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Real-Time Electromagnetic Estimation for Reluctance Actuators

Edgar Ramirez-Laboreo, Eduardo Moya-Lasheras, Carlos Sagues

TL;DR

The paper tackles online estimation of time-varying electrical parameters and flux linkage in reluctance actuators using only discrete voltage and current measurements. It introduces SEMERA, a Kalman-filter-based observer that estimates $r$, $l$, and $\lambda$ with a stochastic observation model, along with a CI-based reliability check and an expert rule for low-SNR periods, and it compares against an integral estimator. Through observability analysis and simulations, it demonstrates robust performance under noise and temperature variations, and it validates the approach experimentally on a valve and a relay, showing accurate tracking of $r$, $l$, and $\lambda$ and practical applicability to various reluctance devices. The work contributes to extending stochastic filtering for online time-variant parameter estimation in magnetically driven actuators and provides insights into observability under practical excitation, with implications for improved control, fault detection, and temperature-aware operation in real-time systems.

Abstract

Several modeling, estimation, and control strategies have been recently presented for simple reluctance devices like solenoid valves and electromagnetic switches. In this paper, we present a new algorithm to online estimate the flux linkage and the electrical time-variant parameters of these devices, namely the resistance and the inductance, only by making use of discrete-time measurements of voltage and current. The algorithm, which is robust against measurement noise, is able to deal with temperature variations of the device and provides accurate estimations during the motion of the armature. Additionally, an integral {estimator} that uses the start of each operation of the actuator as reset condition has been also implemented for comparative purposes. The performances of both estimation methods are studied and compared by means of simulations and experimental tests, and the benefits of our proposal are emphasized. Possible uses of the estimates and further modeling developments are also described and discussed.

Real-Time Electromagnetic Estimation for Reluctance Actuators

TL;DR

The paper tackles online estimation of time-varying electrical parameters and flux linkage in reluctance actuators using only discrete voltage and current measurements. It introduces SEMERA, a Kalman-filter-based observer that estimates , , and with a stochastic observation model, along with a CI-based reliability check and an expert rule for low-SNR periods, and it compares against an integral estimator. Through observability analysis and simulations, it demonstrates robust performance under noise and temperature variations, and it validates the approach experimentally on a valve and a relay, showing accurate tracking of , , and and practical applicability to various reluctance devices. The work contributes to extending stochastic filtering for online time-variant parameter estimation in magnetically driven actuators and provides insights into observability under practical excitation, with implications for improved control, fault detection, and temperature-aware operation in real-time systems.

Abstract

Several modeling, estimation, and control strategies have been recently presented for simple reluctance devices like solenoid valves and electromagnetic switches. In this paper, we present a new algorithm to online estimate the flux linkage and the electrical time-variant parameters of these devices, namely the resistance and the inductance, only by making use of discrete-time measurements of voltage and current. The algorithm, which is robust against measurement noise, is able to deal with temperature variations of the device and provides accurate estimations during the motion of the armature. Additionally, an integral {estimator} that uses the start of each operation of the actuator as reset condition has been also implemented for comparative purposes. The performances of both estimation methods are studied and compared by means of simulations and experimental tests, and the benefits of our proposal are emphasized. Possible uses of the estimates and further modeling developments are also described and discussed.
Paper Structure (11 sections, 47 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 11 sections, 47 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Algorithm formulation
  3. Observation Model and Process Model
  4. Observability and Convergence
  5. Algorithm equations
  6. Integral Estimator
  7. Simulation
  8. Model equations
  9. Simulation results and discussion
  10. Experimental Evaluation
  11. Conclusions

Figures (7)

  • Figure 1: (a) Schematic diagram of a linear solenoid actuator and (b) actual actuator (solenoid valve). The movable core is pulled towards zero gap by reluctance force. The opposite motion is driven by a spring force.
  • Figure 2: Hybrid automaton to model the actuator dynamics. The motion of the plunger is restricted to $h\in\left[h_\mathrm{min},h_\mathrm{max}\right]$. Variable $\varv_h$ represents the velocity of the plunger along the gap direction.
  • Figure 3: Valve simulation results. Four activation-deactivation cycles. From top to bottom: voltage measurement, current measurement (with CI-based classification), resistance estimation, inductance estimation, flux linkage estimation, voltage SNR, current SNR, time steps since the last observable state.
  • Figure 4: SPDT power relay. (a) Schematic diagram of the reluctance actuator and (b) actual relay.
  • Figure 5: Valve experimental results. From top to bottom: voltage measurement, current measurement (with CI-based classification), resistance estimation, inductance estimation, flux linkage estimation.
  • ...and 2 more figures