Structural vibrations in Tip-Tilt modes usually affect the closed-loop performance of astronomically optical telescopes. In this paper, the state of art control methods—proportional integral (PI) control, linear quadratic Gaussian (LQG) control, disturbance feed forward (DFF) control, and disturbance observer control (DOBC) of Tip-Tilt mirror to reject vibrations are first reviewed, and then compared systematically and comprehensively. Some mathematical transfor-mations allow PI, LQG, DFF, and DOBC to be described in a uniform framework of sensitivity function that expresses their advantages and disadvantages. In essence, feed forward control based-inverse model is the main idea of current techniques, which is dependent on accuracies of models in terms of Tip-Tilt mirror and vibrations. DOBC can relax dependences on accuracy model, and therefore this survey concentrates on concise tutorials of this method with clear descriptions of their features in the control area of disturbance rejections. Its applications in various conditions are reviewed with emphasis on the effectiveness. Finally, the open problems, challenges and research prospects of DOBC of Tip-Tilt mirror are discussed.
A review on control methodologies of disturbance rejections in optical telescope
First published at:Oct 18, 2019
1. Chen X, Tomizuka M. Overview and new results in disturbance observer based adaptive vibration rejection with application to advanced manufacturing. Int J Adaptive Control Signal Process 29, 1459–1474 (2015).
2. Shtessel Y, Edwards C, Fridman L, Levant A. Sliding Mode Control and Observation (Springer, New York, 2014).
3. Tomizuka M. Control methodologies for manufacturing applications. Manuf Lett 1, 46–48 (2013).
4. Gao Z Q. Active disturbance rejection control: a paradigm shift in feedback control system design. In Proceedings of 2006 American Control Conference (IEEE, 2006);
5. Han J Q. From PID to active disturbance rejection control. IEEE Trans Ind Electron 56, 900–906 (2009).
6. Deng C , Tang T , Mao Y , et al. Enhanced Disturbance Observer Based on Acceleration Measurement for Fast Steering Mirror Systems. IEEE Photonics Journal 9, 1–11(2017).
7. Lozi J, Guyon O, Jovanovic N, Singh G, Goebel S et al. Characterizing and mitigating vibrations for SCExAO. Proc SPIE 9909, 99090J (2016).
8. Rao C H, Gu N T, Zhu L, Huang J L, Li C et al. 1.8-m solar telescope in China: Chinese large solar telescope. J Astron Telescopes Instrum Syst 1, 024001 (2015).
9. MacMartin D G. Control challenges for extremely large tele-scopes. Proc SPIE 5054, 275–286 (2003).
10. Gawronski W. Control and pointing challenges of large antennas and telescopes. IEEE Trans Control Syst Technol 15, 276–289 (2007).
11. Petit C, Sauvage J F, Fusco T, Sevin A, Suarez M et al. SPHERE extreme AO control scheme: final performance as-sessment and on sky validation of the first auto-tuned LQG based operational system. Proc SPIE, 9148, 91480O (2014).
12. MacMartin D G, Thompson H A. Vibration budget for observatory equipment. J Astron Telesc Instrum Syst 1, 034005 (2015).
13. Böhm M, Pott J U, Kürster M, Sawodny O, Defrère D et al. Delay compensation for real time disturbance estimation at extremely large telescopes. IEEE Trans Control Syst Technol 25, 1384–1393 (2017).
14. Glück M, Pott J U, Sawodny O. Piezo-actuated vibration disturbance mirror for investigating accelerometer-based tip-tilt reconstruction in large telescopes. IFAC-PapersOnLine 49, 361–366 (2016).
15. Ken F, Susumu Y, Nobutaka B, Shin-ichiro S, Atsuo T et al. Accelerometer assisted high bandwidth control of tip-tilt mirror for precision pointing stability. In Proceedings of IEEE on Aerospace Conference (IEEE, 2011);
16. Agapito G, Battistelli G, Mari D, Selvi D, Tesi A et al. Frequency based design of modal controllers for adaptive optics systems. Opt Express 20, 27108–27122 (2012).
17. Muradore R, Pettazzi L, Fedrigo E. Adaptive vibration cancellation in adaptive optics: An experimental validation. In Proceedings of 2014 European Control Conference 2418–2423 (IEEE, 2014); http://doi.org/10.1109/ECC.2014.6862434.
18. Pettazzi L, Fedrigo E, Muradore R, Haguenauer P, Pallanca L. Improving the accuracy of interferometric measurements through adaptive vibration cancellation. In Proceedings of 2015 IEEE Conference on Control Applications 95–100 (IEEE, 2015); http://doi.org/10.1109/CCA.2015.7320616.
19. Yang K J, Yang P, Chen S Q, et al. Vibration identification based on Levenberg-Marquardt optimization for mitigation in adaptive optics systems. Appl Opt 57, 2820–2826 (2018).
20. Böhm M, Pott J U, Kürster M, Sawodny O. Modeling and identification of the optical path at ELTs- a case study at the LBT. IFAC Proc Volumes, 46, 249–255(2013).
