Field stabilization control of the European Extremely Large Telescope under wind disturbance

Kainan Wang; André Preumont

doi:10.1364/AO.58.001174

Applied Optics
Vol. 58,
Issue 4,
pp. 1174-1184
(2019)
•https://doi.org/10.1364/AO.58.001174

Field stabilization control of the European Extremely Large Telescope under wind disturbance

Kainan Wang and André Preumont

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Kainan Wang and André Preumont, "Field stabilization control of the European Extremely Large Telescope under wind disturbance," Appl. Opt. 58, 1174-1184 (2019)

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Abstract

This paper discusses the field stabilization control of the M5 unit under wind disturbances. The first part is a literature survey of the spectral content of the wind disturbance. Next, a simplified model of a tip/tilt mirror control system is used to analyze the conditions for control-structure interaction. The influence of the asymptotic decay rate of the wind tilt disturbance on the magnitude and spectral content of the control torques is pointed out. A full telescope model is developed to justify a decoupled tip/tilt control design and to analyze the response of the primary mirror M1 to the disturbance generated by the control torques of the M5 unit.

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Decay Rate	$f_{c} (Hz)$	$σ_{0} (arcsec / s^{2})$	$f_{0} (Hz)$	RMS Torque $M_{s}$ (N·m)
−8/3	13.3	17973	229	17
−11/3	5.6	748	27.7	0.71
−13/3	4.6	295	10.2	0.28
−17/3	3.85	115	2.4	0.11

Decay Rate	Resid. Error $σ_{e}$ (arcsec)	$σ_{0}$ ( $arcsec / s^{2}$ )	$f_{0}$ (Hz)	RMS Torque $M_{s} (N \cdot m)$
−8/3	0.146	3229	67.2	3.05
−11/3	0.084	651	20.7	0.62
−13/3	0.07	295	10.2	0.28

Decay Rate $a$	Bandwidth $f_{c} (Hz)$	$σ_{e}$ (arcsec)	$f_{e} (Hz)$	$σ_{w} (nm)$	$f_{w} (Hz)$
−8/3	13.3	0.068	27.03	25.9	50.8
−8/3	4.6	0.146	18.52	6.21	49.1
−11/3	5.6	0.070	0.87	0.95	48.8
−11/3	4.6	0.084	0.85	0.66	48.3
−13/3	4.6	0.070	0.39	0.158	47.7

Decay Rate	$f_{c} (Hz)$	$σ_{0} (arcsec / s^{2})$	$f_{0} (Hz)$	RMS Torque $M_{s}$ (N·m)
−8/3	13.3	17973	229	17
−11/3	5.6	748	27.7	0.71
−13/3	4.6	295	10.2	0.28
−17/3	3.85	115	2.4	0.11

Decay Rate	Resid. Error $σ_{e}$ (arcsec)	$σ_{0}$ ( $arcsec / s^{2}$ )	$f_{0}$ (Hz)	RMS Torque $M_{s} (N \cdot m)$
−8/3	0.146	3229	67.2	3.05
−11/3	0.084	651	20.7	0.62
−13/3	0.07	295	10.2	0.28

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Applied Optics