Abstract

An enhancing Coleman–Hodgdon model is introduced to describe the hysteresis curves of the bimorph deformable mirror (DM). Hysteresis curves are measured from a bimorph DM and then experiment is set up for the correction of hysteresis. Finally, step response and transfer functions of a curvature adaptive optics (AO) system are compared in three cases: with DM hysteresis, without hysteresis, and with hysteresis but corrected. Simulation results show that the bandwidth of a curvature AO system is improved significantly under different loop gains after hysteresis of the DM is corrected.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
    [CrossRef]
  2. P. Ge, M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
    [CrossRef]
  3. J. M. Cruz-Hernandez, V. Hayward, “Phase control approach to hysteresis reduction,” IEEE Trans. Control Syst. Technol. 9, 100–109 (2001).
    [CrossRef]
  4. Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
    [CrossRef]
  5. E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
    [CrossRef]
  6. S. Jung, S. Kim, “Improvement of scanning accuracy of PZT piezoelectric actuator by feed-forward model reference control,” Precis. Eng. 16, 49–55 (1994).
    [CrossRef]
  7. M. Goldfarb, N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Syst. Mag.March1997, pp. 69–79.
  8. K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
    [CrossRef]
  9. A. V. Kudryashov, V. I. Shamalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. (Bellingham) 35, 3064–3073 (1996).
    [CrossRef]
  10. E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology, and Medicine, University of London, London, 1999).
  11. R. M. Corless, D. J. Jeffrey, D. E. Knuth, “A sequence of series for the Lambert Wfunction,” in Proceedings of ISSAC ’97 (International Symposium on Symbolic and Algebraic Computation ’97), W. W. Küchlin, ed. (Association for Computing Machinery, New York, 1997), pp. 197–204.
  12. D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).
  13. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
    [CrossRef]

2002 (1)

Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
[CrossRef]

2001 (1)

J. M. Cruz-Hernandez, V. Hayward, “Phase control approach to hysteresis reduction,” IEEE Trans. Control Syst. Technol. 9, 100–109 (2001).
[CrossRef]

2000 (1)

K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
[CrossRef]

1997 (1)

M. Goldfarb, N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Syst. Mag.March1997, pp. 69–79.

1996 (3)

A. V. Kudryashov, V. I. Shamalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. (Bellingham) 35, 3064–3073 (1996).
[CrossRef]

D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

1995 (1)

P. Ge, M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

1994 (1)

S. Jung, S. Kim, “Improvement of scanning accuracy of PZT piezoelectric actuator by feed-forward model reference control,” Precis. Eng. 16, 49–55 (1994).
[CrossRef]

Andersen, B.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Buscher, D. F.

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

Celanovic, N.

M. Goldfarb, N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Syst. Mag.March1997, pp. 69–79.

Chang, M. P.

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

Corless, R. M.

D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

R. M. Corless, D. J. Jeffrey, D. E. Knuth, “A sequence of series for the Lambert Wfunction,” in Proceedings of ISSAC ’97 (International Symposium on Symbolic and Algebraic Computation ’97), W. W. Küchlin, ed. (Association for Computing Machinery, New York, 1997), pp. 197–204.

Cruz-Hernandez, J. M.

J. M. Cruz-Hernandez, V. Hayward, “Phase control approach to hysteresis reduction,” IEEE Trans. Control Syst. Technol. 9, 100–109 (2001).
[CrossRef]

Dirscherl, K.

K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
[CrossRef]

Dukkipati, R.

Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
[CrossRef]

Dunlop, C. N.

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

Ellis, E. M.

E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology, and Medicine, University of London, London, 1999).

Garnas, J.

K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
[CrossRef]

Ge, P.

P. Ge, M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

Goldfarb, M.

M. Goldfarb, N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Syst. Mag.March1997, pp. 69–79.

Gonnet, G. H.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

Hare, D. E. G.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).

Hayward, V.

J. M. Cruz-Hernandez, V. Hayward, “Phase control approach to hysteresis reduction,” IEEE Trans. Control Syst. Technol. 9, 100–109 (2001).
[CrossRef]

James, A.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Jeffrey, D. J.

D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

R. M. Corless, D. J. Jeffrey, D. E. Knuth, “A sequence of series for the Lambert Wfunction,” in Proceedings of ISSAC ’97 (International Symposium on Symbolic and Algebraic Computation ’97), W. W. Küchlin, ed. (Association for Computing Machinery, New York, 1997), pp. 197–204.

Jouaneh, M.

P. Ge, M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

Jung, S.

S. Jung, S. Kim, “Improvement of scanning accuracy of PZT piezoelectric actuator by feed-forward model reference control,” Precis. Eng. 16, 49–55 (1994).
[CrossRef]

Kim, S.

S. Jung, S. Kim, “Improvement of scanning accuracy of PZT piezoelectric actuator by feed-forward model reference control,” Precis. Eng. 16, 49–55 (1994).
[CrossRef]

Klotins, E.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Knuth, D. E.

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

R. M. Corless, D. J. Jeffrey, D. E. Knuth, “A sequence of series for the Lambert Wfunction,” in Proceedings of ISSAC ’97 (International Symposium on Symbolic and Algebraic Computation ’97), W. W. Küchlin, ed. (Association for Computing Machinery, New York, 1997), pp. 197–204.

Kudryashov, A. V.

A. V. Kudryashov, V. I. Shamalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. (Bellingham) 35, 3064–3073 (1996).
[CrossRef]

Kundzins, K.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Naganathan, N.

Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
[CrossRef]

Nielsen, L.

K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
[CrossRef]

Robinson, D. J.

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

Shamalhausen, V. I.

