Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.

Complex dynamics in a relay feedback system with hysteresis and delay / Colombo, A; DI BERNARDO, Mario; HOGAN S., J; Kowalczyk, P.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - STAMPA. - 17:2(2007), pp. 85-108. [10.1007/s00332-005-0745-y]

Complex dynamics in a relay feedback system with hysteresis and delay

DI BERNARDO, MARIO;
2007

Abstract

Relay feedback systems are used to control engineering devices. In practice the switching between different functional forms of the system is never instantaneous, but takes place after a small delay. In this paper we analyse the dynamics and bifurcations of a representative example of such systems. In the absence of delay, negative feedback results only in unimodal symmetric limit cycles, but positive feedback can lead to aperiodic trajectories and chaos. In the presence of delay, the system can behave as an equivalent system without delay, provided that the delay is small in a sense which we define precisely. For larger delays, we identify a new bifurcation phenomenon, an event collision, where the delayed switching manifold intersects the relay hysteretic lines. In this case the dynamics become much more complicated.
2007
Complex dynamics in a relay feedback system with hysteresis and delay / Colombo, A; DI BERNARDO, Mario; HOGAN S., J; Kowalczyk, P.. - In: JOURNAL OF NONLINEAR SCIENCE. - ISSN 0938-8974. - STAMPA. - 17:2(2007), pp. 85-108. [10.1007/s00332-005-0745-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/102528
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