Module Margin Method
The Nyquist diagram consists of plotting the transfer function in the complex plane.
Gain Margin is defined as the reciprocal of the system gain at the pulse where the open loop system phase FTBO reaches -180 °
It corresponds to point N in the Figure above, and is generally expressed in dB
Phase Margin represents the difference between the phase of the FTBO system considered and -180° at the cut-off pulse OmegaC , i.e. the pulsation for which the module is equal to 0 dB
It is also defined by the point M corresponding to the intersection of the Nyquist locus of FTBO with the unit circle centered at the origin and of unit radius
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
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
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