In this work, we present the application of a nonlinear control system, based on variable structure control and sliding modes, to a fiber optic Mach-Zehnder interferometer. We showed that this control system is able to keep the interferometer in quadrature, suppress the signal fading, lead to high accuracy control, featuring ease of implementation and high robustness. Thus, the controlled interferometer was employed for the measurement of frequency response and mechanical resonances of a cylindrical piezoelectric actuator. The advantages of an all-fiber interferometric sensor combined with the proposed nonlinear control system features compactness, light weight, alignment free, electromagnetic immunity, high sensitivity, geometric versatility, robustness, real-time high precision measurement, and possibility of operation in harsh environments.