A. V. Kudryashov, V. I. Shamalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. (Bellingham) 35, 3064–3073 (1996).
[CrossRef]

Sternberg, A. R.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Yu, Y.

Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
[CrossRef]

Zadrozny, A.

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

Zauls, V.

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

Adv. Comput. Math. (1)

R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” Adv. Comput. Math. 5, 329–359 (1996).
[CrossRef]

IEEE Control Syst. Mag. (1)

M. Goldfarb, N. Celanovic, “Modeling piezoelectric stack actuators for control of micromanipulation,” IEEE Control Syst. Mag.March1997, pp. 69–79.

IEEE Trans. Control Syst. Technol. (1)

J. M. Cruz-Hernandez, V. Hayward, “Phase control approach to hysteresis reduction,” IEEE Trans. Control Syst. Technol. 9, 100–109 (2001).
[CrossRef]

J. Vac. Sci. Technol. B (1)

K. Dirscherl, J. Garnas, L. Nielsen, “Modeling the hysteresis of a scanning probe microscope,” J. Vac. Sci. Technol. B 18, 621–625 (2000).
[CrossRef]

Math. Scientist (1)

D. J. Jeffrey, D. E. G. Hare, R. M. Corless, “Unwinding the branches of the Lambert W function,” Math. Scientist 21, 1–7 (1996).

Mech. Machine Theory (1)

Y. Yu, N. Naganathan, R. Dukkipati, “Preisach modeling of hysteresis for piezoceramic actuator system,” Mech. Machine Theory 37, 49–59 (2002).
[CrossRef]

Opt. Eng. (Bellingham) (1)

A. V. Kudryashov, V. I. Shamalhausen, “Semipassive bimorph flexible mirrors for atmospheric adaptive optics applications,” Opt. Eng. (Bellingham) 35, 3064–3073 (1996).
[CrossRef]

Precis. Eng. (2)

P. Ge, M. Jouaneh, “Modeling hysteresis in piezoceramic actuators,” Precis. Eng. 17, 211–221 (1995).
[CrossRef]

S. Jung, S. Kim, “Improvement of scanning accuracy of PZT piezoelectric actuator by feed-forward model reference control,” Precis. Eng. 16, 49–55 (1994).
[CrossRef]

Other (4)

M. P. Chang, A. Zadrozny, D. F. Buscher, C. N. Dunlop, D. J. Robinson, “Hysteresis correction of a piezoelectrically actuated segmented mirror,” in Adaptive Optical System Technologies, D. Bonaccini, R. K. Tyson, eds., Proc. SPIE3353, 864–871 (1998).
[CrossRef]

E. Klotins, K. Kundzins, A. R. Sternberg, V. Zauls, A. James, B. Andersen, “Modeling of trapped charge effects in ferroelectrics: application to piezoactuators,” in Optical Inorganic Dielectric Materials and Devices, A. Krumins, D. K. Millers, A. R. Sternberg, J. Spigulis, eds., Proc. SPIE2967, 138–143 (1997).
[CrossRef]

E. M. Ellis, “Low-cost bimorph mirrors in adaptive optics,” Ph.D. dissertation (Imperial College of Science, Technology, and Medicine, University of London, London, 1999).

R. M. Corless, D. J. Jeffrey, D. E. Knuth, “A sequence of series for the Lambert Wfunction,” in Proceedings of ISSAC ’97 (International Symposium on Symbolic and Algebraic Computation ’97), W. W. Küchlin, ed. (Association for Computing Machinery, New York, 1997), pp. 197–204.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Demonstration of DM hysteresis on a curvature AO system.

Fig. 2
Fig. 2

Three examples of hysteresis curves that were measured in three different days.

Fig. 3
Fig. 3

Tracking expected curvatures when they are sampled regularly. (a) Expected and measured curvature, (b) expected curvature versus measured curvature.

Fig. 4
Fig. 4

Tracking expected curvatures when they are sampled randomly. (a) Expected and measured curvature, (b) expected curvature versus measured curvature.

Fig. 5
Fig. 5

Distribution of measurement error.

Fig. 6
Fig. 6

Step response of a curvature system under the assumptions with and without DM hysteresis. (a) With loop gain 0.2, (b) with loop gain 0.4, (c) with loop gain 0.6.

Fig. 7
Fig. 7

Comparison of three error transfer functions with loop gain 0.2.

Fig. 8
Fig. 8

Comparison of three error transfer functions with loop gain 0.4.

Fig. 9
Fig. 9

Comparison of three error transfer functions with loop gain 0.6.

Tables (3)

Tables Icon

Table 1 Three Sets of Parameters for Eq. (5) Derived from Three Hysteresis Curves

Tables Icon

Table 2 Parameters for Simulations in Subsections 4.A and 4.B

Tables Icon

Table 3 Bandwidths (in Hertz) under Different Loop Gains

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

x±(V)=[A-B exp(-CVR)]VD×1-2exp(EVm)+exp(EVM)×exp(EV),
x±(V)=(A-B)VD[1-exp(EV)].
c(i, j)=(Dx/Nx)-2 2ϕ(i, j)x2+(Dy/Ny)-2 2ϕ(i, j)y2,
c(i, j)=(D/N)-22ϕ(i, j).
c±(V)=[A-B exp(-CVR)]VD×1-2exp(EVm)+exp(EVM)×exp(EV)+F,
c±(V)=GVH[1-exp(IV)].
V(c)=c-a1a2-1a4 Wa3a4a2expa4(c-a1)a2,
a1=FD a2=A-B exp(-CVR), a3=±2Dexp(EVm)+exp(EVM), a4=E,
a1=H, a2=G, a3=±H, a4=I.
eshot=1/N,
eshot0.032.
Ec=0.032*0.05=0.0016 m-1.

Metrics