A Method of Finding the Equivalent Gains of Double-valued Non-linearities†
TL;DR: In this article, a method for computing the sine wave equivalent gain or describing function of a, double-valued nonlinearity is presented, illustrated by considering four common types of such a non-linearity and t.he gains for each of these characteristics as obtained by following the present procedure and the conventional procedure.
Abstract: A method for computing the sine wave equivalent gain or describing function of a, double-valued non-linearity is presented. The method is illustrated by considering four common types of such a non-linearity and t.he gains for each of these characteristics as obtained by following the present procedure and the conventional procedure are compared. It is also pointed out that the present procedure can have advantage over the conventional procedure in that the stability analysis can be simplified raid the design of an optimum compensation schema can be facilitated.
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TL;DR: In this article, a circle of radius A is constructed to represent a sinusoidal input A sin θ, where θ = ωτ, and the ratio of the second area B 1 to the first area A 1 determines the phase shift.
Abstract: A new method is given for evaluating the describing function of hysteresis-type nonlinearities. A circle of radius A is constructed to represent a sinusoidal input A sin θ, where θ = ωτ.In the case of a single-valued nonlinearity, an output contour C with area A 1 is sufficient to represent the output wave-shape. In the general case of double-valued nonlinearities, another output contour C ′ with area B 1 is required to determine the general describing function. The ratio of the second area B 1 to the first area A 1 determines the phase shift. It is to be noted that the second area B 1 is directly related to the area of the hysteresis loop or the backlash.
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