Abstract

The present work concerns with the modeling, development and application of a novel control strategy based on sliding mode control, for two beam quadrature interferometers, with the high-gain approach. In this case, by reading the control signal the demodulation process does not require phase unwrapping algorithms, i.e., the output signal presents a straight-line relationship with the interferometer total phase shift. This system was implemented in a digital platform to control a bulk Michelson interferometer whose performance was experimentally determined, showing its capability on achieving real-time measurement and presenting wider dynamic range and bandwidth (52.5 rad in low frequencies and 5.8 rad up to 500 Hz) when compared with the literature. Moreover, this performance can be improved even further by simply increasing the feedback gain.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. S. K. Sheem, T. G. Giallorenzi, and K. Koo, “Optical techniques to solve the signal fading problem in fiber interferometers,” Appl. Opt. 21(4), 689–693 (1982).
    [Crossref] [PubMed]
  2. K. Fritsch and G. Adamowsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52(7), 996–1000 (1981).
    [Crossref]
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    [Crossref] [PubMed]
  6. E. Udd and W. B. J. Spillman, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2011).
    [Crossref]
  7. T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
    [Crossref]
  8. L. Shao and J. J. Gorman, “Pulsed laser interferometry with sub-picometer resolution using quadrature detection,” Opt. Express 25(6), 6335–6348 (2016).
  9. F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
    [Crossref]
  10. G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
    [Crossref]
  11. A. J. Fleming and B. S. Routley, “A closed-loop phase-locked interferometer for wide bandwidth position sensing,” Rev. Sci. Instrum. 86(11),115001 (2015).
    [Crossref] [PubMed]
  12. Z. Chao and F. Duan, “Closed-loop phase stabilizing and phase stepping methods for fiber-optic projected-fringe digital interferometry,” Rev. Sci. Instrum. 82(11), 113105 (2011).
    [Crossref] [PubMed]
  13. R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
    [Crossref] [PubMed]
  14. R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).
  15. D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
    [Crossref]
  16. J. Zhu, P. Hu, and J. Tan, “Homodyne laser vibrometer capable of detecting nanometer displacements accurately by using optical shutters,” Appl. Opt. 54(34), 10196–10199 (2015).
    [Crossref]
  17. J. G. Park and K. Cho, “High-precision tilt sensor using a folded Mach-Zehnder geometry in-phase and quadrature interferometer,” Appl. Opt. 55(9), 2155–2159 (2016).
    [Crossref] [PubMed]
  18. V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control. 22(2), 212–222 (1977).
    [Crossref]
  19. V. I. Utkin, Sliding Modes on Control and Optimization (Springer-Verlag, 1992).
    [Crossref]
  20. V. I. Utkin, “Sliding Mode Control Design Principles and Applications to Electric Drives,” IEEE Trans. Ind. Electron. 40(1), 23–36 (1977).
    [Crossref]
  21. E. A. Barbashin, Introduction to the theory of stability (Nauka, 1967).
  22. J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, “Direct phase extraction from interferograms with random phase shifts,” Opt. Express 18(20), 20620–20627 (2010).
    [Crossref] [PubMed]
  23. K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
    [Crossref]
  24. J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators,” Int. J. Control. 38(2), 465–492 (1983).
    [Crossref]
  25. J. J. Slotine and W. Li, Applied Nonlinear Control (Prentice Hall, 1991).
  26. J. C. Lozier, “A steady state approach to the theory of saturable servo systems,” IRE Trans. Autom. Control. 1(1), 19–39 (1956).
    [Crossref]
  27. A. Berger and P. O. Gutman, “A new view of anti-windup design for uncertain linear systems in the frequency domain,” Int. J. Robust Nonlinear Control. 26(10), 2116–2135 (2015).
    [Crossref]
  28. M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
    [Crossref]
  29. M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
    [Crossref]
  30. International Standard ISO16063-41, “Methods for the calibration of vibration and shock transducers-Part 41: calibration of Laser vibrometers,” (International Organization for Standardization (ISO), 2011).
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  32. H. J. von Martens, “Expanded and improved traceability of vibration measurements by laser interferometry,” Rev. Sci. Instrum. 84(12), 121601 (2013).
    [Crossref]

2017 (2)

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
[Crossref] [PubMed]

2016 (4)

J. G. Park and K. Cho, “High-precision tilt sensor using a folded Mach-Zehnder geometry in-phase and quadrature interferometer,” Appl. Opt. 55(9), 2155–2159 (2016).
[Crossref] [PubMed]

L. Shao and J. J. Gorman, “Pulsed laser interferometry with sub-picometer resolution using quadrature detection,” Opt. Express 25(6), 6335–6348 (2016).

