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The problem of vessel collisions or near-collision situations on sea, often caused by human error due to incomplete or overwhelming information, is becoming more and more important with rising maritime traffic. Approaches to supply navigators and Vessel Traffic Services with expert knowledge and suggest trajectories for all vessels to avoid collisions, are often aimed at situations where a single planner guides all vessels with perfect information. In contrast, we suggest a two-part procedure which plans trajectories using a specialised A* and negotiates trajectories until a solution is found, which is acceptable for all vessels. The solution obeys collision avoidance rules, includes a dynamic model of all vessels and negotiates trajectories to optimise globally without a global planner and extensive information disclosure. The procedure combines all components necessary to solve a multi-vessel encounter and is tested currently in simulation and on several test beds. The first results show a fast converging optimisation process which after a few negotiation rounds already produce feasible, collision free trajectories.
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.
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.
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.
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].
The improvement of collision avoidance for vessels in close range encounter situations is an important topic for maritime traffic safety. Typical approaches generate evasive trajectories or optimise the trajectories of all involved vessels. Such a collision avoidance system has to produce evasive manoeuvres that do not confuse other navigators. To achieve this behaviour, a probabilistic obstacle handling based on information from a radar sensor with target tracking, that considers measurement and tracking uncertainties is proposed. A grid based path search algorithm, that takes the information from the probabilistic obstacle handling into account, is then used to generate evasive trajectories. The proposed algorithms have been tested and verified in a simulated environment for inland waters.
Motion safety for vessels
(2015)
The improvement of collision avoidance for vessels in close range encounter situations is an important topic for maritime traffic safety. Typical approaches generate evasive trajectories or optimise the trajectories of all involved vessels. The idea of this work is to validate these trajectories related to guaranteed motion safety, which means that it is not sufficient for a trajectory to be collision-free, but it must additionally ensure that an evasive manoeuvre is performable at any time. An approach using the distance and the evolution of the distance to the other vessels is proposed. The concept of Inevitable Collision States (ICS) is adopted to identify the states for which no evasive manoeuvre exist. Furthermore, it is implemented into a collision avoidance system for recreational crafts to demonstrate the performance.
Knowing the position of the spool in a solenoid valve, without using costly position sensors, is of considerable interest in a lot of industrial applications. In this paper, the problem of position estimation based on state observers for fast-switching solenoids, with sole use of simple voltage and current measurements, is investigated. Due to the short spool traveling time in fast-switching valves, convergence of the observer errors has to be achieved very fast. Moreover, the observer has to be robust against modeling uncertainties and parameter variations. Therefore, different state observer approaches are investigated, and compared to each other regarding possible uncertainties. The investigation covers a High-Gain-Observer approach, a combined High-Gain Sliding-Mode-Observer approach, both based on extended linearization, and a nonlinear Sliding-Mode-Observer based on equivalent output injection. The results are discussed by means of numerical simulations for all approaches, and finally physical experiments on a valve-mock-up are thoroughly discussed for the nonlinear Sliding-Mode-Observer.
In this paper, a gain-scheduled nonlinear control structure is proposed for a surface vessel, which takes advantage of extended linearisation techniques. Thereby, an accurate tracking of desired trajectories can be guaranteed that contributes to a safe and reliable water transport. The PI state feedback control is extended by a feedforward control based on an inverse system model. To achieve an accurate trajectory tracking, however, an observer-based disturbance compensation is necessary: external disturbances by cross currents or wind forces in lateral direction and wave-induced measurement disturbances are estimated by a nonlinear observer and used for a compensation. The efficiency and the achieved tracking performance are shown by simulation results using a validated model of the ship Korona at the HTWG Konstanz, Germany. Here, both tracking behaviour and rejection of disturbance forces in lateral direction are considered.
Sliding-mode observation with iterative parameter adaption for fast-switching solenoid valves
(2016)
Control of the armature motion of fast-switching solenoid valves is highly desired to reduce noise emission and wear of material. For feedback control, information of the current position and velocity of the armature are necessary. In mass production applications, however, position sensors are unavailable due to cost and fabrication reasons. Thus, position estimation by measuring merely electrical quantities is a key enabler for advanced control, and, hence, for efficient and robust operation of digital valves in advanced hydraulic applications. The work presented here addresses the problem of state estimation, i.e., position and velocity of the armature, by sole use of electrical measurements. The considered devices typically exhibit nonlinear and very fast dynamics, which makes observer design a challenging task. In view of the presence of parameter uncertainty and possible modeling inaccuracy, the robustness properties of sliding mode observation techniques are deployed here. The focus is on error convergence in the presence of several sources for modeling uncertainty and inaccuracy. Furthermore, the cyclic operation of switching solenoids is exploited to iteratively correct a critical parameter by taking into account the norm of the observation error of past switching cycles of the process. A thorough discussion on real-world experimental results highlights the usefulness of the proposed state observation approach.
The method of signal injection is investigated for position estimation of proportional solenoid valves. A simple observer is proposed to estimate a position-dependent parameter, i.e. the eddy current resistance, from which the position is calculated analytically. Therefore, the relationship of position and impedance in the case of sinusoidal excitation is accurately described by consideration of classical electrodynamics. The observer approach is compared with a standard identification method, and evaluated by practical experiments on an off-the-shelf proportional solenoid valve.
