Abstract

We describe a new technique to reduce tip and tilt vibrations via the design of adaptive optics controllers in a frequency framework. The method synthesizes controllers by minimizing an H2 norm of the tip and tilt residuals. In this approach, open loop slopes (pseudo-open-loop) are reconstructed from on-sky data and input into off-line simulations of the adaptive optics system. The proposed procedure executes a sequence of off-line closed-loop runs with increasing controller complexity and searches for the controller that minimizes the variance of residuals. Although the method avoids any identification of the vibration and turbulence models during the controller synthesis, the actual models are indirectly constructed as a by-product of the H2 norm minimization. The technique has been implemented on and tested with two operational instruments, namely Paranal’s NACO and Gemini-South’s GeMS, showing an effective rejection of the main vibrations in the loop and also improving the overall performance of the system over varying turbulence conditions. It is shown that a superior performance is obtained when compared to the standard integrator controller.

© 2013 OSA

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  1. C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
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  19. G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).
  20. S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A27(11), A122–A132 (2010).
    [CrossRef] [PubMed]
  21. J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995).
    [CrossRef]
  22. E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).
  23. J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965).
    [CrossRef]

2012 (5)

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A29(3), 185–194 (2012).
[CrossRef] [PubMed]

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

2011 (1)

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

2010 (3)

2009 (2)

2006 (2)

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

C. Kulcsár, H. F. Raynaud, C. Petit, J. M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express14(17), 7464–7476 (2006).
[CrossRef] [PubMed]

2004 (1)

2003 (1)

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

2001 (1)

1995 (1)

1994 (1)

E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).

1989 (1)

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Agapito, G.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Araya, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Arriagada, G.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Arsenault, R.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Bec, M.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Boccas, M.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Carrasco, E. R.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Charton, J.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Christou, J.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Clare, R.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Collao, F.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Conan, J. M.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010).
[CrossRef] [PubMed]

C. Kulcsár, H. F. Raynaud, C. Petit, J. M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express14(17), 7464–7476 (2006).
[CrossRef] [PubMed]

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A21(7), 1261–1276 (2004).
[CrossRef]

J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995).
[CrossRef]

Conan, J.-M.

Correia, C.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A29(3), 185–194 (2012).
[CrossRef] [PubMed]

C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010).
[CrossRef] [PubMed]

Darren, E.

J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III,844711 (2010).

Diaz, H.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Diggs, S. J.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

d'Orgeville, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Doyle, J. C.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

Edwards, M. L.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Ellerbroek, B. L.

Esposito, S.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Feautrier, P.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Fedrigo, E.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract.17(1), 122–135 (2009).
[CrossRef]

Fesquet, V.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Francis, B. A.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

Fusco, T.

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A27(11), A122–A132 (2010).
[CrossRef] [PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A21(7), 1261–1276 (2004).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Galvez, R. L.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Gausachs, G.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Gendron, E.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).

Gigan, P.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Glover, K.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

Guesalaga, A.

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

Guyon, O.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Guzman, D.

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

Herriot, G.

Hubin, N. N.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Kern, P. Y.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Khargonekar, P. P.

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

Kulcsár, C.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010).
[CrossRef] [PubMed]

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A27(11), A122–A132 (2010).
[CrossRef] [PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

C. Kulcsár, H. F. Raynaud, C. Petit, J. M. Conan, and P. Viaris de Lesegno, “Optimal control, observers and integrators in adaptive optics,” Opt. Express14(17), 7464–7476 (2006).
[CrossRef] [PubMed]

B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A21(7), 1261–1276 (2004).
[CrossRef]

Lacombe, F.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Lagrange, A.-M.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Le Roux, B.

Lena, P.

E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).

Lopez, A.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Lührs, J.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Madec, P. Y.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995).
[CrossRef]

Maly, J.

J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III,844711 (2010).

Marchant, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Martinache, F.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Mead, R.

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Meimon, S.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A27(11), A122–A132 (2010).
[CrossRef] [PubMed]

Montes, V.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Montri, J.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

Moreno, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Morris, T.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Mouillet, D.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Mugnier, L. M.

Muradore, R.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract.17(1), 122–135 (2009).
[CrossRef]

Neichel, B.