M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
[Crossref]

M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
[Crossref]

2015 (3)

A. Berger and P. O. Gutman, “A new view of anti-windup design for uncertain linear systems in the frequency domain,” Int. J. Robust Nonlinear Control. 26(10), 2116–2135 (2015).
[Crossref]

A. J. Fleming and B. S. Routley, “A closed-loop phase-locked interferometer for wide bandwidth position sensing,” Rev. Sci. Instrum. 86(11),115001 (2015).
[Crossref] [PubMed]

J. Zhu, P. Hu, and J. Tan, “Homodyne laser vibrometer capable of detecting nanometer displacements accurately by using optical shutters,” Appl. Opt. 54(34), 10196–10199 (2015).
[Crossref]

2013 (1)

H. J. von Martens, “Expanded and improved traceability of vibration measurements by laser interferometry,” Rev. Sci. Instrum. 84(12), 121601 (2013).
[Crossref]

2011 (1)

Z. Chao and F. Duan, “Closed-loop phase stabilizing and phase stepping methods for fiber-optic projected-fringe digital interferometry,” Rev. Sci. Instrum. 82(11), 113105 (2011).
[Crossref] [PubMed]

2010 (2)

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

J. Xu, Q. Xu, L. Chai, Y. Li, and H. Wang, “Direct phase extraction from interferograms with random phase shifts,” Opt. Express 18(20), 20620–20627 (2010).
[Crossref] [PubMed]

2004 (1)

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
[Crossref]

1999 (1)

K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
[Crossref]

1991 (1)

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

1983 (1)

J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators,” Int. J. Control. 38(2), 465–492 (1983).
[Crossref]

1982 (3)

1981 (1)

K. Fritsch and G. Adamowsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52(7), 996–1000 (1981).
[Crossref]

1980 (1)

1979 (1)

1977 (2)

V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control. 22(2), 212–222 (1977).
[Crossref]

V. I. Utkin, “Sliding Mode Control Design Principles and Applications to Electric Drives,” IEEE Trans. Ind. Electron. 40(1), 23–36 (1977).
[Crossref]

1956 (1)

J. C. Lozier, “A steady state approach to the theory of saturable servo systems,” IRE Trans. Autom. Control. 1(1), 19–39 (1956).
[Crossref]

Adamowsky, G.

K. Fritsch and G. Adamowsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52(7), 996–1000 (1981).
[Crossref]

Barbashin, E. A.

E. A. Barbashin, Introduction to the theory of stability (Nauka, 1967).

Basile, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Bergamin, A.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Berger, A.

A. Berger and P. O. Gutman, “A new view of anti-windup design for uncertain linear systems in the frequency domain,” Int. J. Robust Nonlinear Control. 26(10), 2116–2135 (2015).
[Crossref]

Bucaro, J. A.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Cavagnero, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Chai, L.

Chao, Z.

Z. Chao and F. Duan, “Closed-loop phase stabilizing and phase stepping methods for fiber-optic projected-fringe digital interferometry,” Rev. Sci. Instrum. 82(11), 113105 (2011).
[Crossref] [PubMed]

Chei, L.

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
[Crossref]

Chen, Z.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

Cho, K.

Cole, J. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Dandridge, A.

Dong, C.

M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
[Crossref]

Duan, F.

Z. Chao and F. Duan, “Closed-loop phase stabilizing and phase stepping methods for fiber-optic projected-fringe digital interferometry,” Rev. Sci. Instrum. 82(11), 113105 (2011).
[Crossref] [PubMed]

Feng, Q.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

Fisher, A. D.

Fleming, A. J.

A. J. Fleming and B. S. Routley, “A closed-loop phase-locked interferometer for wide bandwidth position sensing,” Rev. Sci. Instrum. 86(11),115001 (2015).
[Crossref] [PubMed]

Fritsch, K.

