Analysis and design of nonlinear feedback systems
Analysis and design of nonlinear feedback systems
- Author(s): D.P. Atherton
- DOI: 10.1049/ip-d.1981.0038
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): D.P. Atherton 1
-
-
View affiliations
-
Affiliations:
1: Inter-University Institute of Engineering Control, School of Engineering and Applied Sciences, University of Sussex, Brighton, UK
-
Affiliations:
1: Inter-University Institute of Engineering Control, School of Engineering and Applied Sciences, University of Sussex, Brighton, UK
- Source:
Volume 128, Issue 5,
September 1981,
p.
173 – 180
DOI: 10.1049/ip-d.1981.0038 , Print ISSN 0143-7054, Online ISSN 2053-793X
The paper discusses methods, primarily those using frequency-domain techniques, for the analysis and design of nonlinear feedback control systems. The behavioural properties peculiar to nonlinear feedback systems are first discussed. This is followed by a review and discussion of the applicability of absolute stability criteria and describing-function methods for single-variable and multivariable systems. The calculation of limit cycles in relay systems, time-domain methods of analysis and simulation techniques are then considered. Finally, a few applications are considered which highlight both the applicability and limitations of the available analytical techniques for nonlinear systems.
Inspec keywords: limit cycles; relay control; control system synthesis; nonlinear control systems; describing functions; control system analysis; stability criteria
Other keywords:
Subjects: Control system analysis and synthesis methods; Stability in control theory; Nonlinear control systems
References
-
-
1)
- T.J. Procyk , E.H. Mamdani . A linguistic self-organising process controller. Automatica , 15 - 30
-
2)
- A.I. Mees , J.W. Sparrow . Chaos. IEE Proc. D, Control Theory of Appl. , 5 , 201 - 205
-
3)
- J.C. West , J.L. Douce , R.K. Livesley . The dual-input describing function and its use in the analysis of non-linear feedback systems. Proc. IEE , 4 , 463 - 473
-
4)
- M.A. Aizerman , F.R. Gantmacher . (1964) , Absolute stability of regulator systems.
-
5)
- E.I. Jury , B.W. Lee . The absolute stability of systems with many nonlinearities. Automn & Remote Control , 943 - 961
-
6)
- Marino, R., Nicosia, S.: `Lyapunov functions for stability analysis of synchronous generator', Report R.80-17, July 1980.
-
7)
- El Sakkary, A.K., Atherton, D.P.: `Computer graphics methods for nonlinear multivariable systems', IFAC computer aided design symposium, 1979, Zurich, p. 157–162.
-
8)
- Dodds, S.J.: `An adaptive, high precision, gas jet satellite attitude control system for microprocessor implementation', 8th IFAC space symposium, 1979, Oxford, p. 147–158.
-
9)
- Atherton, D.P.: `Conditions for periodicity in control systems containing several relays', paper 28E, 3rd IFAC Congress, 1966, London.
-
10)
- J.O. Gray , N.B. Nakhla . (1981) , A numerical method for the analysis of harmonic balance conditions in multiloop non-linear feedback systems.
-
11)
- V.I. Utkin . Variable structure systems with sliding modes. IEEE Trans. , 212 - 222
-
12)
- Rao, U.M.: `Studies in satellite attitude control system design', , Ph.D. thesis, University of New Brunswick, Canada.
-
13)
- K.S. Narendra , J.H. Taylor . (1973) , Frequency domain criteria for absolute stability.
-
14)
- J.C. West , J.L. Douce , R. Naylor . The effects of the addition of some nonlinear elements on the transient performance of a simple r.p.c. system possessing torque limitation. Proc. IEE , 156 - 165
-
15)
- R. Balasubramanian . Stability of limit cycles in feedback systems containing a relay. IEE Proc. D. Control Theory & Appl. , 1 , 24 - 29
-
16)
- V.I. Utkin . (1976) , Control systems of variable structure.
-
17)
- E.J. Routh . (1975) , Stability of motion.
-
18)
- J. LASALLE , S. LEFSCHETZ . (1961) , Stability by Liapunov's direct method with applications.
-
19)
- Hopkins, W.G.: `On the prediction of limit cycles in systems containing multiple nonlinearities', paper M-2, IEEE Southeast conference, 1973, Kentucky.
