Abstract

Resonator fiber-optic gyro (RFOG) is a high-accuracy inertial rotation sensor based on the Sagnac effect. A high-accuracy resonant frequency servo loop is indispensable for a high-performance RFOG. It is composed of a frequency discriminator, a loop filter, and a laser actuator. Influences of the loop parameters are fully developed. Optimized loop parameters are obtained by considering the noise reduction and wide dynamic performance of the RFOG. As a result, with the integration time of 10 s, the accuracy of the resonant frequency loop is increased to 0.02 Hz (1σ). It is equivalent to a rotation rate of 0.067°/h, which is close to the shot noise limit for the RFOG, while a minimum rotation of ±0.05°/s has been carried out simultaneously. These are the best results reported to date, to the best of our knowledge, for an RFOG using the miniature semiconductor laser that benefits from the optimization of the resonant frequency servo-loop parameters.

© 2012 Optical Society of America

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References

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  1. S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
    [CrossRef]
  2. G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.
  3. A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.
  4. S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.
  5. G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference Technical Digest(Optical Society of America, 2006), paper ME6.
  6. K. Takiguchi and K. Hotate, “Partially digital-feedback scheme and evaluation of optical Kerr-effect induced bias in optical passive ring-resonator gyro,” IEEE Photon. Technol. Lett. 3, 679–681 (1991).
    [CrossRef]
  7. H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
    [CrossRef]
  8. H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
    [CrossRef]
  9. Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
    [CrossRef]
  10. Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
    [CrossRef]
  11. G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. (Pearson Education, 2007).
  12. X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18, 1677–1683 (2010).
    [CrossRef]
  13. R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
    [CrossRef]

2012 (1)

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

2011 (3)

2010 (1)

1991 (1)

K. Takiguchi and K. Hotate, “Partially digital-feedback scheme and evaluation of optical Kerr-effect induced bias in optical passive ring-resonator gyro,” IEEE Photon. Technol. Lett. 3, 679–681 (1991).
[CrossRef]

1983 (1)

1977 (1)

S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Balsmo, S. K.

S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

Chen, Y.

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
[CrossRef]

Emami-Naeini, A.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. (Pearson Education, 2007).

Ezekiel, S.

R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. 8, 644–646 (1983).
[CrossRef]

S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.

Franklin, G. F.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. (Pearson Education, 2007).

He, Z.

Hotate, K.

H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90° polarization-axis rotated splices,” Opt. Express 18, 1677–1683 (2010).
[CrossRef]

K. Takiguchi and K. Hotate, “Partially digital-feedback scheme and evaluation of optical Kerr-effect induced bias in optical passive ring-resonator gyro,” IEEE Photon. Technol. Lett. 3, 679–681 (1991).
[CrossRef]

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Jin, Z.

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
[CrossRef]

Kumagai, T.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Kurokawa, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Ma, H.

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

H. Ma, Z. He, and K. Hotate, “Reduction of backscattering induced noise by carrier suppression in waveguide-type optical ring resonator gyro,” J. Lightwave Technol. 29, 85–90 (2011).
[CrossRef]

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Mao, H.

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

H. Mao, H. Ma, and Z. Jin, “Polarization maintaining silica waveguide resonator optic gyro using double phase modulation technique,” Opt. Express 19, 4632–4643 (2011).
[CrossRef]

Meyer, R. E.

Nakamura, S.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Ohno, A.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

Pavlath, G. A.

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.

Powell, J. D.

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. (Pearson Education, 2007).

Qiu, T.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference Technical Digest(Optical Society of America, 2006), paper ME6.

Ren, Y.

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
[CrossRef]

Sanders, G. A.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference Technical Digest(Optical Society of America, 2006), paper ME6.

Stowe, D. W.

Strandjord, L. K.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference Technical Digest(Optical Society of America, 2006), paper ME6.

Takiguchi, K.

K. Takiguchi and K. Hotate, “Partially digital-feedback scheme and evaluation of optical Kerr-effect induced bias in optical passive ring-resonator gyro,” IEEE Photon. Technol. Lett. 3, 679–681 (1991).
[CrossRef]

Tekippe, V. J.

Wang, X.

Zhang, G.

