Fig. 1. Optical path diagram of tip-tilt correction system

Fig. 2. Traditional closed-loop feedback control block diagram

Fig. 3. Classical repetitive control block diagram

Fig. 4. Bode response diagram of L(z)

Fig. 5. Comparison of sensitivity transfer function whether time delay is compensated or not

Fig. 6. Build experimental platform

Fig. 7. Tip-tilt errors with/without adding the repetitive controller

Fig. 8. Bode diagram of first-order fractional delay filters with different α

Fig. 9. Amplitude response of F(z) with different fractional filter parameters

Fig. 10. The sensitivity transfer function with different controllers

Fig. 11. Tip-tilt errors with different controllers

Fig. 12. Tip-tilt errors with/without fractional repetitive controllers

Fig. 13. Tip-tilt errors with/without the repetitive controller for periodic disturbances

Fig. 14. The block diagram of multiperiod repetitive control

Fig. 15. Tip-tilt errors with/without the repetitive controller for non-periodic disturbances

Fig. 16. Tip-tilt errors with/without the repetitive controller for ultra-high frequency disturbance