40 M. V. F. de Oliveira et al. -20 -10 -30 10 0 Amplitude (dB) -200 200 -100 100 0 Phase (deg) 100 101 102 103 Frequency (Hz) Closed Loop Transfer Functions - V24 PI Modal Fig. 4.11 Comparison of the Transfer Functions in Closed Loop: PI Controller Modal Controller – NDE (V24) From the analysis of the system performance based on the Closed Loop Transfer Functions of the model it was verified that both controllers were able to adequately attenuate all modes located in their frequency band of interest. In addition, it was possible to conclude that, although the modal controller allows for a higher vibration level than the PI for operating speeds below 8500 rpm, its performance is similar and even surpasses it in some cases for higher operating speeds. On the other hand, since the control effort exerted by the modal controller was always inferior to the one exerted by the PI controller, mainly for speeds above 8500 rpm, it is expected that the control currents follow this same trend, which would represent a considerable power saving. It is recalled that the ecologically compatible machines have as one of their requirements the lowest possible energy consumption. 4.4 Conclusion The present paper is dedicated to the systematization of the Robust Design of Modal Active Control Systems of Supercritical Rotors supported by Magnetic Bearings. Other equally important contributions should be mentioned, namely: the development of representative models of rotary systems for application in active controlled plants, determination and implementation of active control architectures aiming at real world applications in the industry, development of experimental techniques for magnetically supported supercritical rotors, design and characterization of active controllers for magnetic bearings focusing on modal controllers. Acknowledgments The authors are thankful to the Brazilian Research Agencies FAPEMIG, CNPq, and CAPES for the financial support provided for this research effort through the INCT-EIE. References 1. Earnshaw, S.: On the nature of the molecular forces which regulate the constitution of the lumiferous ether. Trans. Camb. Phil. Soc. 7(Part I), 97–112 (1842) 2. Braunbek, W.: Frei schwebende Körper im elektrischen und magnetischen Feld. Z. Phys. 112, 753–763 (1939) 3. Habermann, H., Liard, G.: Le palier magnetique active: un principe revolutionaire. SKF Rev. Roulements Nr. 192 (1977) 4. Schweitzer, G., Maslen, E.H.: Magnetic Bearings: Theory, Design, and Application to Rotating Machinery, 535p. Springer, Berlin (2009) 5. Steffen, V. Jr., Lepore, N.F.P.: A control force to reduce magnetically excited rotor vibrations. Mécanique, Matériaux, Electricité. 65(404), 90–93 (1984)
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