Quantitative feedback controller design and test for an electro-hydraulic position control system in a large-scale reflecting telescope

Abstract

For the primary mirror of a large-scale telescope, an electro-hydraulic position control system (EHPCS) is used in the primary mirror support system. The EHPCS helps the telescope improve imaging quality and requires a micron-level position control capability with a high convergence rate, high tracking accuracy, and stability over a wide mirror cell rotation region. In addition, the EHPCS parameters vary across different working conditions, thus rendering the system nonlinear. In this paper, we propose a robust closed-loop design for the position control system in a primary hydraulic support system. The control system is synthesized based on quantitative feedback theory. The parameter bounds are defined by system modeling and identified using the frequency response method. The proposed controller design achieves robust stability and a reference tracking performance by loop shaping in the frequency domain. Experiment results are included from the test rig for the primary mirror support system, showing the effectiveness of the proposed control design.

Keywords

Large-scale reflecting telescope / Quantitative feedback theory / Electro-hydraulic position control system / Micron- level position control capability / System identification / Robust stability

References

[1] Ahn , K.K., Truong , D.Q., Soo , Y.H., 2007. Self tuning fuzzy PID control for hydraulic load simulator. 6th Int. Conf. on Control, Automation, and Systems, p.345–349. https://doi.org/10.1109/ICCAS.2007.4406935

[2] Bender , F.A., Sonntag , M., Sawodny , O., 2015. Nonlinear model predictive control of a hydraulic excavator using Hammerstein models. 6th Int. Conf. on Automation, Robotics and Applications, p.557–562. https://doi.org/10.1109/ICARA.2015.7081208

[3] Bigongiari , C., Bastieri , D., Galante , N., , 2004. The MAGIC telescope reflecting surface. Nucl. Instr. Meth. Phys. Res. A, 518(1-2):193–194. https://doi.org/10.1016/j.nima.2003.10.058

[4] Chait , Y., Yaniv , O., 1993. Multi-input/single-output computer-aided control design using the quantitative feedback theory. Int. J. Robust Nonl. Contr., 3(1):47–54. https://doi.org/10.1002/rnc.4590030103

[5] Chatlatanagulchai , W., Kijdech , D., Benjalersyarnon , T., , 2016. Quantitative feedback input shaping for flexible- joint robot manipulator. J. Dynam. Syst. Meas. Contr., 138(6):061006. https://doi.org/10.1115/1.4032931

[6] Elbayomy , K.M., Jiao , Z.X., Zhang , H.Q., 2008. PID control-ler optimization by GA and its performances on the electro-hydraulic servo control system. Chin. J. Aeronaut., 21(4):378–384. https://doi.org/10.1016/S1000-9361(08)60049-7

[7] Jin , H., Lim , J., Kim , Y.,, 2013. Optical design of a re-flecting telescope for CubeSat. J. Opt. Soc. Korea, 17(6):533–537. https://doi.org/10.3807/JOSK.2013.17.6.533

[8] Khodabakhshian , A., Hemmati , R., 2012. Robust decentralized multi-machine power system stabilizer design using quantitative feedback theory. Int. J. Electr. Power Energy Syst., 41(1):112–119. https://doi.org/10.1016/j.ijepes.2012.03.023

[9] Knohl , E.D., 1994. VLT primary support system. SPIE, 2199:271–283. https://doi.org/10.1117/12.176196

[10] Liu , G.P., Daley , S., 1999. Optimal-tuning PID controller design in the frequency domain with application to a ro-tary hydraulic system. Contr. Eng. Pract., 7(7):821–830. https://doi.org/10.1016/S0967-0661(99)00047-7

[11] Moeinkhah , H., Akbarzadeh , A., Rezaeepazhand , J., 2014. Design of a robust quantitative feedback theory position controller for an ionic polymer metal composite actuator using an analytical dynamic model. J. Intell. Mater. Syst. Struct., 25(15):1965–1977. https://doi.org/10.1177/1045389X13512906

[12] Park , I., Hong , S., Sunwoo , M., 2014. Robust air-to-fuel ratio and boost pressure controller design for the EGR and VGT systems using quantitative feedback theory. IEEE Trans. Contr. Syst. Technol., 22(6):2218–2231. https://doi.org/10.1109/TCST.2014.2301160

[13] Safarzadeh , O., Khaki-Sedigh , A., Shirani , A.S., 2011. Identi-fication and robust water level control of horizontal steam generators using quantitative feedback theory. Energy Conv. Manag., 52(10):3103–3111. https://doi.org/10.1016/j.enconman.2011.04.023

[14] Singh , V.P., Mohanty , S.R., Kishor , N., , 2013. Robust H-infinity load frequency control in hybrid distributed generation system. Int. J. Electr. Power Energy Syst., 46:294–305. https://doi.org/10.1016/j.ijepes.2012.10.015

[15] Sirouspour , M.R., Salcudean , S.E., 2001. Nonlinear control of hydraulic robots. IEEE Trans. Robot. Autom., 17(2):173–182. https://doi.org/10.1109/70.928562

[16] Stepp , L.M., Huang , E., Cho , M.K., 1994. Gemini primary mirror support system. SPIE, 2199:223–238. https://doi.org/10.1117/12.176192

[17] Wang , Y.Y.,Haskara , I., Yaniv , O., 2011. Quantitative feed-back design of air and boost pressure control system for turbocharged diesel engines. Contr. Eng. Pract., 19(6): 626–637. https://doi.org/10.1016/j.conengprac.2011.02.006

[18] Yao , J.Y., Jiao , Z.X., Ma , D.W., 2014. Extended-state- observer-based output feedback nonlinear robust control of hydraulic systems with backstepping. IEEE Trans. Ind. Electron., 61(11):6285–6293. https://doi.org/10.1109/TIE.2014.2304912

[19] Yao , J.Y., Jiao , Z.X., Ma , D.W., 2015. A practical nonlinear adaptive control of hydraulic servomechanisms with periodic-like disturbances. IEEE/ASME Trans. Mecha-tron., 20(6):2752–2760.https://doi.org/10.1109/TMECH.2015.2409893

RIGHTS & PERMISSIONS

2017 Zhejiang University and Springer-Verlag GmbH Germany