21. Castro M, Escárate P, Zuñiga S, Garcés J, Guesalaga A. Closed loop for tip-tilt vibration mitigation. In Applications of Lasers for Sensing and Free Space Communications 2015 (OSA, 2015); https://doi.org/10.1364/AOMS.2015.JT5A.28.
22. Petit C, Conan J M, Kulcsár C, Raynaud H F. Linear quadratic Gaussian control for adaptive optics and multiconjugate adaptive optics: experimental and numerical analysis. J Opt Soc Am A 26, 1307–1325 (2009).
23. Radke A, Gao Z Q. A survey of state and disturbance observers for practitioners. In Proceedings of 2006 American Control Conference (IEEE, 2006);
24. Sariyildiz E, Ohnishi K. Stability and robustness of disturbance- observer-based motion control systems. IEEE Trans Ind Electron 62, 414–422 (2015).
25. Chen W H, Yang J, Guo L, Li S H. Disturbance-observer-based control and related methods-an overview. IEEE Trans Ind Electron 63, 1083–1095 (2016).
26. Kim J S, Back J, Park G. Design of Q-filters for disturbance observers via BMI approach. In Proceedings of the 14th International Conference on Control, Automation and Systems 1197–1200 (IEEE, 2014);
27. Zheng M H, Zhou S Y, Tomizuka M. A design methodology for disturbance observer with application to precision motion control: an H-infinity based approach. In Proceedings of 2017 American Control Conference 3524–3529 (IEEE, 2017);
28. Tang T, Qi B, Yang T. Youla-Kucera parameterization-based optimally closed-loop control for tip-Tilt compensation. IEEE Sens J 18, 6154–6160 (2018).
29. Tang T, Yang T, Qi B, Cao L, Ren G et al. Error-based plug-in controller of tip–tilt mirror to reject telescope’s structural vibra-tions. J Astron Telesc Instrum Syst 4, 049004 (2018).
30. Chen X, Jiang T Y, Tomizuka M. Pseudo Youla-Kucera parameterization with control of the waterbed effect for local loop shaping. Automatica 62, 177–183 (2015).
31. Jiang T Y, Chen X. Transmission of signal nonsmoothness and transient improvement in add-on servo control. IEEE Trans Control Syst Technol 26, 486–496 (2017).
32. Zhou K L, Wang D W, Zhang B, Wang Y G. Plug-in du-al-mode-structure repetitive controller for CVCF PWM inverters. IEEE Trans Ind Electron 56, 784–791 (2009).
33. Cho Y, Lai J S. Digital plug-in repetitive controller for sin-gle-phase bridgeless PFC converters. IEEE Trans Power Electron 28, 165–175 (2013).
34. Chen X, Tomizuka M. New repetitive control with improved steady-state performance and accelerated transient. IEEE Trans Control Syst Technol 22, 664–675 (2014).
35. Mahani N K Z, Sedigh A K, Bayat F M. Performance evaluation of non-minimum phase linear control systems with fractional order partial pole-zero cancellation. In Proceedings of the 9th Asian Control Conference (IEEE, 2013);
36. Stengel R F. Optimal Control and Estimation (Dover Publications, New York, 1994).
37. Siouris G M. Errata to an engineering approach to optimal control and estimation theory. IEEE Aero Electron Syst Mag 12, 37 (1997).
38. Glück M, Pott J U, Sawodny O. Investigations of an accelerometer-based disturbance feedforward control for vibration suppression in adaptive optics of large telescopes. Pub Astron Soc Pacific 2017, 129, 065001 (2017).
39. Kempf C J, Kobayashi S. Disturbance observer and feedforward design for a high-speed direct-drive positioning table. IEEE Trans Control Syst Technol 7, 513–526 (1999).
40. Kim B K, Chung W K. Advanced disturbance observer design for mechanical positioning systems. IEEE Trans Ind Electron 50, 1207–1216 (2003).
41. Tang T, Xu N S, Yang T, Qi B, Bao Q L. Vibration rejection of Tip-Tilt mirror using improved repetitive control. Mech Syst Signal Process 116, 432–442 (2019).
42. Guesalaga A, Neichel B, O’Neal J, Guzman D. Mitigation of vibrations in adaptive optics by minimization of closed-loop residuals. Opt Express 21, 10676–10696 (2013).
43. Huang Y, Xue W C. Active disturbance rejection control: Methodology and theoretical analysis. ISA Trans 53, 963–976 (2014).
44. Chen W H. Disturbance observer based control for nonlinear systems. IEEE/ASME Trans Mech 9, 706–710 (2004).
45. Won D, Kim W, Shin D, Chung C C. High-gain disturbance observer-based backstepping control with output tracking error constraint for electro-hydraulic systems. IEEE Trans Control Syst Technol 23, 787–795 (2015).
46. Liu L P, Fu Z M, Song X N. Sliding mode control with disturbance observer for a class of nonlinear systems. Int J Autom Comput 9, 487–491 (2012).
Youth Innovation Promotion Association, Chinese Academy of Sciences
Get Citation: Tang T, Niu S X, Ma J G, Qi B, Ren G et al. A review on control methodologies of disturbance rejections in optical telescope. Opto-Electron Adv 2, 190011 (2019).