Minimum variance control for mitigation of vibrations in adaptive optics systems

Area of Science:

• Control Systems Engineering
• Optical Engineering
• Astronomy Instrumentation

Background:

• Adaptive optics (AO) systems in telescopes are susceptible to vibrations from environmental factors like wind and internal sources such as fans.
• Mechanical resonance is a significant non-turbulent perturbation affecting AO system performance.
• Frequency-based controllers have been explored for vibration mitigation in recent years.

Purpose of the Study:

• To design a minimum variance controller (MVC) for mitigating vibrations in adaptive optics (AO) systems.
• To establish the equivalence between MVC and Linear Quadratic Gaussian (LQG) controllers for AO systems.
• To provide frequency-domain insights into controller behavior and performance.

Main Methods:

• Formulating the AO system model for MVC design, focusing on zero-input signal tracking.
• Demonstrating the mathematical equivalence between the MVC and LQG controller for AO systems.
• Deriving transfer function expressions for the MVC to analyze frequency-domain characteristics.

Main Results:

• The MVC is shown to be an equivalent representation of the LQG controller for AO systems.
• Transfer function expressions derived from the MVC offer insights into controller behavior and expected frequency-domain performance.
• The analysis highlights the influence of system and perturbation model accuracy on vibration mitigation effectiveness.

Conclusions:

• The minimum variance controller (MVC) provides an effective framework for vibration mitigation in telescope adaptive optics (AO) systems.
• The MVC offers a valuable perspective on controller design and performance analysis in the frequency domain.
• Accurate modeling of the system and perturbations is crucial for optimizing vibration mitigation in AO systems.