Abstract
This work presents a novel nonlinear control system designed for interferometry based on variable structure control and sliding modes. This approach can fully compensate the nonlinear behavior of the interferometer and lead to high accuracy control for large disturbances, featuring low cost, ease of implementation and high robustness, without a reset circuit (when compared with a linear control system). A deep stability analysis was accomplished and the global asymptotic stability of the system was proved. The results showed that the nonlinear control is able to keep the interferometer in the quadrature point and suppress signal fading for arbitrary signals, sinusoidal signals, or zero input signal, even under strong external disturbances. The system showed itself suitable to characterize a multi-axis piezoelectric flextentional actuator, which displacements that are much smaller than half wavelength. The high robustness allows the system to be embedded and to operate in harsh environments as factories, bringing the interferometry outside the laboratory.
Highlights
Linear control methods have been regularly employed to stabilize interferometers and accurately estimate phase [1,2,3,4,5]
Despite the wide variety of linear systems techniques, their application to nonlinear systems, such as interferometers, can bring limitations and do not ensure the necessary robustness in the system performance, since linear control methods rely on the key assumption of a small-value disturbance for the linear model to be valid
In this work, we propose a nonlinear control system designed for interferometry, based on variable structure control and sliding modes (VS/SM)
Summary
Linear control methods have been regularly employed to stabilize interferometers and accurately estimate phase [1,2,3,4,5]. Linear control systems that are able to handle strong disturbances usually comprises a reset circuit, which increases the complexity of the circuitry and can introduce spurious signals during reset [4,5,6]. In this work, we propose a nonlinear control system designed for interferometry, based on variable structure control and sliding modes (VS/SM). This approach can fully compensate the nonlinear behavior of the interferometer and lead to high-accuracy control for strong disturbances, featuring ease of implementation and high robustness [7]. The high robustness allows the system to be embedded and to operate in a place with great mechanical or environmental disturbances, being suitable to operate in harsh environments, as factories, taking the interferometry outside the laboratory
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