Phase synchronization: Theory and applications

Automation and Remote Control

Volumn 67, Issue 10, 2006, Pages 1573-1609

  Leonov, G A ^a  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRIC MOTORS; PHASE COMPOSITION; REMOTE CONTROL; ROTORS; THEOREM PROVING;

PHASE SYNCHRONIZATION; UNBALANCED ROTORS; YAKUBOVICH-KALMAN FREQUENCY THEOREM;

SYNCHRONIZATION;

EID: 33750195767     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0005117906100031     Document Type: Article

References (84)

1. Tricomi, F., Integrazione di unequazione differenziale presentasi in electrotechnica Annal. della Roma Schuola Normale Superiore de Pisa, 1933, vol. 2, no. 2, pp. 1-20.
2. Andronov, A.A., Vitt, A.A., and Kkaikin, S.E., Teoriya kolebanii (Oscillation Theory), Moscow: Fizmatgiz, 1959.
3. Amerio, L., Determinazione delle condizioni di stabilita per gli integrali di unequazione interessante l'electrotechnica, Annali Matematica Pura Appl., 1949, vol. 30, no. 4, pp. 75-90.
4. Seifert, G., On the Existence of Certain Solutions of Nonlinear Differential Equations, Zeitschrift Angewandte Math. Physik, 1952, vol. 3, no. 6, pp. 468-471.
5. Bohm, C., Nuovi criteri di esistenza di soluzione periodiche di una nota equazione differenziale non lineare, Annali Matematica Pura Appl., 1953, vol. 35, no. 4, pp. 343-353.
6. Hayes, W.D., On the Equation for a Damped Pendulum under Constant Torque, Zeitschrift Angewandte Math. Physik, 1953, vol. 4, no. 5, pp. 398-101.
7. Belyustina, L.N., Bykov, V.V., Kiveleva, K.G., and Shalfeev, V.D., On the Value of the Locking Band of PLL with Proportional-Integrating Filter, Izv. Vuzov, Radiofiz., 1970, vol. 13, no. 4, pp. 561-567.
8. Gubar', N.A., Study of One Piecewise-Linear Dynamic System with Three Parameters, Prikl. Mat. Mekh., 1961, vol. 25, no. 6, pp. 1011-1023.
9. Barbashin, E.A. and Tabueva, V.A., Dinamicheskie sistemy s tsilindricheskim fazovym prostranstvom (Dynamic Systems with Cylindrical Phase Space), Moscow: Nauka, 1969.
10. Ivanov-Smolenskii, A.V., Elektricheskie mashiny (Electrical Machines), Moscow: Energiya, 1980.
11. Haendel, A., Grundgesetze der Physik, Leipzig: Fachbuchverlag, 1958.
12. Translated under the title Osnovnye zakony fiziki, Moscow: Fizmatgiz, 1959.
13. Yanko-Trinitskii, A.A., Novyi metod analiza raboty sinkhronnykh dvigatelei pri rezkoperemennykh nagruzkakh (A New Method of Analysis of Operation of the Synchronous Motors under Sharply Varying Loads), Moscow: Gosenergoizdat, 1958.
14. Barbashin, E.A., Vvedenie v teoriyu ustoichivosti (Introduction to the Theory of Stability), Moscow: Nauka, 1967.
15. Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost' nelineinykh sistem s needinstvennym sostoyaniem ravnovesiya (Stability of Nonlinear Systems with Nonunique Equilibrium State), Moscow: Nauka, 1978.
16. Shakhgil'dyan, V.V. and Lyakhovkin, A.A., Sistemy fazovoi avtopodstroiki chastoty (Phase Locked Loops), Moscow: Svyaz', 1972.
