becomes nonlinear by the inclusion of saturation effects due to the material's B/H-curve. A flatness based solution of the semilinear PDE is shown as well as a convergence proof of its series solution. By numerical simulation results the adaptability of the approach is demonstrated, and differences between the linear and the nonlinear case are discussed. The major contribution of this paper is the inclusion of saturation effects into the magnetic field governing linear diffusion equation, and the development of a flatness based solution for the resulting semilinear PDE as an extension of previous works [1] and [2].
An approach for an adaptive position-dependent friction estimation for linear electromagnetic actuators with altered characteristics is proposed in this paper. The objective is to obtain a friction model that can be used to describe different stages of aging of magnetic actuators. It is compared to a classical Stribeck friction model by means of model fit, sensitivity, and parameter correlation. The identifiability of the parameters in the friction model is of special interest since the model is supposed to be used for diagnostic and prognostic purposes. A method based on the Fisher information matrix is employed to analyze the quality of the model structure and the parameter estimates.
The trajectory tracking problem for a fully-actuated real-scaled surface vessel is addressed in this paper by designing a backstepping controller with a multivariable integral action, considering the thruster allocation problem. The performance and robustness of this controller are evaluated in simulation, taking into account environmental disturbance forces and modeling mismatch, using a docking maneuver as a reference trajectory. Furthermore, a comparison between the backstepping controller and a nonlinear position PID-Control with flatness based-feedforward is also analyzed.
Comparison and Identifiability Analysis of Friction Models for the Dither Motion of a Solenoid
(2018)
In this paper, the mechanical subsystem of a proportional solenoid excited by a dither signal is considered. The objective is to find a suitable friction model that reflects the characteristic mechanical properties of the dynamic system. Several different friction models from the literature are compared. The friction models are evaluated with respect to their accuracy as well as their practical identifiability, the latter being quantified based on the Fisher information matrix.
In this paper, a systematic comparison of three different advanced control strategies for automated docking of a vessel is presented. The controllers are automatically tuned offline by applying an optimization process using simulations of the whole system including trajectory planner and state and disturbance observer. Then investigations are conducted subject to performance and robustness using Monte Carlos simulation with varying model parameters and disturbances. The control strategies have also been tested in full scale experiments using the solar research vessel Solgenia. The investigated control strategies all have demonstrated very good performance in both, simulation and real world experiments. Videos are available under https://www.htwg-konstanz.de/forschung-und-transfer/institute-und-labore/isd/regelungstechnik/videos/
This paper presents a systematic comparison of different advanced approaches for motion prediction of vessels for docking scenarios. Therefore, a conventional nonlinear gray-box-model, its extension to a hybrid model using an additional regression neural network (RNN) and a black-box-model only based on a RNN are compared. The optimal hyperparameters are found by grid search. The training and validation data for the different models is collected in full-scale experiments using the solar research vessel Solgenia. The performances of the different prediction models are compared in full-scale scenarios. %To use the investigated approaches for controller design, a general optimal control problem containing the advanced models is described. These can improve advanced control strategies e.g., nonlinear model predictive control (NMPC) or reinforcement learning (RL). This paper explores the question of what the advantages and disadvantages of the different presented prediction approaches are and how they can be used to improve the docking behavior of a vessel.
Comparison of Data-Driven Modeling and Identification Approaches for a Self-Balancing Vehicle
(2023)
This paper gives a systematic comparison of different state–of–the–art modeling approaches and the corresponding parameter identification processes for a self–balancing vehicle. In detail, a nonlinear grey box model, its extension to consider friction effects, a parametric black box model based on regression neural networks, and a hybrid approach are presented. The parameters of the models are identified by solving a nonlinear least squares problem. The training, validation, and test datasets are collected in full–scale experiments using a self–balancing vehicle. The performance of the different models used for ego–motion prediction are compared in full–scale scenarios, as well. The investigated model architectures can be used to improve both, simulation environments and model–based controller design. This paper shows the upsides and downsides arising from using the different modeling approaches. Videos showing the self–balancing vehicle in action are available at: https://tinyurl.com/mvn8j7vf22nd
In this paper, utilisation of an Unscented Kalman Filter for concurrently performing disturbance estimation and wave filtering is investigated. Experimental results are provided that demonstrate very good performance subject to both tasks. For the filter, a dynamic model has been used which was optimised via correlation analysis in order to obtain a minimum set of relevant parameters. This model has also been validated by experiments deploying a small vessel. A simulation study is presented to evaluate the performance using known quantities. Experimental trials have been performed on the Rhine river. The results show that for instance flow direction and varying current velocities can continuously be estimated with decent precision, even while the boat is performing turning manoeuvres. Moreover, the filtering properties are very satisfactory. This makes the filter suitable for being used, for instance, in autonomous vessel applications or assistance systems.
