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Probability-Based Optimal Control Design for Soft Landing of Short-Stroke Actuators

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

TL;DR

The work tackles soft landing for fast, short-stroke actuators under uncertainty in contact position by formulating a probability-based open-loop trajectory optimization. It introduces a cost functional that minimizes the expected contact velocity and bounced acceleration while adding a regularization term, solved as a two-point boundary value problem for a lumped-parameter model of a reluctance actuator. The approach compares probability-based (POS) with energy-based (EOS) solutions, showing POS reduces expected contact velocity and acceleration and, in experiments on a solenoid valve, lowers impact-noise energy despite a modest energy increase. The method enhances robustness for low-cost actuators lacking real-time position sensing and demonstrates practical impact on actuator longevity and performance.

Abstract

The impact forces during switching operations of short-stroke actuators may cause bouncing, audible noise and mechanical wear. The application of soft-landing control strategies to these devices aims at minimizing the impact velocities of their moving components to ultimately improve their lifetime and performance. In this paper, a novel approach for soft-landing trajectory planning, including probability functions, is proposed for optimal control of the actuators. The main contribution of the proposal is that it considers uncertainty in the contact position and hence the obtained trajectories are more robust against system uncertainties. The problem is formulated as an optimal control problem and transformed into a two-point boundary value problem for its numerical resolution. Simulated and experimental tests have been performed using a dynamic model and a commercial short-stroke solenoid valve. The results show a significant improvement in the expected velocities and accelerations at contact with respect to past solutions in which the contact position is assumed to be perfectly known.

Probability-Based Optimal Control Design for Soft Landing of Short-Stroke Actuators

TL;DR

The work tackles soft landing for fast, short-stroke actuators under uncertainty in contact position by formulating a probability-based open-loop trajectory optimization. It introduces a cost functional that minimizes the expected contact velocity and bounced acceleration while adding a regularization term, solved as a two-point boundary value problem for a lumped-parameter model of a reluctance actuator. The approach compares probability-based (POS) with energy-based (EOS) solutions, showing POS reduces expected contact velocity and acceleration and, in experiments on a solenoid valve, lowers impact-noise energy despite a modest energy increase. The method enhances robustness for low-cost actuators lacking real-time position sensing and demonstrates practical impact on actuator longevity and performance.

Abstract

The impact forces during switching operations of short-stroke actuators may cause bouncing, audible noise and mechanical wear. The application of soft-landing control strategies to these devices aims at minimizing the impact velocities of their moving components to ultimately improve their lifetime and performance. In this paper, a novel approach for soft-landing trajectory planning, including probability functions, is proposed for optimal control of the actuators. The main contribution of the proposal is that it considers uncertainty in the contact position and hence the obtained trajectories are more robust against system uncertainties. The problem is formulated as an optimal control problem and transformed into a two-point boundary value problem for its numerical resolution. Simulated and experimental tests have been performed using a dynamic model and a commercial short-stroke solenoid valve. The results show a significant improvement in the expected velocities and accelerations at contact with respect to past solutions in which the contact position is assumed to be perfectly known.
Paper Structure (15 sections, 44 equations, 5 figures, 2 tables)

This paper contains 15 sections, 44 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem statement
  3. Soft-landing cost functional
  4. Expected contact velocity
  5. Expected bounced acceleration
  6. Regularization term
  7. Reluctance actuator
  8. Description of actuator and dynamic model
  9. Model identification
  10. Analysis
  11. Optimal voltage signal
  12. Optimization specifications
  13. Comparison via simulation
  14. Comparison via experimentation
  15. Conclusions

Figures (5)

  • Figure 1: Linear-travel short-stroke solenoid valve (left) and experimental setup with the valve, a micrometer to limit the maximum gap and an electret microphone to measure the impact noise (right).
  • Figure 2: Experimental and simulated results for voltage pulses of $25$, $30$ and $50 \ \mathrm V$. In the first one, the valve does not move.
  • Figure 3: Comparison of simulated results from EOS and POS.
  • Figure 4: Absolute values of expected contact velocity (top) and acceleration (bottom) in making (left) and breaking (right) operations, for different $\sigma_z$.
  • Figure 5: Relative frequency histograms of the normalized energies from the audio signals. Comparison between EOS and POS.