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

Nelder, J. A.

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Osborn, J.

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

Pargett, T.

J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III,844711 (2010).

Pessev, P.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Petit, C.

Pettazzi, L.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Puget, P.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Quiros-Pacheco, F.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Quirós-Pacheco, F.

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Rabaud, D.

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Rabou, P.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Rambold, W. N.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Raynaud, H. F.

Raynaud, H.-F.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

Riccardi, A.

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Rigaut, F.

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Comparison of vibration mitigation controllers for adaptive optics systems,” Appl. Opt.51(19), 4520–4535 (2012).
[CrossRef] [PubMed]

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

B. L. Ellerbroek and F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A18(10), 2539–2547 (2001).
[CrossRef] [PubMed]

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

Rodriguez, I.

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

Rousset, G.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995).
[CrossRef]

Serio, A.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Sivo, G.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Stadler, E.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Tesi, P.

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Trancho, G.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Trujillo, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Urrutia, C.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Véran, J. P.

Véran, J.-P.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Viaris de Lesegno, P.

Vidal, F.

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Vucina, T. B.

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

Zilio, D.

E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract.17(1), 122–135 (2009).
[CrossRef]

Zins, G.

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

Adaptive Optics Systems (1)

C. Kulcsár, G. Sivo, H.-F. Raynaud, B. Neichel, F. Rigaut, J. Christou, A. Guesalaga, C. Correia, J.-P. Véran, E. Gendron, F. Vidal, G. Rousset, T. Morris, S. Esposito, F. Quiros-Pacheco, G. Agapito, E. Fedrigo, L. Pettazzi, R. Clare, R. Muradore, O. Guyon, F. Martinache, S. Meimon, and J. M. Conan, “Vibrations in AO control: a short analysis of on-sky data around the world,” Proc. SPIE 8447, Adaptive Optics SystemsIII, 84471C (2012).

Advances in Adaptive Optics II (1)

C. Petit, J. M. Conan, T. Fusco, J. Montri, C. Kulcsár, H. F. Raynaud, and D. Rabaud, “First laboratory demonstration of closed-loop Kalman based optimal control for vibration filtering and simplified MCAO,” Proc. SPIE 6272, Advances in Adaptive Optics II, 62721T (2006).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

E. Gendron and P. Lena, “Astronomical adaptive optics I. modal control optimization,” Astron. Astrophys.291, 337 (1994).

Comput. J. (1)

J. A. Nelder and R. Mead, “A Simplex Method for Function Minimization,” Comput. J.7(4), 308–313 (1965).
[CrossRef]

Control Eng. Pract. (1)

E. Fedrigo, R. Muradore, and D. Zilio, “High performance adaptive optics system with fine tip/tilt control,” Control Eng. Pract.17(1), 122–135 (2009).
[CrossRef]

Euro. J. of Control (1)

G. Agapito, F. Quirós-Pacheco, P. Tesi, A. Riccardi, and S. Esposito, “Observer-based control techniques for the LBT adaptive optics under telescope vibrations,” Euro. J. of Control17(3), 316–326 (2011).
[CrossRef]

Ground-based and Airborne Telescopes III (1)

J. Maly, E. Darren, and T. Pargett, “Vibration suppression for the Gemini planet image,” Proc. SPIE 7733, Ground-based and Airborne Telescopes III,844711 (2010).

IEEE Trans. Automat. Contr. (1)

J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, “State-space solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr.34(8), 831–847 (1989).
[CrossRef]

J. Opt. Soc. Am. A (7)

B. L. Ellerbroek and F. Rigaut, “Methods for correcting tilt anisoplanatism in laser-guide-star-based multiconjugate adaptive optics,” J. Opt. Soc. Am. A18(10), 2539–2547 (2001).
[CrossRef] [PubMed]

C. Correia, H. F. Raynaud, C. Kulcsár, and J. M. Conan, “On the optimal reconstruction and control of adaptive optical systems with mirror dynamics,” J. Opt. Soc. Am. A27(2), 333–349 (2010).
[CrossRef] [PubMed]

C. Correia, J. P. Véran, and G. Herriot, “Advanced vibration suppression algorithms in adaptive optics systems,” J. Opt. Soc. Am. A29(3), 185–194 (2012).
[CrossRef] [PubMed]

