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Exact determination of the limit cycles in relay control systems with additional nonlinearities in the feedback loops

Exact determination of the limit cycles in relay control systems with additional nonlinearities in the feedback loops

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The A-function method is extended to analyse a relay feedback control system with additional nonlinearities in the feedback loops. The situation considered is where the output of the plant and/or its successive derivatives are fed back to the input through nonlinearities that are assumed to be of polynomial type. An example is also given to show that, in some cases, the method can be used in systems with saturation or a linear segmented nonlinearity in the feedback path.

Inspec keywords: limit cycles; control system CAD; polynomials; control nonlinearities; feedback; relay control

Other keywords: relay control systems; saturation; polynomial; nonlinearities; CAD; limit cycles; feedback

Subjects: Algebra; Nonlinear control systems; Control system analysis and synthesis methods; Algebra; Control system design and analysis

References

    1. 1)
      • Atherton, D.P.: `Conditions for periodicity in control systems containingseveral relays', 28E, 3rd IFAC Congress, 1966, London.
    2. 2)
      • P.A. Cook . (1994) Nonlinear dynamical systems.
    3. 3)
      • Moeini, A., Atherton, D.P.: `A new software tool for the analysis and design of relay control systems', Proc. NOLCOS '95 IFAC Symposium on Nonlinear systems design, 1995, 2, Tahoe City, California, p. 883–888.
    4. 4)
      • Moeini, A.: `Computer aided design and analysis of nonlinear phenomena in relay controlsystems', 1996, PhD, Sussex University.
    5. 5)
      • D.P. Atherton . (1975) Nonlinear control engineering.
    6. 6)
      • A. Gelb , L.J. Henrikson . On the analytical applications of Tsypkin's method. IEEE Trans. , 69 - 70
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