A Lyapunov Function for Vector Control Drives in Induction Machines
In this paper a useful Lyapunov function for vector control of induction machines is introduced. To do this, some beneficial theorems are reviewed and by applying these theorems and state equations to a vector control drive, its candidate Lyapunov function is achieved. Range of set points such as reference speed, reference flux linkage values and speed controller gain is obtained for such a drive and therefore these values can be set offline to avoid unstable behavior. The simulated and experimental results are given in the last section of the paper to show the efficacy of the given Lyapunov function.
Keywords:Lyapunov function, stable Area, vector control drives
Z. Park, J. B. Park, Y. H. Joo, B. Zhang, G. Chen, “Bifurcation and chaos in a permanent magnet synchronous motor”, IEEE Transaction on Circuits-I, Vol. 49, pp. 383-387, 2002 DOI: https://doi.org/10.1109/81.989176
D. Q. Wei, X. S. Luo, B. H. Wang, J. Q. Fang, “Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor”, Phys. Letter A, Vol. 363, pp. 71-77, 2007 DOI: https://doi.org/10.1016/j.physleta.2006.10.074
M. Babaei, J. Nazarzadeh, J. Faiz, “Nonlinear feedback control of chaos in synchronous reluctance motor drive systems”, IEEE International Conference on Industrial Technology (ICIT 2008), pp. 1-5, China, 2008 DOI: https://doi.org/10.1109/ICIT.2008.4608524
Y. Gao, K. T. Chau, “Hopf Bifurcation and Chaos in Synchronous Reluctance Motor Drives”, IEEE TRNSACTION On ENERGY CONVER, Vol. 19, pp. 296-302, 2004 DOI: https://doi.org/10.1109/TEC.2004.827012
J H Chen, K T Chau, C C Chan, Q Jiang, “Subharmonics and Chaos in Switched Reluctance Motor Drives”, Ieee Transaction on Energy Convertion, Vol. 17, pp. 73-78, 2002 DOI: https://doi.org/10.1109/60.986440
H. Ren, D. Liu, “Nonlinear Feedback Control of Chaos in Permanent Magnet Synchronous Motor”, IEEE Transaction on Circuits-II Vol. 53, pp. 45-50, 2006 DOI: https://doi.org/10.1109/TCSII.2005.854592
T Tang, M Yang, H Li, D Shen, “A New Discovery and Analysis on Chaos and Bifurcation in DC Motor Drive System with Full-bridge Converter”, 1ST IEEE Conference on Industrial Electronics and Applications, pp. 1-6, Singapore, 2006 DOI: https://doi.org/10.1109/ICIEA.2006.257313
I. Nagy, “Tolerance band based current control of induction machines highlighted with the theory of chaos”, 3rd IEEE International Power Electronics Congress, CIEP '94, pp. 155-160, Mexico, 1994
Z. Suto, I. Nagy, E. Masada, “Avoiding chaotic processes in current control of AC drive”, 29th Annual IEEE Power Electronics Specialists Conference, PESC 98, pp. 255-261, Japan,1998
T. Asakura, K. Yoneda, Y. Saito, M. Shioya, “Chaos detection in velocity control of induction motor and its control by using neural network”, 5th IEEE International Conference on Signal Processing Proceedings; pp. 1633-1638, China, 2000
T. Asakura, Y. Saito, M. Shioya, “Chaos detection and neuro-control in vector control system”, IEEE Region 10 Conference on Computers, Communications, Control and Power Engineering, pp. 1347-1350, China, 2002
F. Salas, R. Ortega, J. Aracil, “Hopf bifurcation in indirect field-oriented control of induction motors”, Automatica, Vol. 38, pp. 829-835, 2002 DOI: https://doi.org/10.1016/S0005-1098(01)00274-6
A. B. Ozer, E. Akin, “Chaos Control in Vector-controlled Induction Motor Drive”, Electric Power Components and Systems, Vol. 36, pp. 733-740, 2008 DOI: https://doi.org/10.1080/15325000701881977
R. A. Sangrody, J. Nazarzadeh, K. Y. Nikravesh, “Inherent Chaotic Behavior in Vector Control Drives of Induction Machines”, Electric Power Components and Systems, Vol. 40, pp.1-20, 2012 DOI: https://doi.org/10.1080/15325008.2011.621509
H. Zhang, X. Ma, B. Xue, W. Liu, “Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models”, Chaos Soliton Fractal, Vol. 23, pp. 431-444, 2005 DOI: https://doi.org/10.1016/j.chaos.2004.04.020
K. Y. Nikranesh, Nonlinear system stability analysis Lyapunov-based approach, USA: CRC Press, pp. 106-111, 2013 DOI: https://doi.org/10.1201/b13731
P. Vas, Sensorless Vector and direct torque control, UK: Oxford University Press, 1998
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