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Hybrid Dynamical Model for Reluctance Actuators Including Saturation, Hysteresis and Eddy Currents

Edgar Ramirez-Laboreo, Maurice G. L. Roes, Carlos Sagues

TL;DR

This work addresses the challenge of accurately and efficiently modeling short-stroke reluctance actuators that exhibit hysteresis, saturation, eddy currents, and flux fringing. It develops a hybrid dynamical model that integrates a generalized Preisach model (GPM) for magnetic hysteresis with an explicit, inversion-free solution using incremental permeability, and couples it to the armature dynamics via a six-mode hybrid automaton that enforces both mechanical limits and Preisach-direction-dependent behavior. The main contributions are an explicit GPM-based electromagnetic model, a robust six-mode hybrid framework, a practical identification procedure for GPM parameters and eddy-current effects, and experimental validation on a solenoid valve showing RMSEs on the order of a few percent and real-time capability. The approach enables fast, accurate transient simulations suitable for estimator and controller design in high-precision electromechanical systems, with direct applicability to soft-landing and accurate actuation tasks.

Abstract

A novel hybrid dynamical model for single-coil, short-stroke reluctance actuators is presented in this paper. The model, which is partially based on the principles of magnetic equivalent circuits, includes the magnetic phenomena of hysteresis and saturation by means of the generalized Preisach model. In addition, the eddy currents induced in the iron core are also considered, and the flux fringing effect in the air is incorporated by using results from finite element simulations. An explicit solution of the dynamics without need of inverting the Preisach model is derived, and the hybrid automaton that results from combining the electromagnetic and motion equations is presented and discussed. Finally, an identification method to determine the model parameters is proposed and experimentally illustrated on a real actuator. The results are presented and the advantages of our modeling method are emphasized.

Hybrid Dynamical Model for Reluctance Actuators Including Saturation, Hysteresis and Eddy Currents

TL;DR

This work addresses the challenge of accurately and efficiently modeling short-stroke reluctance actuators that exhibit hysteresis, saturation, eddy currents, and flux fringing. It develops a hybrid dynamical model that integrates a generalized Preisach model (GPM) for magnetic hysteresis with an explicit, inversion-free solution using incremental permeability, and couples it to the armature dynamics via a six-mode hybrid automaton that enforces both mechanical limits and Preisach-direction-dependent behavior. The main contributions are an explicit GPM-based electromagnetic model, a robust six-mode hybrid framework, a practical identification procedure for GPM parameters and eddy-current effects, and experimental validation on a solenoid valve showing RMSEs on the order of a few percent and real-time capability. The approach enables fast, accurate transient simulations suitable for estimator and controller design in high-precision electromechanical systems, with direct applicability to soft-landing and accurate actuation tasks.

Abstract

A novel hybrid dynamical model for single-coil, short-stroke reluctance actuators is presented in this paper. The model, which is partially based on the principles of magnetic equivalent circuits, includes the magnetic phenomena of hysteresis and saturation by means of the generalized Preisach model. In addition, the eddy currents induced in the iron core are also considered, and the flux fringing effect in the air is incorporated by using results from finite element simulations. An explicit solution of the dynamics without need of inverting the Preisach model is derived, and the hybrid automaton that results from combining the electromagnetic and motion equations is presented and discussed. Finally, an identification method to determine the model parameters is proposed and experimentally illustrated on a real actuator. The results are presented and the advantages of our modeling method are emphasized.
Paper Structure (14 sections, 43 equations, 9 figures, 3 tables)

This paper contains 14 sections, 43 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Hysteresis and Saturation Model
  3. Classical Preisach Model
  4. Limitations and Generalization
  5. Time Derivative of the GPM
  6. Hybrid Dynamical Model
  7. Electromagnetic dynamics
  8. Motion dynamics
  9. Hybrid Automaton
  10. Experiments and Results
  11. Actuator and Experimental Setup
  12. Parameter Identification
  13. Model Validation and Analysis
  14. Conclusions

Figures (9)

  • Figure 1: Hysteron operator with threshold values $\alpha$ and $\beta$.
  • Figure 4: Reluctance actuator diagram showing an air gap and part of the iron core. The arrows indicate the sign convention for $\phi$, $i$ and $i_\mathrm{ec}$.
  • Figure 5: Hybrid automaton modeling the dynamics of the reluctance actuator.
  • Figure 6: Solenoid valve and its geometry.
  • Figure 7: Magnetic flux lines in the air gap. Results from FEM simulations at gap lengths of 1, 2, and 3 mm, respectively. The FEM model is only used to characterize the air gap reluctance.
  • ...and 4 more figures