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Nonlinear control system for optical interferometry based on variable structure control and sliding modes.

Roberta I Martin, João M S Sakamoto, Marcelo C M Teixeira

|April 7, 2017

Summary

This summary is machine-generated.

This study introduces a novel nonlinear control system for interferometry, offering high accuracy and robustness against disturbances. The system effectively maintains the interferometer

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Area of Science:

Control Systems Engineering
Optical Metrology
Nonlinear Dynamics

Background:

Interferometry systems often exhibit nonlinear behavior, complicating precise measurements.
Linear control systems struggle with large disturbances and nonlinearities, limiting practical applications.
Existing methods may require complex components like reset circuits, increasing cost and implementation difficulty.

Purpose of the Study:

To develop a novel nonlinear control system for interferometry.
To achieve high-accuracy control capable of compensating for nonlinearities and large disturbances.
To demonstrate robustness and suitability for real-world, harsh environments.

Main Methods:

Implementation of a variable structure control (VSC) and sliding mode control (SMC) approach.
Rigorous mathematical analysis to prove global asymptotic stability of the closed-loop system.
Experimental validation using a multi-axis piezoelectric flextensional actuator.

Main Results:

The nonlinear control system successfully compensated for interferometer nonlinearities.
High-accuracy control was maintained even under significant external disturbances.
The system effectively suppressed signal fading for various input signal types.
Global asymptotic stability of the control system was mathematically proven.

Conclusions:

The proposed nonlinear control system offers a robust, low-cost, and easily implementable solution for interferometry.
It enables precise measurements in challenging environments, extending interferometry's application beyond laboratory settings.
The system's ability to maintain quadrature point and suppress signal fading is crucial for reliable optical metrology.