Modeling and state-space identification of deformable mirrors

Area of Science:

• Mechatronics and Adaptive Optics

Background:

• Accurate state-space models of deformable mirrors (DMs) are crucial for high-performance adaptive optics (AO) systems.
• Developing realistic, large-scale finite element (FE) models with damping, actuator dynamics, and multi-physics is challenging.
• Estimating state-space models from experimental data is difficult due to the infinite-dimensional nature and high modal density of DMs.

Purpose of the Study:

• To develop automated modeling and estimation frameworks for deformable mirror (DM) state-space models.
• To address challenges in creating accurate FE models and estimating reduced-order models from experimental data.
• To provide essential tools for the adaptive optics (AO) and mechatronics communities.

Main Methods:

• Developed an automated FE state-space model for a faceplate DM using COMSOL Multiphysics and LiveLink for MATLAB, incorporating damping and actuator dynamics.
• Generated estimation data from the FE model and employed a subspace identification algorithm to estimate reduced-order DM models.
• Investigated frequency and time domain responses, and addressed model-order selection and validation.

Main Results:

• Successfully developed an automated FE state-space modeling framework for DMs.
• Demonstrated the estimation of reduced-order DM models from generated data using subspace identification.
• Validated the model-order selection and model performance.

Conclusions:

• The developed frameworks provide essential tools for modeling and estimating DM state-space models.
• Automation and estimation techniques enhance the development of high-performance AO controllers.
• Open-source code (Python, MATLAB, COMSOL) is available to the scientific community.