-
20)
- J. Erschler . Automation of a hydroelectric power station using variable-structure control systems. Automatica , 31 - 36
-
21)
- J.K.C. Chung , D.P. Atherton . The determination of periodic modes in relay systems using the state space approach. Int. J. Control , 105 - 126
-
22)
- J.C. West , J.L. Douce . The mechanism of sub-harmonic generation in a feedback system. Proc. IEE , 5 , 569 - 574
-
23)
- Taylor, J.R.: `A new algorithmic limit cycle analysis method for multivariable systems', Report TIM-612-2, TASC., 1977.
-
24)
- A.I. Mees , D.P. Atherton . The Popov criterion for multiple-loop feedback systems. IEEE Trans. , 924 - 928
-
25)
- D.P. Atherton . (1975) , Nonlinear control engineering: describing function analysis and design.
-
26)
- D.R. Fannin , A.J. Rushing . Verification of the Kalman conjecture based on locus curvature. Proc. IEEE , 542 - 543
-
27)
- J.B. Roberts . Response of nonlinear mechanical systems to random excitation. Pts. I & II. Shock & Vib. Dig. , 5 , 15 - 29
-
28)
- Cellier, F.E.: `Combined continuous/discrete system simulation by use of digital computers: techniques and tools', 1979, Dr. Tech. Sciences dissertation, ETH, Zurich.
-
29)
- S.S. Lamba , R.J. Kavanagh . Jump-resonance criteria for systems containing double-valued and frequency-dependent nonlinearities. Proc. IEE , 7 , 1225 - 1228
-
30)
- D.P. Atherton . (1981) , Stability of nonlinear systems.
-
31)
- S.K. Choudhury , D.P. Atherton . Limit cycles in high order nonlinear systems. Proc. IEE , 7 , 717 - 724
-
32)
- N.J. Kriekelis . State feedback integral control with intelligent integrators. Int. J. Control , 465 - 473
-
33)
- Haddad, E.K.: `New criteria for bounded-input bounded-output and asymptotic stability of nonlinear systems', paper 32.2, Proceedings of the 5th IFAC Congress, Paris, pt.4.
-
34)
- A. Gleb , W.E. Vander Velde . (1968) , Multiple-input describing functions and nonlinear system design.
-
35)
- Vigneron, F.R., Millar, R.A.: `Flight performance of the three-axis stabilization system of the communications technology satellite', AIAA guidance & control conference, 1977, Florida.
-
36)
- A. Mees . Describing functions, circle criteria and multiple-loop feedback systems. Proc. IEE. , 126 - 130
-
37)
- A.T. Fuller . Approximate analysis of stochastic relay control systems - II. Int. J. Control , 625 - 643
-
38)
- Balasubramanian, R., Atherton, D.P.: `Limit cycles in systems with single and multiple relays', JACC, August 1980, San Francisco.
-
39)
- Rao, U.M., Atherton, D.P.: `Multi-pulse oscillations in relay systems', paper 42.4, Proceedings of 7th IFAC Congress, 1978, Helsinki, p. 1747–1754.
-
40)
- P.J. Fleming , C.W. Jones . Use of mixed performance criteria in gas turbine engine controller design. IEE Conf. Publ. 194 , 91 - 95
-
41)
- J.C. West , J.L. Douce . The frequency response of a certain class of nonlinear feedback systems. Br. J. Appl. Phys.
-
42)
- Gray, J.O., Taylor, P.M.: `Frequency response methods in the design of multivariable nonlinear feedback systems', Proceedings of IFAC symposium on multivariable technological systems, 1977, Fredericton, p. 225–232.
-
43)
- J.C. West , M.J. Somerville . Integral control with torque limitation. Proc. IEE , 3 , 407 - 412
-
44)
- F. El-Geldawi . On the phase plane analysis of relay control system with dead time. Int. J. Control. , 123 - 131
-
45)
- Mees, A.I., Rapp, P.E.: `Stability criteria for multiple-loop nonlinear feedback systems', Proceeedings of IFAC symposium on multivariable technological systems, Fredericton, p. 183–188.
-
46)
- D.P. Atherton , S. Shankar . Some observations on the Aizerman conjecture. Proc. IEE , 12 , 1305 - 1306
-
47)
- Ramani, N.: `Some aspects of the analysis and design of multivariable systems', 1975, Ph.D. dissertation, University of New Brunswick, Fredericton.
