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.
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/
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.
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.
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 the development of a control system for an industrial heating application. In this process a moving substrate is passing through a heating zone with variable speed. Heat is applied by hot air to the substrate with the air flow rate being the manipulated variable. The aim is to control the substrate’s temperature at a specific location after passing the heating zone. First, a model is derived for a point attached to the moving substrate. This is modified to reflect the temperature of the moving substrate at the specified location. In order to regulate the temperature a nonlinear model predictive control approach is applied using an implicit Euler scheme to integrate the model and an augmented gradient based optimization approach. The performance of the controller has been validated both by simulations and experiments on the physical plant. The respective results are presented in this paper.
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.
Analysing observability is an important step in the
process of designing state feedback controllers. While for linear
systems observability has been widely studied and easy-to-check
necessary and sufficient conditions are available, for nonlinear
systems, such a general recipe does not exist and different classes
of systems require different techniques. In this paper, we analyse
observability for an industrial heating process where a stripe-
shaped plastic workpiece is moving through a heating zone where
it is heated up to a specific temperature by applying hot air to its
surface through a nozzle. A modeling approach for this process
is briefly presented, yielding a nonlinear Ordinary Differential
Equation model. Sensitivity-based observability analysis is used
to identify unobservable states and make suggestions for addi-
tional sensor locations. In practice, however, it is not possible
to place additional sensors, so the available measurements are
used to implement a simple open-loop state estimator with
offset compensation and numerical and experimental results are
presented.
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.
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.
A lot of procedures for estimating the spool position in linear electromagnetic actuators using voltage and current measurements only, can be found in the literature. Subject to the accuracy of the estimated spool position some achieve better, some worse results. However, in almost every approach hysteresis has a huge impact on the estimation accuracy that can be achieved. Regardless whether these effects are caused by magnetic or mechanical hysteresis, they will limit the accuracy of the position estimate, if not taken into account. In this paper, a model is introduced which covers the hysteresis effects as well as other nonlinear ities occurring in estimated position-dependent parameters. A classical Preisach model is deployed first, which is then adjusted by using novel elementary preceding Relay-Operators. The resulting model for the estimated position-dependent parameters including the adjusted Preisach model can be easily applied to position estimation tasks. It is shown that the considered model distinctly improves the accuracy for the spool position estimate, while it is kept as simple as possible for real-time implementation reasons.
Probabilistic data association for tracking extended targets under clutter using random matrices
(2015)
The use of random matrices for tracking extended objects has received high attention in recent years. It is an efficient approach for tracking objects that give rise to more than one measurement per time step. In this paper, the concept of random matrices is used to track surface vessels using highresolution automotive radar sensors. Since the radar also receives a large number of clutter measurements from the water, for the data association problem, a generalized probabilistic data association filter is applied. Additionally, a modification of the filter update step is proposed to incorporate the Doppler velocity measurements. The presented tracking algorithm is validated using Monte Carlo Simulation, and some performance results with real radar data are shown as well.
Small vessels or unmanned surface vehicles only have a limited amount of space and energy available. If these vessels require an active sensing collision avoidance system it is often not possible to mount large sensor systems like X-Band radars. Thus, in this paper an energy efficient automotive radar and a laser range sensor are evaluated for tracking surrounding vessels. For these targets, those type of sensors typically generate more than one detection per scan. Therefore, an extended target tracking problem has to be solved to estimate state end extension of the vessels. In this paper, an extended version of the probabilistic data association filter that uses random matrices is applied. The performance of the tracking system using either radar or laser range data is demonstrated in real experiments.
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.
Extracting suitable features from acquired data to accurately depict the current health state of a system is crucial in data driven condition monitoring and prediction. Usually, analogue sensor data is sampled at rates far exceeding the Nyquist-rate containing substantial amounts of redundancies and noise, imposing high computational loads due to the subsequent and necessary feature processing chain (generation, dimensionality reduction, rating and selection). To overcome these problems, Compressed Sensing can be used to sample directly to a compressed space, provided the signal at hand and the employed compression/measurement system meet certain criteria. Theory states, that during this compression step enough information is conserved, such that a reconstruction of the original signal is possible with high probability. The proposed approach however does not rely on reconstructed data for condition monitoring purposes, but uses directly the compressed signal representation as feature vector. It is hence assumed that enough information is conveyed by the compression for condition monitoring purposes. To fuse the compressed coefficients into one health index that can be used as input for remaining useful life prediction algorithms and is limited to a reasonable range between 1 and 0, a logistic regression approach is used. Run-to-failure data of three translational electromagnetic actuators is used to demonstrate the health index generation procedure. A comparison to the time domain ground truth signals obtained from Nyquist sampled coil current measurements shows reasonable agreement. I.e. underlying wear-out phenomena can be reproduced by the proposed approach enabling further investigation of the application of prognostic methods.
In this paper an approach towards databased fault diagnosis of linear electromagnetic actuators is presented. Time and time-frequency-domain methods were applied to extract fault related features from current and voltage measurements. The resulting features were transformed to enhance class separability using either Principal Component Analysis (PCA) or Optimal Transformation. Feature selection and dimensionality reduction was performed employing a modified Fisher-ratio. Fault detection was carried out using a Support-Vector-Machine classifier trained with randomly selected data subsets. Results showed, that not only the used feature sets (time-domain/time-frequency-domain) are crucial for fault detection and classification, but also feature pre-processing. PCA transformed time-domain features allow fault detection and classification without misclassification, relying on current and voltage measurements making two sensors necessary to generate the data. Optimal transformed time-frequency-domain features allow a misclassification free result as well, but as they are calculated from current measurements only, a dedicated voltage sensor is not necessary. Using those features is a promising alternative even for detecting purely supply voltage related faults.
The trajectory tracking problem for a real-scaled fully-actuated surface vessel is addressed in this paper. A nonlinear model predictive control (NMPC) scheme was designed to track a reference trajectory, considering state and input constraints, and environmental disturbances, which were assumed to be constant over the prediction horizon. The controller was tested by performing docking maneuvers using the real-scaled research vessel from the University of Applied Sciences Konstanz at the Rhine river in Germany. A comparison between the experimental results and the simulated ones was analyzed to validate the NMPC controller.