17. Leonov, G.A. and Seledzhi, S.M., Sistemy fazovoi sinkhronizatsii v analogovoi i tsifrovoi skhemotekhnike (Systems of Phase Synchronization in Analog and Digital Circuit Technology), St. Petersburg: Nevskii Dialekt, 2002.
18. Leonov, G.A., Ponomarenko, D.V., and Smirnova, V.B., Frequency-Domain Methods for Nonlinear Analysis. Theory and Applications, Singapore: World Scientific, 1996.
19. Leonov, G.A., Reitmann, V., and Smirnova, V.B., Nonlocal Methods for Pendulum-Like Feedback Systems, Stuttgart: Teubner, 1992.
20. Leonov, G.A., Mathematical Problems of Control Theory, Singapore: World Scientific, 2001.
21. Belykh, V.N. and Lebedeva, L.N., Studying Map of Circle, Prikl. Mat. Mekh., 1982, no. 5, pp. 611-615.
22. Shakhtarin, B.I., Stability of Discrete First-order Systems, Radiotekh. Elektron., 1977, no. 11, pp. 2418-2420.
23. Shakhtarin, B.I. and Arkhangel'skii, V.A., Dynamic Characteristics of the Phase Systems, Radiotekh. Elektron., 1977, no. 5, pp. 978-987.
24. Osborne, H.C., Stability Analysis of an Nth Power Digital Phase Locked Loop. Part. I: First-order DPLL, IEEE Trans. Commun., 1980, vol. 28, pp. 1343-1354.
25. Leonov, G.A. and Seledzhi, S.M., Stability and Bifurcations of Phase-loocked Loops for Digital Signal Processors, Int. J. Bifurcat. Chaos, 2005, vol. 15, no. 4, pp. 1347-1360.
26. Viterbi, A. J., Principles of Coherent Communications, New York: McGraw-Hill, 1966.
27. Translated under the title Printsipy kogerentnoi svyazi, Moscow: Sovetskoe Radio, 1970.
28. Gardner, F.M., Phase-Lock Techniques, New York: Wiley, 1966.
29. Gupta, S.C., Phase Locked Loops, Proc. IEEE., 1975, vol. 63, no. 2, pp. 291-306.
30. Lindsey, W.C., Synchronization Systems in Communication and Control, New York: Prentice-Hall, 1972.
31. Translated under the title Sistemy sinkhronizatsii v svyazi i upravlenii, Moscow: Sovetskoe Radio, 1978.
32. Sistemy fazovoi sinkhronizatsii (Phase Synchronization Systems), Shakhgil'dyan, V.V. and Belyustina, L.N., Eds., Moscow: Radio i Svyaz', 1982.
33. Sistemy fazovoi avtopodstroiki chastoty s elementami diskretizatsii (Phase Locked Loops with Elements of Discretization), Shakhgil'dyan, V.V., Ed., Moscow: Svyaz', 1979.
34. Borner, H., Phasenkopplungssysteme in der Nachrichten. Mess-und Regelungstechnik, Berlin: Technik, 1976.
35. Nash, G., Phase Locked Loop, Design Fundamentals, Phoenix: Motorola, 1994.
36. Leonov, G.A., Burkin, I.M., and Shepeljavy, A.I., Frequency Methods in Oscillation Theory, Dordrecht: Kluwer, 1996.
37. Leonov, G.A. and Smirnova, V.B., Matematicheskie problemy teorii fazovoi sinkhronizatsii (Mathematical Problems of the Phase Synchronization Theory), St. Petersburg: Nauka, 2000.
38. Shakhtarin, B.I., Analiz kusochno-lineinykh sistem s fazovym regulirovaniem (Analysis of Piecewise-Linear Systems with Phase Control), Moscow: Mashinostroenie, 1991.
39. Lindsey, W.C. and Chie, C.M., A Survey of Digital Phase Locked Loops, Proc. IEEE, 1981, vol. 69, no. 4, pp. 671-685.
40. Ugryumov, E.P., Tsifrovaya skhemotekhnika (Digital Circuit Technology), St. Petersburg: BHV, 2000.
