Takagi–Sugeno Fuzzy Nonlinear Control System for Optical Interferometry

Abstract

The Takagi-Sugeno (T-S) fuzzy control is a nonlinear method that uses a combination of linear controllers as its control law. This method has been applied in various fields of scientific research: buck converters, biomedicine, civil engineering, etc. To the best of the authors’ knowledge, although works on traditional fuzzy control and optical interferometry have already been published, this is the first time that T-S fuzzy (specifically) is applied to demodulate interferometry signals. Through a proof-of-concept experiment, the paper describes the fusion of an open-loop interferometer with an external closed-loop digital observer based on T-S fuzzy (both simple and inexpensive), which actuates like a closed-loop interferometer (but without its drawbacks). The observer design is based on stability conditions using linear matrix inequalities (LMIs) solutions. The system is maintained at the optimal (Formula presented.) operation point (compensating for environmental drifts) and enables the demodulation of optical phase signals with low modulation index. Simulations and measurements were performed by using a Michelson interferometer, verifying that the method demodulates signals up to (Formula presented.) rad amplitudes and higher than 100 Hz frequencies (with maximum error of 0.45%). When compared to the important arc tangent method, both presented the same frequency response for the test PZT actuator.