C. Petit, J.-M. Conan, C. Kulcsár, H.-F. Raynaud, T. Fusco, J. Montri, and D. Rabaud, “Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis,” J. Opt. Soc. Am. A26(6), 1307–1325 (2009).
[CrossRef] [PubMed]

B. Le Roux, J. M. Conan, C. Kulcsár, H. F. Raynaud, L. M. Mugnier, and T. Fusco, “Optimal control law for classical and multiconjugate adaptative optics,” J. Opt. Soc. Am. A21(7), 1261–1276 (2004).
[CrossRef]

S. Meimon, C. Petit, T. Fusco, and C. Kulcsár, “Tip-tilt disturbance model identification for Kalman-based control scheme: application to XAO and ELT systems,” J. Opt. Soc. Am. A27(11), A122–A132 (2010).
[CrossRef] [PubMed]

J. M. Conan, G. Rousset, and P. Y. Madec, “Wave-front temporal spectra in high-resolution imaging through turbulence,” J. Opt. Soc. Am. A12(7), 1559–1570 (1995).
[CrossRef]

Opt. Express (1)

Proc. SPIE (3)

B. Neichel, F. Rigaut, A. Serio, G. Arriagada, M. Boccas, C. d'Orgeville, V. Fesquet, C. Trujillo, W. N. Rambold, R. L. Galvez, G. Gausachs, T. B. Vucina, V. Montes, C. Urrutia, C. Moreno, S. J. Diggs, C. Araya, J. Lührs, G. Trancho, M. Bec, C. Marchant, F. Collao, E. R. Carrasco, M. L. Edwards, P. Pessev, A. Lopez, and H. Diaz, “Science readiness of the Gemini MCAO System: GeMS,” Proc. SPIE8447, Adaptive Optics Systems III, 84474Q (2012).

G. Rousset, F. Lacombe, P. Puget, N. N. Hubin, E. Gendron, T. Fusco, R. Arsenault, J. Charton, P. Feautrier, P. Gigan, P. Y. Kern, A.-M. Lagrange, P. Y. Madec, D. Mouillet, D. Rabaud, P. Rabou, E. Stadler, and G. Zins, “NAOS, the first AO system of the VLT: on-sky performance,” Proc. SPIE. 4839, Adaptive Optical System Technologies II,140 (2003).

A. Guesalaga, B. Neichel, F. Rigaut, J. Osborn, and D. Guzman, “Design of frequency-based controllers for vibration mitigation at the Gemini-South telescope,” Proc. SPIE. 8447, Adaptive Optics Systems III, 844711 (2012).

Other (3)

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998).

J. M. Conan, H. F. Raynaud, C. Kulcsár, and S. Meimon, “Are integral controllers adapted to the new era of ELT adaptive optics?” Proc. of the 2nd AO4ELT Conference (2011).

B. Neichel, F. Rigaut, A. Guesalaga, I. Rodriguez, and D. Guzman, “Kalman and H-infinity controllers for GeMS,” OSA Conf. on Adaptive Optics (2011).

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Figures (17)

Fig. 1
Fig. 1

Standard configuration for H/H2 synthesis [15].

Fig. 2
Fig. 2

Left: servo-control problem. Right: the rearrangement of the servo loop into the augmented configuration used to synthesize the H2 controller. Functions We(s) and Wy(s) have been introduced to penalize control errors and weigh the noise, respectively.

Fig. 3
Fig. 3

On-sky PSDs for the measured tilt from NGSWFS POL slopes. Left: data from March 2011, Right: data acquired in April 2011. The noise level is estimated from the rms values of the residuals above 200 Hz.

Fig. 4
Fig. 4

Step 2: Minimum variance for optimal integrator gain for the slow and fast turbulences.

Fig. 5
Fig. 5

Step 3: residual PSD for optimum first order turbulence model. PSDs of integrator residuals are also shown.

Fig. 6
Fig. 6

Step 3: Weighting functions We and Wy that result from the optimal C0 and C1 values.

Fig. 7
Fig. 7

Frequency response of notch filters for ωo = 2π∙50 rad/s.

