Abstract
An exact method of analysis of non-linear systems containing a two-position relay element and a dead-time element is given using the phase-plane concept. Equations of the switching lines for both unsymmetrical and symmetrical relay characteristics are obtained under consideration of the dead time. Expressions to evaluate the period and amplitude of the self-oscillation of the system are derived from the stable limit cycle in the phase plane. This method is developed for a second-order system with a zero in its transfer function. For such a system it is indicated with a help of an example that approximation methods as the describing function yield large errors because the low-pass condition is not satisfied. The phase-plane method will be developed for other relay characteristics.
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