Graphical method of prediction of limit cycle for multivariable nonlinear systems

IEE Proceedings: Control Theory and Applications

Volumn 143, Issue 5, 1996, Pages 423-428

  Patra, K C ^a   Singh, Y P ^b  

^a INDIRA GANDHI INSTITUTE OF TECHNOLOGY   (India)

^b INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Limit cycle; Multivariable; Nonlinear system; Phasor diagram

Indexed keywords

COMPUTER GRAPHICS; COMPUTER SIMULATION; CONTROL SYSTEM ANALYSIS; GRAPHIC METHODS; MULTIVARIABLE CONTROL SYSTEMS;

LIMIT CYCLES; MULTIVARIABLE NONLINEAR SYSTEM;

NONLINEAR CONTROL SYSTEMS;

EID: 0030232489     PISSN: 13502379     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-cta:19960520     Document Type: Article

References (24)

1. LOH, A.P., and VASANI, V.V.: 'Necessary conditions for limit cycles in multiloop relay systems', IEE Proc., Control Theory Appl., 1994, 141, (3), pp. 163-168
2. ZHUANG, M., and ARTHERTON, O.P.: 'PID controller desisn for TITO system', IEE Proc., Control Theory Appl., 1994, 141, (2), pp. 111-120
3. ATHERTON, D.P., and DORRAH, H.T.: 'A survey on non-linear oscillations', Int. J. Control, 31, (6), pp. 1041-1105
4. COOK, P.A.: 'Nonlinear dynamical systems' (Prentice-Hall, Englewood Cliffs, NJ, 1986)
5. GELB, A., and VADER-VELDE, W.E.: 'Multiple-input describing functions and nonlinear system desien' (McGraw-Hill, New York, 1968)
6. ATHERTON, D.P.: 'Nonlinear control engineering - Describing function analysis and design' (Van Nostrand Reinhold, London, 1975)
7. PILLAI, V.K., and NELSON, H.D.: 'A new algorithm for limit cycle analysis of nonlinear systems', Trans. ASME, J. Dyn. Syst. Afeas. Control, 1988, 110, pp. 272-277
8. CHANG, H.C., PAN, C.T., HUANG, C.L., and WEI, C.C.: 'A general approach for constructing the limit cycle loci of multiplenonlinearity systems', IEEE Trans. Atitoin. Control, 1987, AC-32, (9), pp. 845-848
9. .GENESIO, R., and TESI, A.: 'On limit cycles of feedback polynomial systems', IEEE Trans. Circuits Syst., 1988, 35, (12), pp. 1523-1528
10. SEBASTIAN, L.: The self-oscillation determination to a category of nonlinear closed loop systems', IEEE Trans. Autom. Control, 1985, AC-30, (7), pp. 700-704
11. GELB, A.: 'Limit cycles in symmetric multiple nonlinear systems', IEEE Trans. Autom. Control, 1963, AC-8, pp. 177-178
12. JUD, H.G.: 'Limit cycle determination of parallel linear and nonlinear elements', IEEE Trans. Autom. Control, 1964, AC-9, pp. 183-184.
13. GRAN, R., and RIMER, M.: 'Stability analysis of systems with multiple nonlinearities', IEEE Trans. Autom. Control, 1965, 10, pp. 94-97
14. RAJU, O.S., and JOSSELSON, R.: 'Stability of reactor control systems in coupled core reactors', IEEE Trans. Niicl. Sci., NS-18, pp. 388-394
15. PARLOS, A.G., HENRY, A.F., SCHWEPPE, F.C., GOULD, L.A., and LANNING, D.D.: 'Nonlinear multivariable control of nuclear power plants based on the unknown but bounded disturbance model', IEEE Trans. Autom. Control, 1988, AC-33, (2), pp. 130-134
16. FENDRICH, O.K.: 'Describing functions and limit cycles', IEEE Trans. Autoin. Control, 1992, AC-37, (4), pp. 486-487
17. PATRA, K.C.: 'Analysis of self oscillations and signal stabilisation of two-dimensional nonlinear systems'. PhD Thesis, IIT, Kharacpur, India, 1986)
18. DA VISON, E.J., and CONSTANTINESCU, D.: 'Describing function technique for multiple nonlinearity in a single feedback system', IEEE Trans. Aiitom. Control, 1971, AC-16, pp. 50-60
19. VISWANDHAM, N., and DEEKSHATULU, B.L.: 'Stability analysis of nonlinear multivariable systems', Int. J. Control, 1966, 5, pp. 369-375
20. SINGH, Y.P., and SUBRAMANIAN, S.: 'Frequency response identification of structure of nonlinear systems', IEE Proc. D, 1980, 127, pp. 77-82
21. MEES, A.I.: 'Describing function: Ten years on', IAIA J. Appl. Math., 1984, 34, pp. 221-233
22. PATRA, K.C., SWAIN, A.K., and MAJHI, S.: 'Application of neural network in the prediction of self-oscillations and signal stabilisation in nonlinear multivariable systems'. Proceedings of ANZIIS-93, Western Australia, 1993, pp. 585-589
23. NIKIFORUK, P.N., and WINTONYK, B.L.M.: 'Frequency response analysis of two-dimensional nonlinear symmetrical and non symmetrical control systems', Int. J. Control, 1968, 7, pp. 4962
24. PATRA, K.C., and SINGH, Y.P.: 'Structural formulation and prediction of limit cycle for multivariable nonlinear system', IETE, Tech. Rev. (India), 1994, 40, (5 & 6), pp. 253-260