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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.
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.
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.
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.
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.
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.
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.