Faster Run-to-Run Feedforward Control of Electromechanical Switching Devices: a Sensitivity-Based Approach

TL;DR

The paper tackles slow convergence of run-to-run feedforward control for electromechanical switching devices by introducing two sensitivity-based dimensionality-reduction strategies. The methods prune low-influence parameters (integral-square sensitivity) and reparameterize via a Fisher-information-based orthogonal basis, both operating on a differential-flatness–derived feedforward law. Simulations show substantial reductions in the number of operations needed to achieve near-optimal performance and lower cumulative costs compared with a baseline, with orthogonal reduction (r≈4) often offering the best trade-off. The work suggests practical speedups for real-world soft-landing controllers and points to hardware testing and periodic basis updates as future directions.

Abstract

Electromechanical switching devices, such as solenoid valves, contactors, and relays, suffer from undesirable phenomena like clicking, mechanical wear, and contact bounce. Despite that, they are still widely used in industry due to their various economic and technical advantages. This has encouraged the development of controllers aimed at reducing the collisions that occur at the end of the switching operations. One of the most successful approaches has been the use of iterative techniques. However, these algorithms typically require a large number of operations to converge, which is definitely a clear drawback. This paper presents a strategy to improve the convergence rate of such controllers. Our proposal, which is based on the sensitivity of the control law with respect to the parameters, assumes that the performance of the system is more heavily affected by some parameters than others. Thus, by avoiding movements in the directions that have less impact, the search algorithm is expected to drive the system to near-optimal behaviors using fewer operations. Results obtained by simulation show significant improvement in the convergence rate of a state-of-the-art run-to-run feedforward controller, which demonstrates the high potential of the proposal.

Figures (4)

• Figure 1: Control diagram. The superscript $[n]$ denotes the variables of the $n$th operation. The feedforward block computes $u _{f{\!}f}$ from the parameter vector $\theta$ and the desired trajectory $z_\mathrm{d}$. The adaptation law updates $\theta$ once per operation using the cost $J$, which is derived from the measurable output $y$.
• Figure 2: Integral-square sensitivities of the feedforward control law with respect to the control parameters.
• Figure 3: Cost values with respect to the number of switching operations. Each graph shows the median ($P_{50}$) and the 10th and 90th percentiles ($P_{10}$ and $P_{90}$, respectively) of the distribution of values obtained for the 10 000 simulated experiments. The cost without control is also represented.
• Figure 4: Integrated costs with respect to the number of iterations. Each line represents the mean values for the 10 000 simulated experiments. Comparison between different reduction methods.