41. Lapsley, P., Bier, J., Shoham, A., and Lee, E.A., DSP Processor Fundamentals Archicture and Features, New York: IEE Press, 1997.
42. Smith, S.W., The Scientist and Engineers Guide to Digital Signal Processing, San Diego: California Technical Publishing, 1999.
43. Colonina, A., Ulakhovich, D., and Yakovlev, L., Tsifrovye protsessory obrabotki signalov firmy Motorola (Motorola Digital Signal Processors), St. Petersburg: BHV, 2000.
44. Colonina, A., Ulakhovich, D., and Yakovlev, L., Algoritmy i protsessory tsifrovoi obrabotki signalov (Algorithms and Processors for Digital Signal Processing), St. Petersburg: BHV, 2001.
45. Leonov, G.A. and Seledzhi, S.M., Methods of Misphasing Correction in Digital Signal Processors, Vestn. S.-Peterburg. Gos. Univ., 2004, vol. 10, no. 1-2, pp. 36-47.
46. Leonov, G.A. and Seledzhi, S.M., Design of Block Diagram and Stability Analysis of the Floating Phase Locked Loops for the Digital Signal Processors, Avtom. Telemekh., 2005, no. 3, pp. 11-19.
47. Leonov, G.A. and Seledzhi, S.M., Design of Phase-locked Loops for Digital Signal Processors, Int. J. Innovative Comput. Inform. Control, 2005, vol. 1, no. 4, pp. 1-11.
48. Alekseenko, A.G., Osnovy mikroskhemotekhniki (Fundamentals of Microcurcuit Technology), Moscow: Yunimediastail, 2002.
49. Tanenbaum, A., Structured Computer Organization, New Jersey: Prentice Hall, 1999.
50. Translated under the title Arkhitektura komp'yutera, Moscow: Piter, 2003.
51. Horowitz, P. and Hill, W., The Art of Electronics Cambridge: Cambridge Univ. Press, 1998.
52. Translated under the title Iskusstvo skhemotekhniki, Moscow: Mir, 2003.
53. Abramovich, I.M., Blekhman, I.I., Lavrov, B.P., and Plis, D.A., Phenomenon of Synchronization of Rotating Bodies (Rotors), Otkrytiya, izobreteniya, 1988, no. 1, diploma no. 333. Registered by the State Committee of the USSR for Inventions and Discoveries, May 14, 1987.
54. Blekhman, I.I., Self-synchronization of the Vibrators of some Vibrating Machines, Inzhenernyi Sb., 1953, vol. 16.
55. Blekhman, I.I., Sinkhronizatsiya dinamicheskikh sistem (Synchronization of Dynamic Systems), Moscow: Nauka, 1971.
56. Blekhman, I.I., Sinkhronizatsiya v prirode i tekhnike (Synchronization in Nature and Engineering), Moscow: Nauka, 1981.
57. Blekhman, I.I. and Malakhova, O.Z., Extremal Attributes of Stability of some Motions, Prikl. Mat. Mekh., 1990, vol. 54, no. 1, pp. 142-161.
58. Blekhman, I.I., Vibratsionnaya mekhanika (Vibrational Mechanics), Moscow: Fizmatgiz, 1994.
59. Selected Topics in Vibrational Mechanics, Blekhman, I.I., Ed., Singapore: World Scientific, 2003.
60. Panovko, Ya.G. and Gubanova, I.I., Ustoichivost' i kolebaniya uprugikh sistem (Stability and Oscillations of Elastic System), Moscow: Nauka, 1979.
61. Stephenson, A.A., A New Type of Dynamical Stability, Mem. Proc. Manchr. Cit. Philos. Soc., 1908, vol. 52, pp. 15-21.
62. Kapitsa, P.L., Dynamic Stability of the Pendulum with Oscillationg Suspension Point, Zh. Eksp. Teor. Fiz., 1951, vol. 21, no. 5, pp. 588-598.