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

Appl. Phys. Lett. (1)

S. Ezekiel and S. K. Balsmo, “Passive ring resonator laser gyroscope,” Appl. Phys. Lett. 30, 478–480 (1977).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Takiguchi and K. Hotate, “Partially digital-feedback scheme and evaluation of optical Kerr-effect induced bias in optical passive ring-resonator gyro,” IEEE Photon. Technol. Lett. 3, 679–681 (1991).
[CrossRef]

J. Lightwave Technol. (1)

J. Zhejiang Univ. Sci. C (1)

Y. Ren, Z. Jin, Y. Chen, and H. Ma, “Optimization of the resonant frequency servo loop technique in the resonator micro optic gyro,” J. Zhejiang Univ. Sci. C 12, 942–950 (2011).
[CrossRef]

Opt. Commun. (1)

Z. Jin, G. Zhang, H. Mao, and H. Ma, “Resonator micro optic gyro with double phase modulation technique using an FPGA-based digital processor,” Opt. Commun. 285, 645–649 (2012).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Other (5)

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. (Pearson Education, 2007).

G. A. Pavlath, “Fiber optic gyros: the vision realized,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA3.

A. Ohno, A. Kurokawa, T. Kumagai, S. Nakamura, and K. Hotate, “Applications and technical progress of fiber optic gyros in Japan,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MA4.

S. Ezekiel, “Optical gyroscope options: principles and challenges,” in 18th International Optical Fiber Sensors Conference Technical Digest (Optical Society of America, 2006), paper MC1.

G. A. Sanders, L. K. Strandjord, and T. Qiu, “Hollow core fiber optic ring resonator for rotation sensing,” in 18th International Optical Fiber Sensors Conference Technical Digest(Optical Society of America, 2006), paper ME6.

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Figures (12)

Fig. 1.
Fig. 1.

Basic configuration of the RFOG based on the digital resonant frequency servo loop: C1, C2, C3, couplers; PM1, PM2, phase modulators; PD1, PD2, photodetectors; LIA1, LIA2, lock-in amplifiers; OFRR, optical fiber-ring resonator; PI, proportional integral.

Fig. 2.
Fig. 2.

Block diagram of a PI controller. e(k): error signal as an input of the controller; u(k): output of the system; I: integral term; ki: integral gain; P: proportional term; kp: proportional gain.

Figure 3.
Figure 3.

Model of the digital resonant frequency servo loop.

Fig. 4.
Fig. 4.

Bode magnitude plots of the open-loop transfer function and the error transfer function. (a) Open-loop transfer function and (b) error transfer function.

Fig. 5.
Fig. 5.

Bode plot of the open-loop transfer function. The time constant of the LPF takes four different values of 0, 0.01 s, 0.1 s, and 1 s.

Fig. 6.
Fig. 6.

Bode plots of the open-loop and the closed-loop transfer functions. The loop gain takes four different values of 102, 103, 104, and 105. (a) Bode magnitude plot of the open-loop transfer function; (b) Bode phase plot of the open-loop transfer function; (c) Magnitude plot of the closed-loop transfer function; (d) Magnitude plot of the error transfer function.

Fig. 7.
Fig. 7.

Bode plots of the open-loop and the closed-loop transfer functions. The integration time of the PI controller takes four different values of 0.0001, 0.001, 0.01, and 0.1 s. (a) Bode magnitude plot of the open-loop transfer function; (b) Bode phase plot of the open-loop transfer function; (c) Bode magnitude plot of the closed-loop transfer function; (d) Magnitude plot of the error transfer function.

Fig. 8.
Fig. 8.

Bode plots of the open-loop and the closed-loop transfer functions. The loop delay takes four different values of 1, 1, 100, and 1000 μs. (a) Bode magnitude plot of the open-loop transfer function; (b) Bode phase plot of the open-loop transfer function; (c) Magnitude plot of the closed-loop transfer function; (d) Magnitude plot of the error transfer function.

Fig. 9.
Fig. 9.

Maximum loop gain at different loop delays. (a) Bode magnitude plot of the open-loop transfer function; (b) Bode phase plot of the open-loop transfer function; (c) Magnitude plot of the closed-loop transfer function; (d) Magnitude plot of the error transfer function.

Fig. 10.
Fig. 10.

Bode plots of the open-loop and the closed-loop transfer functions at optimal loop parameters. (a) Bode magnitude plot of the open-loop transfer function; (b) Bode phase plot of the open-loop transfer function; (c) Magnitude plot of the closed-loop transfer function; (d) Magnitude plot of the error transfer function.

Fig. 11.
Fig. 11.

Measured equivalent bias stabilities of the RFOG. (a) Equivalent noise output for the resonant frequency servo loop; (b) open-loop output.

Fig. 12.
Fig. 12.

Rotation measurement results of the RFOG.

Equations (3)

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Ho(s)=k·(1+1τis)·11+τlsesτd,
{H(s)=Ho(s)1+Ho(s)He(s)=11+Ho(s).
Ho(s)=k·(1+1τis)11+τlsesτd{kτisesτdω<1/τlkτlsesτdω>1/τi.

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