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ModuleMargin

Module Margin Method

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Stability criterion in the Nyquist plane

The Nyquist diagram consists of plotting the transfer function in the complex plane.

Module Margin

The objective is to force the FTBO (regulator + process) to pass through an imposed point P in the Nyquist plane)

ma denotes the margin module, and is represented by a circle of radius ma centered on the critical point (-1.0).

The point P targeted indicates the intersection between this circle and the line passing through the points (-1,0) and (0,-1).

The angle between this line and the axis Re is therefore equal to pi/4.

Typically, ma is set to obtain a gain margin of 6 dB from the FTBO. This value is commonly accepted by operators

Module Margin Adjustment to +3 dB

The circle of radius ma is tangent to the circle of radius +3 dB: : 20*log(1+ma)= 3 dB i.e ma=10^(3/20) -1 = 0.4125375

Module Margin Adjustment to -3 dB

The circle of radius ma is tangent to the circle of radius -3 dB: : 20*log(1-ma)= -3 dB i.e ma=1-10^(-3/20) = 0.2920542


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