K. Fritsch and G. Adamowsky, “Simple circuit for feedback stabilization of a single-mode optical fiber interferometer,” Rev. Sci. Instrum. 52(7), 996–1000 (1981).
[Crossref]

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

S. K. Sheem, T. G. Giallorenzi, and K. Koo, “Optical techniques to solve the signal fading problem in fiber interferometers,” Appl. Opt. 21(4), 689–693 (1982).
[Crossref] [PubMed]

Gorman, J. J.

Gutman, P. O.

A. Berger and P. O. Gutman, “A new view of anti-windup design for uncertain linear systems in the frequency domain,” Int. J. Robust Nonlinear Control. 26(10), 2116–2135 (2015).
[Crossref]

Herrmann, G.

M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
[Crossref]

Hu, P.

Jackson, D. A.

Kitano, C.

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
[Crossref] [PubMed]

Koo, K.

Li, J.

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
[Crossref]

Li, W.

J. J. Slotine and W. Li, Applied Nonlinear Control (Prentice Hall, 1991).

Li, Y.

Lozier, J. C.

J. C. Lozier, “A steady state approach to the theory of saturable servo systems,” IRE Trans. Autom. Control. 1(1), 19–39 (1956).
[Crossref]

Mana, G.

G. Basile, A. Bergamin, G. Cavagnero, and G. Mana, “Phase Modulation in High-resolution Optical Interferometry,” Metrologia 28(6), 455–461 (1991).
[Crossref]

Martin, R. I.

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
[Crossref] [PubMed]

Martinez, G. A.

Ozguner, U.

K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
[Crossref]

Park, J. G.

Pereira, F. C.

Priest, R.

Priest, R. G.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Ran, M.

M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
[Crossref]

Rashleigh, S. C.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Ren, J.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

Routley, B. S.

A. J. Fleming and B. S. Routley, “A closed-loop phase-locked interferometer for wide bandwidth position sensing,” Rev. Sci. Instrum. 86(11),115001 (2015).
[Crossref] [PubMed]

Sakamoto, J. M. S.

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
[Crossref] [PubMed]

Sastry, S. S.

J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators,” Int. J. Control. 38(2), 465–492 (1983).
[Crossref]

Shao, L.

Sheem, S. K.

Siegel, G. H.

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Slotine, J. J.

J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators,” Int. J. Control. 38(2), 465–492 (1983).
[Crossref]

J. J. Slotine and W. Li, Applied Nonlinear Control (Prentice Hall, 1991).

Sofrony, J.

M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
[Crossref]

Spillman, W. B. J.

E. Udd and W. B. J. Spillman, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2011).
[Crossref]

Tan, J.

Teixeira, M. C. M.

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, G. A. Martinez, F. C. Pereira, and C. Kitano, “Nonlinear control system for optical interferometry based on variable structure control and sliding modes,” Opt. Express 25(6), 6335–6348 (2017).
[Crossref] [PubMed]

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

Turner, M. C.

M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
[Crossref]

Tveten, A. B.

Udd, E.

E. Udd and W. B. J. Spillman, Fiber Optic Sensors: An Introduction for Engineers and Scientists (Wiley, 2011).
[Crossref]

Utkin, V. I.

K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
[Crossref]

V. I. Utkin, “Sliding Mode Control Design Principles and Applications to Electric Drives,” IEEE Trans. Ind. Electron. 40(1), 23–36 (1977).
[Crossref]

V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control. 22(2), 212–222 (1977).
[Crossref]

V. I. Utkin, Sliding Modes on Control and Optimization (Springer-Verlag, 1992).
[Crossref]

von Martens, H. J.

H. J. von Martens, “Expanded and improved traceability of vibration measurements by laser interferometry,” Rev. Sci. Instrum. 84(12), 121601 (2013).
[Crossref]

Wang, H.

Wang, Q.

M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
[Crossref]

Warde, C.

Wu, D.

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
[Crossref]

Xie, F.

F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

Xu, J.

Xu, Q.

Young, K. D.

K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
[Crossref]

Zhu, J.

Zhu, R.