-
48)
- A.I. Mees , A.R. Bergen . Describing function revisited. IEEE Trans. , 473 - 478
-
49)
- G.F. Turnbull , D.P. Atherton , J.M. Townsend . Method for the theoretical analysis of relay feedback systems. Proc. IEE , 5 , 1039 - 1055
-
50)
- P.E. Rapp , A.I. Mees . Spurious predictions of limit cycles in a nonlinear feedback system by the describing function method. Int. J. Control , 821 - 829
-
51)
- D.P. Atherton , D.H. Owens . Boundedness properties of nonlinear multivariable feedback systems. Electron. Lett. , 18 , 559 - 561
-
52)
- M. VIDYASAGAR . (1978) , Nonlinear systems analysis.
-
53)
- P.A. Cook , D.J. Bell . (1973) Modified, multivariable circle theorems, Recent mathematical developments in control theory.
-
54)
- A.S.I. Zinober . Analysis of an adaptive third-order relay control system using nonlinear switching surface theory. Proc. R. Soc. Edinburgh Sect. A , 76 , 239 - 254
-
55)
- A.I. Mees . The describing function matrix. J. Inst. Math. Applic. , 49 - 67
-
56)
- Rao, U.M.: `Some aspects of the stability of nonlinear control systems', 1975, M.Sc.E. thesis, University of New Brunswick, Canada.
-
57)
- E.A. Freeman . Characterization of nonlinearity for transient processes — Its evaluation and application. IEEE Trans. , 491 - 501
-
58)
- Y.S. Cho , K.S. Narendra . An off-axis circle criterion for the stability of feedback systems with a monotonic nonlinearity. IEEE Trans. , 413 - 416
-
59)
- N. Minorsky . (1962) , Nonlinear oscillations.
-
60)
- Y.Z. Tsypkin . (1955) , Theory of relay control systems.
-
61)
- V.I. UTKIN . , Sliding modes and their application in variable structure systems.
-
62)
- A.M. Foss . Criterion to assess stability of a ‘lowest wins’ control strategy. IEE Proc. D, Control Theory & Appl. , 1 , 1 - 8
-
63)
- J.-C. Gille , M.J. Pélegrin , P. Decaulne . , Feedback control systems.
-
64)
- D.A. Owens . On the effect of nonlinearities in multivariable first order process control. IEE Conf. Publ. 194 , 240 - 244
-
65)
- W.G. Vogt , J.H. George . On Aizerman's conjecture and boundedness. IEEE Trans. , 338 - 339
-
66)
- S. Shankar , D.P. Atherton . Graphical stability analysis of nonlinear multivariable control systems. Int. J. Control , 375 - 388
-
67)
- D.P. Atherton , H.T. Dorrah . A survey on nonlinear oscillations. Int. J. Control , 1041 - 1105
-
68)
- F. Fallside , M.R. Patel . On the application of the Lyapunov method to synchronous machine stability. Int. J. Control
-
69)
- Bennett, B.S.: `The role of simulation in power system transient stability assessment', report 478, 1980.
-
70)
- P.M. Larsen . Industrial applications of fuzzy logic control. Int. J. Man-Mach. Stud. , 3 - 10
-
71)
- Millar, R.A., Vigneron, F.A.: `Attitude stability of flexible space-craft which use dual time constant feedback lag network pseudorate control', AIAA/CASI 6th communications satellite conference, 1976, Montreal.
-
72)
- Fleming, P.J.: `A CAD program for suboptimal linear regulators - design applications', IASTED symposium, 1981, Switzerland, Davos.
-
73)
- Falb, P.L., Freedman, M.I., Zames, G.: `Input-output stability - a general viewpoint', Proceedings of the 4th IFAC Congress, 1969, Warsaw, p. 3–15, session 41.
-
74)
- Rosenbrock, H.H.: `Multivariable circle theorems', IMA conference on recent developments on control, 1972, Bath.
-
75)
- G.J. Thaler , N.P. Pastel . (1962) , Analysis and design of nonlinear feedback control systems.
-
76)
- R.E. Fitts . Two counterexamples to Aizerman's conjecture. IEEE Trans. , 553 - 556
-
1)