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Related Experiment Video

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Bringing the Visible Universe into Focus with Robo-AO

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Published on: February 12, 2013

Interaction matrix uncertainty in active (and adaptive) optics.

Douglas G Macmynowski¹

¹Control and Dynamical Systems, California Institute of Technology, 1200 East California Boulevard, Pasadena, California 91125, USA. macmardg@cds.caltech.edu

|April 14, 2009

Summary

This summary is machine-generated.

Control systems for segmented mirrors are sensitive to errors in their interaction matrix. Geometric errors are particularly problematic, especially for systems with many segments, impacting telescope performance.

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Area of Science:

Optical engineering
Control systems theory
Astronomy instrumentation

Background:

Segmented mirrors are crucial for large telescopes but their control is challenged by uncertainties in the sensor-actuator interaction matrix.
Ill-conditioning of the interaction matrix amplifies sensitivity to errors, potentially causing performance degradation or instability.

Purpose of the Study:

To analyze the robustness of control systems for segmented mirrors against various uncertainties in the interaction matrix.
To quantify the impact of different error types, particularly geometric errors, on control performance.

Main Methods:

Utilized the small gain theorem and structured singular values to bound the robustness to uncertainty.
Investigated sensitivity to actuator gain, sensor gain, sensor dihedral and height sensitivity, and geometric errors.

Main Results:

Control systems demonstrate robustness to moderate uncertainties in actuator/sensor gains and certain sensitivity ratios.
Extreme sensitivity was found for geometric errors, with tolerable error scaling inversely with the number of segments.
Adaptive optics systems, with better-conditioned matrices, show less sensitivity to uncertainty.

Conclusions:

Geometric precision is critical for segmented mirror control, especially in large-scale systems.
The analytical tools used provide a framework for understanding and mitigating control uncertainties in optical systems.
Adaptive optics systems offer improved robustness to interaction matrix uncertainties compared to segmented mirror control.