Nonlinear control system based on variable structure and sliding modes for two beam optical interferometry
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Data
2018-03-21
Autores
Martin, Roberta Irma
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Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho apresenta um estudo teórico e experimental de um sistema de controle não linear baseado em estrutura variável e modos deslizantes desenvolvido para interferômetro de dois feixes. O sistema proposto apresenta alta precisão, robustez e, além disso, é simples e de baixo custo, aumentando a capacidade de medição para diferentes aplicações de sensores interferométricos. Comparado a outras técnicas de controle aplicadas a interferometria óptica, esta técnica apresenta importantes vantagens e leva em consideração a característica não linear do interferometro, aumentando seu poder de medição. Consequentemente, um circuito de reset não é necessário, o interferometro pode trabalhar em ambientes com grandes perturbações, a montagem e ajuste dos parâmetros é mais simples (fácil implementação), com simples configuração e custo efetivo, atingindo alta robustez e acurácia. Comparado as técnicas de demodulação baseado no espectro do sinal (J1..J4), o sistema proposto tem faixa dinâmica e resolução maiores, podendo medir atraso no tempo e operar com formas de onda arbitrárias. Além disso, aperfeiçoa os métodos de demodulação temporais aumentando a precisão para sinais de baixa amplitude, mantendo a condição de quadratura (ponto máximo de sensibilidade) e, portanto, elimina o efeito do desvanecimento do sinal, mesmo diante de grandes perturbações ao redor do sistema como, vibrações, variações de temperatura e correntes de ar. A estabilidade do sistema linearizado foi estudada através do método de linearização de Lyapunov e a estabilidade local dos pontos de equilíbrio foram provadas. Através do método do plano de fase, todas as não linearidades do sistema foram consideradas, e provou-se que para qualquer condição inicial, o sistema não linear é estável e converge para o ponto de equilíbrio. Como resultado, o sistema é globalmente assintóticamente estável e não tende a um ciclo limite ou à intabilidade. Finalmente, foi obtido a equação de Lyapunov do sistema não linear considerando a análise do plano de fase, provando novamente a estabilidade do sistema de controle. Portanto, essa abordagem pode compensar o comportamento não linear do interfometro, mantendo-o na condição de quadratura e eliminando o efeito do desvanecimento do sinal para formas de onda arbitrárias, senoidais ou sem sinal de entrada, mesmo diante de grandes perturbações externas. O sistema provou ser eficiente para operações dinâmicas em diferentes aplicações como: caracterização de atuadores piezoelétricos, caracterização da resposta da fibra à temperatura, detecção de ultrassom e detecção de ondas longitudinais geradas por um laser Q-switched em amostras de alumínio e aço, conforme mostrado neste trabalho. A alta robustez oferecida pelo controlador permite que o sistema seja embarcado e opere em ambientes com grandes perturbações como fábricas, trazendo a interferometria para fora do laboratório.
This work presents the theoretical and experimental study of a nonlinear control system designed for two beam optical interferometry based on variable structure and sliding modes. The proposed system presents high accuracy, robustness and, furthermore, is simple and low cost, increasing the measurement capability for different applications of interferometric sensors. Compared with other control techniques applied in optical interferometry, this control technique presents important features and takes in account the nonlinear characteristic of the interferometer, increasing its measurement capability. Consequently, a reset circuit is not necessary, the interferometer can work in harsh environments, the assembly and adjustment of the parameters is simpler (easy implementation), with simple setup and the effective cost, achieving high robustness and accuracy. Regarding demodulation techniques based on signal spectrum (J1..J4), the proposed system has a higher dynamic range, resolution, can measure time delay and operate with arbitrary signal waveforms. Also, it improves the temporal demodulation methods increasing the accuracy for small amplitude signals, maintaining the quadrature condition (maximum point of sensitivity) and, therefore, eliminates the effect of signal fading, even under strong external disturbances around the interferometer setup such as vibration, temperature variation and air current flow. The stability of the linearized system was studied through the Lyapunov’s linearization method and the local stability of the equilibrium points were proved. Through the phase plane method, we considered all the nonlinearities from the system, and we proved that for any initial condition, the nonlinear system is stable and converges to the equilibrium point. As a result, the system is globally asymptotically stable and it does not tend to a limit cycle nor to instability. Finally, we obtained the Lyapunov equation for the nonlinear system taking into account the phase plane analysis, proving the system’s stability. Therefore, this approach can fully compensate the nonlinear behavior of the interferometer, keep it in the quadrature point and suppress the signal fading for arbitrary signal waveforms, sinusoidal signals or zero input signal, even under strong external disturbances. The system proved to be suitable for dynamic operations, in different applications as: characterization of piezoelectric actuators, characterization of fiber response to temperature, ultrasound detection and the detection of longitudinal waves generated by a Q-switched laser on aluminum and steel samples, as shown in this work. The high robustness allows the system to be embedded and to operate in harsh environments such as factories, bringing the interferometry outside the laboratory.
This work presents the theoretical and experimental study of a nonlinear control system designed for two beam optical interferometry based on variable structure and sliding modes. The proposed system presents high accuracy, robustness and, furthermore, is simple and low cost, increasing the measurement capability for different applications of interferometric sensors. Compared with other control techniques applied in optical interferometry, this control technique presents important features and takes in account the nonlinear characteristic of the interferometer, increasing its measurement capability. Consequently, a reset circuit is not necessary, the interferometer can work in harsh environments, the assembly and adjustment of the parameters is simpler (easy implementation), with simple setup and the effective cost, achieving high robustness and accuracy. Regarding demodulation techniques based on signal spectrum (J1..J4), the proposed system has a higher dynamic range, resolution, can measure time delay and operate with arbitrary signal waveforms. Also, it improves the temporal demodulation methods increasing the accuracy for small amplitude signals, maintaining the quadrature condition (maximum point of sensitivity) and, therefore, eliminates the effect of signal fading, even under strong external disturbances around the interferometer setup such as vibration, temperature variation and air current flow. The stability of the linearized system was studied through the Lyapunov’s linearization method and the local stability of the equilibrium points were proved. Through the phase plane method, we considered all the nonlinearities from the system, and we proved that for any initial condition, the nonlinear system is stable and converges to the equilibrium point. As a result, the system is globally asymptotically stable and it does not tend to a limit cycle nor to instability. Finally, we obtained the Lyapunov equation for the nonlinear system taking into account the phase plane analysis, proving the system’s stability. Therefore, this approach can fully compensate the nonlinear behavior of the interferometer, keep it in the quadrature point and suppress the signal fading for arbitrary signal waveforms, sinusoidal signals or zero input signal, even under strong external disturbances. The system proved to be suitable for dynamic operations, in different applications as: characterization of piezoelectric actuators, characterization of fiber response to temperature, ultrasound detection and the detection of longitudinal waves generated by a Q-switched laser on aluminum and steel samples, as shown in this work. The high robustness allows the system to be embedded and to operate in harsh environments such as factories, bringing the interferometry outside the laboratory.
Descrição
Palavras-chave
Interferometria óptica de dois feixes, Controle não linear, Estrutura variável e modos deslizantes, Two beam optical interferometry, Nonlinear control, Variable Structure and sliding modes