Docking Control of a Fully-Actuated Autonomous Vessel using Model Predictive Path Integral Control
(2022)
This paper presents the docking control of an autonomous vessel using the nonlinear Model Predictive Path Integral (MPPI) approach. This algorithm is based on a path integral over stochastic trajectories and can be parallelized easily. The controller parameters are tuned offline using knowledge of the system and simulations, including nonlinear state and disturbance observer. The cost function implicitly contains information regarding the surrounding of the docking position. This approach allows continuous optimization of the trajectory with respect to the system state, disturbance state and actuator dynamics. The control strategy has been tested in full-scale experiments using the solar research vessel Solgenia. The investigated MPPI controller has demonstrated excellent performance in both, simulation and real-world experiments. This paper addresses the question of how the MPPI algorithm can be applied to dock a fully-actuated vessel and what benefits its application achieves.
This paper compares novel methods to efficiently include input constraints using the nonlinear Model Predictive Path Integral (MPPI) approach. The MPPI algorithm solves stochastic optimal control problems and is based on sampled trajectories. MPPI results from the physical path integral framework. Sample-based algorithms are characterized by the fact that they can be computed in parallel and offer the possibility to handle discontinuous dynamics and cost functions. However, using standard MPPI the input costs in the Lagrange term have to be chosen quadratic. This fact is unfavorable for various real applications. Further, in standard nonlinear model predictive control (NMPC) approaches hard box constraints on the control input trajectory can be treated directly. In this contribution, novel architectures based on integrator action are compared. The investigated input constraint MPPI controllers were tested on an autonomous self-balancing vehicle. Therefore both, simulation and real-world experiments are presented. This paper addresses the question of how the MPPI algorithm can be further developed to consider input box constraints. Videos of the self-balancing vehicle are available at: https: https://tinyurl.com/mvn8j7vf
Standardmäßig werden zur Modellierung magnetischer Systeme für regelungstechnische Anwendungen oder im Bereich der Diagnose und Prognose konzentriert parametrische Modelle verwendet. Falls eine hohe Qualität der Prozessabbildung erforderlich ist, z.B. um Wirbelströme oder Sättigung geeignet zu berücksichtigen, nehmen diese Modelle schnell relativ hohe Ordnungen an. Es ist seit einiger Zeit bekannt, dass verteilparametrische Systeme, die z.B. (Feld-)Diffusionsprozesse beinhalten, durch niederdimensionale Modelle mit nicht ganzzahligen Ableitungen, so genannte fraktionale Modelle, sehr gut abgebildet werden können. Im Bereich der magnetischen Aktuatoren wurden diese vor rund 10 Jahren zum ersten Mal untersucht. Seitdem wird auf diesem Gebiet in verschiedenen Arbeitsgruppen geforscht. Während im Frequenzbereich die Handhabung fraktionaler Systeme einfach ist, sind Anwendungen im Zeitbereich bisher insbesondere bei zeitkritischen Anwendungen kaum anzutreffen. Der Beitrag stellt die prinzipielle Idee dar und zeigt Möglichkeiten zum Einsatz dieser Verfahren im Bereich magnetischer Aktoren auf. In einer konkreten Anwendung wird in Simulation und Experiment demonstriert, wie mit Hilfe dieser Modelle Zustandsschätzung in Magnetaktuatoren erfolgen kann und welche Vorteile sich dadurch ergeben.
The random matrix approach is a robust algorithm to filter the mean and covariance matrix of noisy observations of a dynamic object. Afterward, virtual measurement models can be used to find iteratively the extent parameters of an object that would cause the same statistical moments within their measurements. In previous work, this was limited to elliptical targets and only contour measurements.In this paper, we introduce the parallel use of an elliptical, triangular and rectangular-shaped virtual measurement model and a shape classification that selects the model that fits best to the measurements. The measurement likelihood is modeled either via ray tracing, a uniformly or normally spatial distribution over the object’s extent or as a combination of those.The results show that the extent estimation works precisely and that the classification accuracy highly depends on the measurement noise.