Vibration rejection of Tip-Tilt mirror using improved repetitive control

Mechanical vibrations in Tip-Tilt modes affect the closed-loop performance of astronomical telescopes. Large integration time of the image sensor can restrict the Tip-Tilt mirror control bandwidth, which is not sufficient to mitigate structural vibrations. This paper proposes an improved repetitive control (IRC) of the Tip-Tilt mirror based on Youla parameterization to mitigate telescope vibrations. As a learning-type control strategy, repetitive controllers can achieve optimal performance when frequencies of vibrations are provided. Although the control bandwidth of the Tip-Tilt mirror is not improved with this proposed controller, the disturbance attenuation is enhanced. Furthermore, vibrations rejection provided by this proposed control method is not restricted by an accurate model, because this repetitive controller is a plug-in type. To reduce the waterbed effect induced by the IRC, a new Q-filter based on moving average filter is proposed. Simulations and experiments demonstrate a clear improvement of performance for the IRC in comparison with the classical repetitive controller.