Open Access

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.

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 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

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.