A Hybrid Algorithm for Iterative Adaptation of Feedforward Controllers: an Application on Electromechanical Switches

TL;DR

The paper tackles slow convergence in iterative feedforward adaptation for soft-landing control in electromechanical switches by introducing R2R-AC, which automates basis changes via Fisher information and decomposes a high-dimensional search into sequential one-dimensional optimizations. It combines a structured exploration-exploitation strategy with a hybrid step-size mechanism that toggles between derivative-free and gradient-based updates to accelerate convergence while maintaining robustness. Simulated experiments show that the hybrid approach substantially reduces the number of switchings required to achieve good performance, even under substantial parameter uncertainties, outperforming prior methods. The work suggests broad applicability to differentiable controllers and motivates future lab validation and enhancements for noisy environments.

Abstract

Electromechanical switching devices such as relays, solenoid valves, and contactors offer several technical and economic advantages that make them widely used in industry. However, uncontrolled operations result in undesirable impact-related phenomena at the end of the stroke. As a solution, different soft-landing controls have been proposed. Among them, feedforward control with iterative techniques that adapt its parameters is a solution when real-time feedback is not available. However, these techniques typically require a large number of operations to converge or are computationally intensive, which limits a real implementation. In this paper, we present a new algorithm for the iterative adaptation that is able to eventually adapt the search coordinate system and to reduce the search dimensional size in order to accelerate convergence. Moreover, it automatically toggles between a derivative-free and a gradient-based method to balance exploration and exploitation. To demonstrate the high potential of the proposal, each novel part of the algorithm is compared with a state-of-the-art approach via simulation.

Figures (5)

• Figure 1: General control diagram. The subscript $k$ denotes the variables of the $k$-th evaluation of the run-to-run adaptation law. The feedforward block computes $u _{f{\!}f}$ from the parameter vector $\theta$ and the desired reference signal $r$. The adaptation law updates the feedforward parameters $\theta$ using the cost $J$, which is derived from the measurable output $y$.
• Figure 2: Geometric interpretation of the first-order method adopted
• Figure 3: Cost values with respect to the number of switching operations when parameter perturbations set to $5\,\%$. 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. The 97.5th percentil ($P_{97.5}$) is also represented in (b) and (d) to show the hybrid method improvement.
• Figure 4: Effect of the Hybrid strategy versus Derivative-Free strategy. Evolution of $J$ in two specific processes selected as representative. (a) Process with slow convergence. (b) Process with convergence to an unacceptable cost
• Figure 5: Cost values with respect to the number of switching operations when parameter perturbations set to $25\,\%$. 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.