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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.
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.
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.
Extended Target Tracking With a Lidar Sensor Using Random Matrices and a Virtual Measurement Model
(2022)
Random matrices are widely used to estimate the extent of an elliptically contoured object. Usually, it is assumed that the measurements follow a normal distribution, with its standard deviation being proportional to the object’s extent. However, the random matrix approach can filter the center of gravity and the covariance matrix of measurements independently of the measurement model. This work considers the whole chain from data acquisition to the linear Kalman Filter with extension estimation as a reference plant. The input is the (unknown) ground truth (position and extent). The output is the filtered center of gravity and the filtered covariance matrix of the measurement distribution. A virtual measurement model emulates the behavior of the reference plant. The input of the virtual measurement model is adapted using the proposed algorithm until the output parameters of the virtual measurement model match the result of the reference plant. After the adaptation, the input to the virtual measurement model is considered an estimation for position and extent. The main contribution of this paper is the reference model concept and an adaptation algorithm to optimize the input of the virtual measurement model.
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.
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].
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).
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.
