nyquistfrequencybounds

Parameters

H

A SISO or SIMO linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.

bounds

A 2 by 2 array: [Rmin Imin;Rmax Imax] that defines a complex-plane rectangle.

fmin

a real: the lowest frequency (Hz) such that the nyquist locus enters the given rectangle or 0 if the 0 Hz point lies in the rectangle or [] if the locus is completely outside the rectangle.

fmax

a real: the highest frequency (Hz) such that the nyquist locus leaves the given rectangle or %inf if the %inf (hz) point is in the rectangle or [] if the locus is completely outside the rectangle.

Description

Given a C plane rectangle, nyquistfrequencybounds Computes the lowest frequency for which the nyquist locus enters the rectangle and the highest frequency for which the nyquist locus leaves the rectangle.

Examples

s=%s
num=2+9*s-9*s^2-11*s^3+0.01*s^4;
den=43*s^2+65*s^3+34*s^4+8*s^5+s^6+0.1*s^7
H=syslin('c',num,den)-1

clf;set(gcf(),'axes_size',[805,549])
subplot(221)
nyquist(H)

subplot(222)
bounds=[-2 -2;2 2]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));

subplot(223)
bounds=[-1.3 -0.3;0 0.3]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,fmax)
title("bounds:"+sci2exp(bounds,0));

subplot(224)
bounds=[-1.1 -0.1;-0.8 0.1]
[fmin,fmax]=nyquistfrequencybounds(H,bounds)
nyquist(H,fmin,1d8)
title("bounds:"+sci2exp(bounds,0));

See also

• nyquist — nyquist plot

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