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
[Crossref]

Appl. Opt. (4)

IEEE Trans. Autom. Control. (1)

V. I. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Autom. Control. 22(2), 212–222 (1977).
[Crossref]

IEEE Trans. Control. Syst. Technol. (1)

K. D. Young, V. I. Utkin, and U. Ozguner, “A control engineer’s guide to sliding mode control,” IEEE Trans. Control. Syst. Technol. 7(3), 328–342 (1999).
[Crossref]

IEEE Trans. Ind. Electron. (1)

V. I. Utkin, “Sliding Mode Control Design Principles and Applications to Electric Drives,” IEEE Trans. Ind. Electron. 40(1), 23–36 (1977).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

T. G. Giallorenzi, J. A. Bucaro, A. Dandridge, G. H. Siegel, J. H. Cole, S. C. Rashleigh, and R. G. Priest, “Optical fiber sensor technology,” IEEE Trans. Microw. Theory Tech. 30(4), 472–511 (1982).
[Crossref]

Int. J. Control. (1)

J. J. Slotine and S. S. Sastry, “Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators,” Int. J. Control. 38(2), 465–492 (1983).
[Crossref]

Int. J. Robust Nonlinear Control. (3)

A. Berger and P. O. Gutman, “A new view of anti-windup design for uncertain linear systems in the frequency domain,” Int. J. Robust Nonlinear Control. 26(10), 2116–2135 (2015).
[Crossref]

M. C. Turner, J. Sofrony, and G. Herrmann, “An alternative approach to anti-windup in anticipation of actuator saturation,” Int. J. Robust Nonlinear Control. 27(6), 963–980 (2016).
[Crossref]

M. Ran, Q. Wang, and C. Dong, “Anti-windup design for uncertain nonlinear systems subject to actuator saturation and external disturbance,” Int. J. Robust Nonlinear Control. 26(15), 3421–3438 (2016).
[Crossref]

IRE Trans. Autom. Control. (1)

J. C. Lozier, “A steady state approach to the theory of saturable servo systems,” IRE Trans. Autom. Control. 1(1), 19–39 (1956).
[Crossref]

Metrologia (1)

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[Crossref]

Opt. Express (3)

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F. Xie, J. Ren, Z. Chen, and Q. Feng, “Vibration-displacement measurements with a highly stabilised optical fiber Michelson interferometer system,” Opt. Laser Technol. 42(1), 208–213 (2010).
[Crossref]

Opt. Lett. (2)

Optik (1)

D. Wu, R. Zhu, L. Chei, and J. Li, “Transverse spatial phase-shifting method used in vibration-compensated interferometer,” Optik 115(8), 343–346 (2004).
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Proc. SPIE (1)

R. I. Martin, J. M. S. Sakamoto, M. C. M. Teixeira, and C. Kitano, “Variable structure and sliding modes nonlinear control system applied to a fiber optic interferometer,” Proc. SPIE 10453, 104531W (2017).

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Supplementary Material (1)

NameDescription
» Visualization 1       This video shows firstly the output signals of the interferometer operating in open-loop, while a huge displacement is induced on the mirror by exerting pressure at the mirror placed on the sensor arm of the interferometer. When the control system is

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Figures (14)