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.
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 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.
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.
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.
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.
In extended object tracking, a target is capable to generate more than one measurement per scan. Assuming the target being of elliptical shape and given a point cloud of measurements, the Random Matrix Framework can be applied to concurrently estimate the target’s dynamic state and extension. If the point cloud contains also clutter measurements or origins from more than one target, the data association problem has to be solved as well. However, the well-known joint probabilistic data association method assumes that a target can generate at most one detection. In this article, this constraint is relaxed, and a multi-detection version of the joint integrated probabilistic data association is proposed. The data association method is then combined with the Random Matrix framework to track targets with elliptical shape. The final filter is evaluated in the context of tracking smaller vessels using a high resolution radar sensor. The performance of the filter is shown in simulation and in several experiments.
Sensorlose Positionsregelung eines hydraulischen Proportional-Wegeventils mittels Signalinjektion
(2017)
Es wird eine Methode zur sensorlosen Positionsbestimmung bei elektromagnetisch betätigten Aktoren vorgestellt. Dabei werden basierend auf einer Signalinjektion die positionsabhängigen Parameter bei der injizierten Frequenz bestimmt und daraus über ein geeignetes Modell die Position des Magnetankers ermittelt. Die Eignung des Verfahrens zur sensorlosen Positionsregelung wird an einem bidirektionalen Proportionalventil anhand praktischer Versuche demonstriert.
A constructive method for the design of nonlinear observers is discussed. To formulate conditions for the construction of the observer gains, stability results for nonlinear singularly perturbed systems are utilised. The nonlinear observer is designed directly in the given coordinates, where the error dynamics between the plant and the observer becomes singularly perturbed by a high-gain part of the observer injection, and the information of the slow manifold is exploited to construct the observer gains of the reduced-order dynamics. This is in contrast to typical high-gain observer approaches, where the observer gains are chosen such that the nonlinearities are dominated by a linear system. It will be demonstrated that the considered approach is particularly suited for self-sensing electromechanical systems. Two variants of the proposed observer design are illustrated for a nonlinear electromagnetic actuator, where the mechanical quantities, i.e. the position and the velocity, are not measured
A constructive nonlinear observer design for self-sensing of digital (ON/OFF) single coil electromagnetic actuators is studied. Self-sensing in this context means that solely the available energizing signals, i.e., coil current and driving voltage are used to estimate the position and velocity trajectories of the moving plunger. A nonlinear sliding mode observer is considered, where the stability of the reduced error dynamics is analyzed by the equivalent control method. No simplifications are made regarding magnetic saturation and eddy currents in the underlying dynamical model. The observer gains are constructed by taking into account some generic properties of the systems nonlinearities. Two possible choices of the observer gains are discussed. Furthermore, an observer-based tracking control scheme to achieve sensorless soft landing is considered and its closed-loop stability is studied. Experimental results for observer-based soft landing of a fast-switching solenoid valve under dry conditions are presented to demonstrate the usefulness of the approach.
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.
This paper focuses on the multivariable control of a drawing tower process. The nature of the process together with the differences in measurement noise levels that affect the variables to be controlled motivated the development of a new MPC algorithm. An extension of a multivariable predictive control algorithm with separated prediction horizons is proposed. The obtained experimental results show the usefulness of the proposed algorithm..
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.
In this paper, the problem of controlling the dissolved oxygen level (DO) during an aerobic fermentation is considered. The proposed approach deals with three major difficulties in respect to the nonlinear dynamics of the DO, the poor accuracy of the empirical models for the oxygen consumption rate and the fact that only sampled measurements are available on-line. A nonlinear integral high-gain control law including a continuous-discrete time observer is designed to keep the DO in the neighborhood of a set point value without any knowledge on the dissolved oxygen consumption rate. The local stability of the control algorithm is proved using Lyapunov tools. The performance of the control scheme is first analyzed in simulation and then experimentally evaluated during a successfull fermentation of the bacteria over a period of three days. Pseudomonas putida mt-2
This paper presents a new likelihood-based partitioning method of the measurement set for the extended object probability hypothesis density (PHD) filter framework. Recent work has mostly relied on heuristic partitioning methods that cluster the measurement data based on a distance measure between the single measurements. This can lead to poor filter performance if the tracked extended objects are closely spaced. The proposed method called Stochastic Partitioning (StP) is based on sampling methods and was inspired by a former work of Granström et. al. In this work, the StP method is applied to a Gaussian inverse Wishart (GIW) PHD filter and compared to a second filter implementation that uses the heuristic Distance Partitioning (DP) method. The performance is evaluated in Monte Carlo simulations in a scenario where two objects approach each other. It is shown that the sampling based StP method leads to an improved filter performance compared to DP.
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.