Fig. 8
Fig. 8

Step 4: scanning of the notch filter in search for vibrations. The minimum of the variance (bottom plot) corresponds to the strong vibration shown in the top panel.

Fig. 9
Fig. 9

Step 4: PSDs of disturbances and noise for minimum variance.

Fig. 10
Fig. 10

Step 5: residual PSD for the fifth order We. PSDs of residuals generated by the integrators are also shown.

Fig. 11
Fig. 11

Step 5: PSD of tilt slopes and associated model for minimum variance.

Fig. 12
Fig. 12

Step 5: Sensitivity functions for integral and final H2 controllers.

Fig. 13
Fig. 13

Progressive reduction of the variance of residuals for the sequence of design steps.

Fig. 14
Fig. 14

Left: open loop PSDs of residuals and associated model (coarse line); Right: PSDs of NAOS residuals using the default integrator and H2 controllers. Data from the night of November 2nd, 2011.

Fig. 15
Fig. 15

Reduction in tip-tilt residual variance for increasing complexity of controller.

Fig. 16
Fig. 16

Result from optical bench experiments using artificially generated turbulence and vibrations. Left: PSDs of POL slopes and the associated tilt residuals for the H2 and integrator controllers. Right: sensitivity functions for integral and H2 controllers.

Fig. 17
Fig. 17

Results from on-line implementation for on-sky run (May 10th, 2012). Left: PSDs of POL tilt and residuals for the H2 and integrator controllers. The variance for the integrator and H2 controllers are 9.7e-4 arcsec2 and 7.5e-4 arcsec2, respectively. Right: sensitivity functions for integral and H2 controllers.

Tables (2)

Tables Icon

Table 1 Reduction in residuals for the classical integrator and H2 controllers

Tables Icon

Table 2 Processing time (per axis) required for different size of disturbance models and resulting controller size

Equations (25)

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

C(z)= K i 1a z 1 ,
[ z e ]=P(s)[ w u ]=[ P 11 (s) P 12 (s) P 21 (s) P 22 (s) ][ w u ],
P(s)=[ P 11 (s) P 12 (s) P 21 (s) P 22 (s) ]=[ W e (s) W e (s)M(s) 0 W y (s)M(s) 1 M(s) ],
P(s):[ A B 1 B 2 C 1 D 11 D 12 C 2 D 21 D 22 ],
P 11 (s)=[ W e (s) 0 ]= C 1 (sIA) 1 B 1 + D 11 ,
P 12 (s)=[ W e (s)M(s) W y (s)M(s) ]= C 1 (sIA) 1 B 2 + D 12 ,
P 21 (s)=1= D 21 ,
P 22 (s)=M(s)= C 2 (sIA) 1 B 2 + D 22 .
z= F l (P,G)w,
F l (P,G)= P 11 + P 12 G (I P 22 G) 1 P 21 .
min G F l (P,G) 2 = min G W e SF W y NSF 2 ,
F l (P,G) 2 = ( 1 2π trace[ F l (P,G) (jω) * × F l (P,G)(jω)]dω ) 1/2 ,
SF(s)= e(s) w(s) = 1 1+M(s)G(s) ,
NTF(s)= y(s) w(s) = M(s)G(s) 1+M(s)G(s) .
A G =A B 2 B 2 ' X 2 Y 2 C 2 ' C 2 , B G = B 2 ' X 2 , C G = Y 2 C 2 ' , D G =0,
X 2 =Ric[ A B 2 B 2 ' B 1 B 1 ' A ] and Y 2 =Ric[ A' C 2 C 2 ' B 1 B 1 ' A ].
G(s) C G (sI A G ) 1 B G + D G .
S k tur = S k res +iMat u k1 .
w k =iMa t 1 S k tur .
Min G(s) σ e 2 = 1 N1 k=0 N1 | e k | 2 ,
e 2 = ω 1 1+M(jω)G(jω) 2 w(jω) 2 dω.
M(s)= e 2Δs 0.0025s+1 ,
W e (s)= C 0 s+ C 1 .
W e (s)= C 0 s+ C 1 s 2 +2 η 1 ω o s+ ω o 2 s 2 +2 η 2 ω o s+ ω o 2 .
η 1 (jω) η 2 (jω) =A 1+ W y (jω) 2 W e (jω) 2 ,

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