63. Leonov, G.A. and Shumafov, M.M., Metody stabilizatsii lineinykh upravlyaemykh sistem (Methods of Stabilization of Linear Controllable Systems), St. Petersburg: S.-Peterburg. Gos. Univ., 2005.
64. Yakubovich, V.A., Leonov, G.A., and Gelig, A.Kh., Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities, Singapore: World Scientific, 2004.
65. Leonov, G.A., On One Class of Dynamic Systems with Cylindrical Phase Space, Sib. Mat. Zh., 1976, vol. 17, no. 1, pp. 91-112.
66. Leonov, G.A., Second Lyapunov Method in the Theory of Phase Synchronization, Prikl. Mat. Mekh., 1976, vol. 40, no. 2, pp. 238-244.
67. Hale, J.K., Some Examples of Infinite Dimensional Systems, Contemporary Math., 1987, vol. 58, pp. 215-226.
68. Blekhman, I.I., Fradkov, A.L., Nijmeijer, H., and Pogromsky, A.Yu., On Self-synchronization and Controlled Synchronization, Syst. Control Lett., 1997, vol. 31, pp. 299-305.
69. Blekhman, I.I., Fradkov, A.L., Tomchina, O.P., and Bogdanov, D.E., Self-synchronization and Controlled Synchronization: General Definition and Example Design, Math. Comput. Simulation, 2000, vol. 58, no. 4-6, pp. 367-384.
70. Blekhman, I.I. and Fradkov, A.L., On General Definitions of Synchronization, in Selected Topics in Vibrational Mechanics, Blekhman, I.I., Ed., Singapore: World Scientific, 2004, pp. 179-188.
71. Fradkov, A.L., Kiberneticheskaya fizika: printsipy i primery (Cybernetic Physics: Principles and Examples), St. Petersburg: Nauka, 2003.
72. Rosenblum, M.G., Pikovsky, A.S., and Kurths, J., Phase Synchronization of Chaotic Oscillators, Phys. Rev. Lett., 1996, vol. 76, pp. 1804-1807.
73. Pikovsky, A.S., Rosenblum, M.G., and Kurths, J., Synchronization. A Universal Concept in Nonlinear Sciences, Cambridge: Cambridge Univ. Press, 2001.
74. Barbashin, E.A. and Krasovskii, N.N., On Motion Stability in the Large, Dokl. Akad. Nauk SSSR, 1952, vol. 86, no. 3, pp. 453-459.
75. La Salle, J.P. and Lefechets, S., Stability by Lyapunov'a Direct Method, New York: Academic, 1961.
76. Translated under the title Issledovanie ustoichivosti pryamym metodom Lyapunova, Moscow: Mir, 1964.
77. Lefechetz, S., Stability of Nonlinear Control Systems, New York: Academic, 1965.
78. Translated under the title Ustoichivost' nelineinykh sistem automaticheskogo upravleniya, Moscow: Mir, 1967.
79. Bakaev, Yu.N., Some Questions of the Nonlinear Theory of Phase Systems, Proc. Zhukovskii VVIA, 1959, vol. 800.
80. Fagiuoli, E. and Szegö, G.P., Qualitative Analysis by Modern Methods of a Stability Problem in Power-system Analysis, J. Franklin Inst., 1970, vol. 290, no. 2, pp. 103-111.
81. Leonov, G.A., On Boundedness of the Trajectories of the Phase Systems, Sib. Mat. Zh., 1974, vol. 15, no. 3, pp. 687-692.
82. Noldus, E., New Direct Lyapunov-type Method for Studying Synchronization Problems, Automatika, 1977, vol. 13, no. 2, pp. 139-151.
83. Leonov, G.A., Stability and Oscillaitons of the Phase Systems, Sib. Mat. Zh., 1975, vol. 16, no. 5, pp. 1031-1052.
84. Leonov, G.A., Discontinuous Load Rating Problem for Inductor Motors, Technische Mechanik, 2004, vol. 24, no. 3-4, pp. 271-276.