Reference: Nonlinear systems: the Describing Function method for closed-loop system response.
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ESDU 84032 extends the use of the Describing Function method introduced in ESDU 84009 to include determining the response of a closed-loop system to a sinusoidal input. Two alternative methods are described. The first is essentially an analytical method based on finding the amplitude response of the input signal to the non-linear element. The second is essentially graphical, using a chart on a transparent overlay that applies to all such closed-loop systems and that is constructed from the known characteristics of the phasor diagram for such a system; superimposing this universally applicable transparent overlay on the characteristic of the Describing Function chosen to represent appropriately the non-linearity allows the closed loop response to be determined. The use of the two methods is illustrated with worked examples that include sketches of the closed-loop frequency response showing the phenomenon of jump resonance.