Fig. 1
Fig. 1 Modified Michelson interferometer and fringe pattern with different phase shifts.
Fig. 2
Fig. 2 Block diagram of the interferometric dynamical system.
Fig. 3
Fig. 3 Equilibrium points in the interferometric characteristic curve.
Fig. 4
Fig. 4 Closed loop block diagram in Simulink software.
Fig. 5
Fig. 5 Open and closed loop simulations for: (a) x1 for t between 0 and 0.01 s and initial condition 0.7π. (b) x1 for t between 0 and 0.01 s initial condition 1.0001π. (c) f for t between 0 and 0.01 s and initial condition 0.7π. (d) f for t between 0 and 0.01 s and initial condition 1.0001π.
Fig. 6
Fig. 6 Open and closed loop input phases. (a) Simulation for t between 0 and 0.02 s for initial condition 0.7π rad. (b) Simulation for t between 0 and 0.02 s for initial condition 1.0001π rad.
Fig. 7
Fig. 7 Block diagram of the implemented control system.
Fig. 8
Fig. 8 Modified Michelson interferometer assemblies. (a) Assembled Modified Michelson interferometer 1. (b) Modified Michelson interferometer with PK2 actuator.
Fig. 9
Fig. 9 Modified Michelson interferometer output signals. (a) Lissajous figure of the quadrature interferometer. (b) Applied voltage to PZT and output signals of the interferometer. (c) Input (in yellow) and output quadrature signals (in purple and green) with low modulation depth.
Fig. 10
Fig. 10 Frequency response of the feedback actuator assembly.
Fig. 11
Fig. 11 Interferometer output signals x1 (yellow), f (green), input applied voltage to PK2 actuator (purple) and inverted control signal (pink) with high modulation depth at 10 Hz. (a) Open loop interferometer. (b) Closed loop interferometer.
Fig. 12
Fig. 12 Interferometer operating under deep phase-modulation. Output signals x1 (yellow), f (green), control signal (purple) and input applied voltage to PK2 actuator (pink). (a) Transition from open to closed loop. (b) Closed loop interferometer with arbitrary signal.
Fig. 13
Fig. 13 Supressing capability for different values of gain.
Fig. 14
Fig. 14 Comparison of frequency response of the PK2 actuator.

Equations (23)

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v ac 1 ( t ) = A 1 V 1 cos ( Δ ϕ ( t ) + ϕ 0 ( t ) + ϕ c ( t ) ) ,
v ac 2 ( t ) = A 2 V 2 sin ( Δ ϕ ( t ) + ϕ 0 ( t ) + ϕ c ( t ) ) .
x ˙ = f ( t , x , u ) ,
u = { u + ( x ) if s ( x ) > 0 u ( x ) if s ( x ) < 0 ,
lim s 0 + s ˙ < 0 and lim s 0 s ˙ > 0 .
d d t ( 1 2 s 2 ( x ) ) = s ( x ) s ˙ ( x ) η | s ( x ) | ,
s ( x ) = x 1 ( t ) = v ac 1 ( t ) ,
s ˙ ( x ) = x ˙ 1 = f ( Δ ϕ + ϕ 0 + ϕ c ) ( Δ ϕ ˙ + ϕ ˙ 0 + ϕ ˙ c ) ,
{ s ( x ) = x 1 = 0 s ˙ ( x ) = x ˙ 1 = 0 { ϕ c = Δ ϕ ϕ 0 + k π 2 ϕ ˙ c = Δ ϕ ˙ ϕ ˙ 0 where k is odd .
u = C sgn ( x 1 f ) ,
s s ˙ = ( x 1 f ) [ Δ ϕ ˙ + ϕ ˙ 0 C sgn ( x 1 f ) ] = ( x 1 f ) ( Δ ϕ ˙ + ϕ ˙ 0 ) C | x 1 f | .
C > C n + | Δ ϕ ˙ + ϕ ˙ 0 | ,
s s ˙ < ( x 1 f ) ( Δ ϕ ˙ + ϕ ˙ 0 ) C n | x 1 f | | Δ ϕ ˙ + ϕ ˙ 0 | | x 1 f | .
s s ˙ < C n | f | | s | .
f ˙ = A 1 V 1 cos ( Δ ϕ + ϕ 0 + ϕ c ) [ Δ ϕ ˙ + ϕ ˙ 0 C sgn ( x 1 f ) ] ,
f f ˙ = x 1 f [ Δ ϕ ˙ + ϕ ˙ 0 C sgn ( x 1 f ) ] ,
f f ˙ = x 1 f ( Δ ϕ ˙ + ϕ ˙ 0 ) + C | x 1 f | .
f f ˙ > x 1 f ( Δ ϕ ˙ + ϕ ˙ 0 ) + C n | x 1 f | + | x 1 f | | Δ ϕ ˙ + ϕ ˙ 0 | ,
f f ˙ C n | x 1 | | f | .
f ˙ = A 1 V 1 ( Δ ϕ ˙ + ϕ ˙ 0 C sgn ( x 1 f ) ) ,
u = C sgn [ ( A 1 V 1 ) 2 2 sin ( 2 ϕ t ) ] .
C = C sgn C LVA C PZT .
sgn ( x 1 f ) ( x 1 f ) ( | x 1 f | + ) ,

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