A novel method for adaptive control of deformable mirrors

TL;DR

This paper introduces a data-driven adaptive control method for deformable mirrors that updates control models in real-time to handle nonlinearities and time-varying behaviors, improving performance in adaptive optics systems.

Contribution

The paper presents a novel recursive least squares based control approach that dynamically updates deformable mirror models during operation, addressing nonlinearities and model changes.

Findings

Successful experimental verification on a MEMS DM with 140 actuators

Demonstrated potential for improved closed-loop performance

Effective handling of nonlinear and time-varying DM behavior

Abstract

For sufficiently wide ranges of applied control signals (control voltages), MEMS and piezoelectric Deformable Mirrors (DMs), exhibit nonlinear behavior. The nonlinear behavior manifests itself in nonlinear actuator couplings, nonlinear actuator deformation characteristics, and in the case of piezoelectric DMs, hysteresis. Furthermore, in a number of situations, DM behavior can change over time, and this requires a procedure for updating the DM models on the basis of the observed data. If not properly modeled and if not taken into account when designing control algorithms, nonlinearities, and time-varying DM behavior, can significantly degrade the achievable closed-loop performance of Adaptive Optics (AO) systems. Widely used approaches for DM control are based on pre-estimated linear time-invariant DM models in the form of influence matrices. Often, these models are not being updated during system operation. Consequently, when the nonlinear DM behavior is excited by control signals with wide operating ranges, or when the DM behavior changes over time, the state-of-the-art DM control approaches relying upon linear control methods, might not be able to produce a satisfactory closed-loop performance of an AO system. Motivated by these key facts, we present a novel method for data-driven DM control. Our approach combines a simple open-loop control method with a recursive least squares method for dynamically updating the DM model. The DM model is constantly being updated on the basis of the dynamically changing DM operating points. That is, the proposed method updates both the control actions and the DM model during the system operation. We experimentally verify this approach on a Boston Micromachines MEMS DM with 140 actuators. Preliminary experimental results reported in this manuscript demonstrate good potential for using the developed method for DM control.