Elektromanyetik Yataklı Rotorların MIMO PID Kontrolu

Abstract

Elektromanyetik yataklı rotorlar kararsız sistemler oldukları için geribeslemeli kontrol çalışma şartlarının ayrılmaz bir parçasıdır. Rotor dinamiği sabit hızda doğrusal ve zamanla değişmeyen özellikte olmakla birlikte, elektromanyetik yatak dinamiği doğrusal değildir. Doğrusal olmayan yatak dinamiği sabit bir sapma akımı kullanılarak bir çalışma noktası civarında doğrusallaştırılabilir. Bu makalede yatay rotor/aktif manyetik yataklı sistemler için MIMO PID kontrolör tasarlayarak SISO PID kontrol ile performansını karşılaştırmaktayız. Rotor dinamiğindeki dinamik eşleşme birbirine dik yönlerde jiroskopik kuvvetler oluşturmaktadır. Eşleşik (dinamik) dengesizlik kuvvetler nedeniyle oluşabilecek yanal yönlerdeki açısal hareketlerin meydana getirdiği jiroskopik kuvvetlerin kompanzasyonu için SISO PID kontrol yeterli performansa sahip değildir.

Keywords

• Konveks optimizasyon,MIMO PID kontrol,dinamik balanssızlık giderme,jiroskopik rotor dinamiği,elektromanyetik yataklar

MIMO PID Control of Rotors with Electromagnetic Bearings

Abstract

Rotors with electromagnetic bearings are inherently unstable systems; hence feedback control is an integral part of  their operation.  While the rotor dynamics is linear and time-invariant  at  constant  operation  speed,  electromagnetic bearing  model  is  non-linear. Non-linear bearing dynamics can be linearized at an operating point using a constant bias current. In this paper we design a MIMO PID controller for horizontal rotor/active magnetic bearing systems and compare its performance with respect to SISO decentralized PID control. Dynamic coupling in rotor dynamics causes gyroscopic forces to act at orthogonal directions on the rotor. SISO PID control lacks  sufficient  performance  as  it  has  limited capability to compensate for the gyroscopic effects due to angular motions in transverse directions which can be caused by couple (dynamic) unbalance forces. 

Keywords

• Konveks optimizasyon,MIMO PID kontrol,dinamik balanssızlık giderme,jiroskopik rotor dinamiği,elektromanyetik yataklar

References

1. 1. Burrows C.R., Sahinkaya N., Traxler A., and Schweitzer G. (1988) Design and application of a magnetic bearing for vibration control and stabilization of a flexible rotor, 1st International Symposium on Magnetic Bearings, pp. 159-168.
2. 2. Herzog R., Bühler P., Gähler C., and Larsonneur R. (1996) Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings. IEEE Transactions on Control Systems Technology, vol. 4, no. 5, pp. 580-586.
3. 3. Kuseyri S. (2012) Robust control and unbalance compensation of rotor/active magnetic bearing systems, Journal of Vibration and Control, 12: 817-832.
4. 4. Cao, Y.-Y., Lam, J., and Sun, Y.-X. (1998) Static output feedback stabilization: An ILMI approach, Automatica, vol. 34, pp. 1641-1645.
5. 5. Fujita M., Hatake K., and Matsumura F. (1993) Loop shaping based robust control of a magnetic bearing, IEEE Control Systems Magazine, vol. 13, no. 4, pp. 57-65.
6. 6. Gahinet P. and Apkarian P. (1994) A linear matrix inequality approach to H∞ control, International Journal of Robust and Nonlinear Control, vol. 4, pp. 421-448.
7. 7. Sturm J.F. (1999) Using SEDUMI 1.02: A MATLAB®Toolbox for Optimization Over Symmetric Cones, Optimization Methods and Software, 11(12), pp. 625-653. 8. Fittro R.L. and Knospe C.R. (2002) The mu approach to control of active magnetic bearings, Journal of Engineering for Gas Turbines and Power, vol. 124, no. 3, pp. 566-570.
8. 9. Sivrioğlu S. and Nanomi K. (1996) LMI approach to gain scheduled H∞ beyond PID control for gyroscopic rotor-magnetic bearing system, Proceedings of the 35th Conference on Decision and Control, pp. 3694-3699.

9. 10. Schweitzer G. and Maslen E. (Editors) (2009) Magnetic Bearings. Springer-Verlag, Heidelberg.
10. 11. Zheng F., Wang Q.G., and Lee T.H. (2002) On the design of multivariable PID controllers via LMI approach, Automatica, vol.38, pp. 517-526.
11. 12. Boyd S., Hast M., and Astrom K.J. (2016) MIMO PID tuning via iterated LMI restriction, Int. J. Robust Nonlinear Control, vol. 26, pp. 1718-1731.
12. 13. Syrmos, V. L., Abdallah, C. T., Dorato, P., and Grigoriadis, K. (1997) Static output feedback survey. Automatica, vol.33, pp.125-137.
13. 14. Köroğlu H., and Falcone P. (2014) New LMI conditions for static output feedback synthesis with multiple performance objectives. Proceedings of IEEE 53rd Annual Conference on Decision and Control, DOI: 10.1109/CDC.2014.7039490.
14. 15. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994) Linear matrix inequalities in system and control theory. Philadelphia: SIAM.
15. 16. Lösch F. (2002) Identification and Automated Controller Design for Active Magnetic Bearing Systems. Ph.D. Thesis, ETH Zurich. 17. Löfberg J. (2004) YALMIP: A toolbox for modeling and optimization in MATLAB®, Proceedings of the CACSD Conference, Taipei, Taiwan.