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Takagi-Sugeno Fuzzy Nonlinear Control System for Optical Interferometry.

Murilo Franco Coradini1, Luiz Henrique Vitti Felão1, Stephany de Souza Lyra1

  • 1Electrical Engineering Department, School of Engineering, São Paulo State University (UNESP), Ilha Solteira 15385-007, SP, Brazil.

Sensors (Basel, Switzerland)
|April 28, 2025
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Summary

This study introduces Takagi-Sugeno (T-S) fuzzy control for optical interferometry signal demodulation. The novel approach enhances interferometer performance without drawbacks of traditional closed-loop systems.

Keywords:
LMITakagi–Sugenofuzzy logicinterferometrynanodisplacementphase detection

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Area of Science:

  • Optoelectronics
  • Control Systems Engineering
  • Nonlinear Control Theory

Background:

  • Takagi-Sugeno (T-S) fuzzy control is a versatile nonlinear control method applied across diverse scientific fields.
  • Optical interferometry is crucial for precise measurements, but signal demodulation can be challenging.
  • Existing fuzzy control applications have not yet addressed interferometry signal demodulation.

Purpose of the Study:

  • To apply T-S fuzzy control for the first time to demodulate interferometry signals.
  • To develop a simple, inexpensive T-S fuzzy-based digital observer for open-loop interferometers.
  • To demonstrate the fusion of an open-loop interferometer with a T-S fuzzy observer to achieve closed-loop performance.

Main Methods:

  • Designing a T-S fuzzy digital observer based on linear matrix inequalities (LMIs) for stability.
  • Integrating the observer with an open-loop Michelson interferometer.
  • Utilizing the observer to maintain the system at an optimal 90° operating point and compensate for environmental drifts.

Main Results:

  • The T-S fuzzy observer successfully enabled demodulation of optical phase signals with low modulation index.
  • The system demonstrated accurate demodulation of signals up to π/2 rad amplitudes and frequencies exceeding 100 Hz.
  • Performance was validated through simulations and measurements, showing a maximum error of 0.45% and comparable frequency response to the arc tangent method.

Conclusions:

  • T-S fuzzy control offers a viable and effective method for interferometry signal demodulation.
  • The proposed T-S fuzzy observer provides a cost-effective alternative to traditional closed-loop interferometers.
  • This approach enhances the precision and robustness of optical measurement systems.