Flatness-based feed-forward control of solenoid actuators is considered. For precise motion planning and accurate steering of conventional solenoids, eddy currents cannot be neglected. The system of ordinary differential equations including eddy currents, that describes the nonlinear dynamics of such actuators, is not differentially flat. Thus, a distributed parameter approach based on a diffusion equation is considered, that enables the parametrization of the eddy current by the armature position and its time derivatives. In order to design the feedforward control, the distributed parameter model of the eddy current subsystem is combined with a typical nonlinear lumped parameter model for the electrical and mechanical subsystems of the solenoid. The control design and its application are illustrated by numerical and practical results for an industrial solenoid actuator.
This paper presents the integration of a spline based extension model into a probability hypothesis density (PHD) filter for extended targets. Using this filter the position and extension of each object as well as the number of present objects can jointly be estimated. Therefore, the spline extension model and the PHD filter are addressed and merged in a Gaussian mixture (GM) implementation. Simulation results using artificial laser measurements are used to evaluate the performance of the presented filter. Finally, the results are illustrated and discussed.
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.
A nonlinear mathematical model for the dynamics of permanent magnet synchronous machines with interior magnets is discussed. The model of the current dynamics captures saturation and dependency on the rotor angle. Based on the model, a flatness-based field-oriented closed-loop controller and a feed-forward compensation of torque ripples are derived. Effectiveness and robustness of the proposed algorithms are demonstrated by simulation results.
Trajectory Tracking of a Fully-actuated Surface Vessel using Nonlinear Model Predictive Control
(2021)
The trajectory tracking problem for a fully-actuated real-scaled surface vessel is addressed in this paper. The unknown hydrodynamic and propulsion parameters of the vessel’s dynamic model were identified using an experimental maneuver-based identification process. Then, a nonlinear model predictive control (NMPC) scheme is designed and the controller’s performance is assessed through the variation of NMPC parameters and constraints tightening for tracking a curved trajectory.
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.
In multi-extended object tracking, parameters (e.g., extent) and trajectory are often determined independently. In this paper, we propose a joint parameter and trajectory (JPT) state and its integration into the Bayesian framework. This allows processing measurements that contain information about parameters and states. Examples of such measurements are bounding boxes given from an image processing algorithm. It is shown that this approach can consider correlations between states and parameters. In this paper, we present the JPT Bernoulli filter. Since parameters and state elements are considered in the weighting of the measurement data assignment hypotheses, the performance is higher than with the conventional Bernoulli filter. The JPT approach can be also used for other Bayes filters.
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/
With the high resolution of modern sensors such as multilayer LiDARs, estimating the 3D shape in an extended object tracking procedure is possible. In recent years, 3D shapes have been estimated in spherical coordinates using Gaussian processes, spherical double Fourier series or spherical harmonics. However, observations have shown that in many scenarios only a few measurements are obtained from top or bottom surfaces, leading to error-prone estimates in spherical coordinates. Therefore, in this paper we propose to estimate the shape in cylindrical coordinates instead, applying harmonic functions. Specifically, we derive an expansion for 3D shapes in cylindrical coordinates by solving a boundary value problem for the Laplace equation. This shape representation is then integrated in a plain greedy association model and compared to shape estimation procedures in spherical coordinates. Since the shape representation is only integrated in a basic estimator, the results are preliminary and a detailed discussion for future work is presented at the end of the paper.
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.
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.
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.
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.
In this paper, approximating the shape of a sailing boat using elliptic cones is investigated. Measurements are assumed to be gathered from the target's surface recorded by 3D scanning devices such as multilayer LiDAR sensors. Therefore, different models for estimating the sailing boat's extent are presented and evaluated in simulated and real-world scenarios. In particular, the measurement source association problem is addressed in the models. Simulated investigations are conducted with a static and a moving elliptic cone. The real-world scenario was recorded with a Velodyne Alpha Prime (VLP-128) mounted on a ferry of Lake Constance. Final results of this paper constitute the extent estimation of a single sailing boat using LiDAR data applying various measurement models.
Reliability Assessment of an Unscented Kalman Filter by Using Ellipsoidal Enclosure Techniques
(2022)
The Unscented Kalman Filter (UKF) is widely used for the state, disturbance, and parameter estimation of nonlinear dynamic systems, for which both process and measurement uncertainties are represented in a probabilistic form. Although the UKF can often be shown to be more reliable for nonlinear processes than the linearization-based Extended Kalman Filter (EKF) due to the enhanced approximation capabilities of its underlying probability distribution, it is not a priori obvious whether its strategy for selecting sigma points is sufficiently accurate to handle nonlinearities in the system dynamics and output equations. Such inaccuracies may arise for sufficiently strong nonlinearities in combination with large state, disturbance, and parameter covariances. Then, computationally more demanding approaches such as particle filters or the representation of (multi-modal) probability densities with the help of (Gaussian) mixture representations are possible ways to resolve this issue. To detect cases in a systematic manner that are not reliably handled by a standard EKF or UKF, this paper proposes the computation of outer bounds for state domains that are compatible with a certain percentage of confidence under the assumption of normally distributed states with the help of a set-based ellipsoidal calculus. The practical applicability of this approach is demonstrated for the estimation of state variables and parameters for the nonlinear dynamics of an unmanned surface vessel (USV).