On the analysis of two-variable relay control systems with a linear-asymmetric plant

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Abstract
An exact method for the analysis of a two-variable non-linear system containing two-position relays and a linear-asymmetric plant is given. The elements of the transfer-function matrix of such a linear-asymmetric plant depend on the direction of a step-input applied to it. Based on the necessary conditions for limit cycling behaviour, a scheme for computing the frequency, amplitude and other characteristic parameters of a self-oscillation is given, using an approach in the state space. The method is developed for relays with hysteresis only, but can be extended to those containing a dead-zone as well.

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