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Incorrect indentation direction of poles in Nyquist plot #1191
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What version of python-control are you running (use
ct.__version__to find out).One likely issue is that numerical approximations are giving poles that are not quite on the imaginary axis:
>>> import control as ct >>> sys = ct.tf([1, 11, 10], [0.01,1,0.01,1]) >>> sys.poles() array([-1.00000000e+02+0.j, -9.05723062e-16+1.j, -9.05723062e-16-1.j])As described in the documentation for
nyquist_response:If a continuous-time system contains poles on or near the imaginary axis, a small indentation will be used to avoid the pole. The radius of the indentation is given by indent_radius and it is taken to the right of stable poles and the left of unstable poles. If a pole is exactly on the imaginary axis, the indent_direction parameter can be used to set the direction of indentation. Setting indent_direction to ‘none’ will turn off indentation.
In this case, the pole is not "exactly on the imaginary axis" and so
indent_directionis not used. Instead, since the real part of the pole is negative, the indentation will always be to the right (so that no new net encirclements are created).The curve that I get (with v0.10.2) is different than yours:
Hi there,
I am using python control in a streamlit application, and in the requirements.txt i am requiring version >=0.10.2
The transfer function is being created with the command
self.sys = ct.TransferFunction(num, den)
And the Nyquist plot called as follows
ct.nyquist_plot(self.sys, omega=self.w, plot=True,indent_radius=0.2,indent_direction="right")To be completely transparent about it, I am quite new to this, and the code Is the only public repository in my profile, if you want to investigate it further.
What is setting
self.w? I ran your command without that line (so thatomegawas chosen automatically) and got the same plot as I showed above.Getting
omegaright is important: you need to put in extra points in the indentation region since those points are very expanded. Thenyquist_plotprogram does that automatically.@INGELETTR Let us know if the above explanation fixes your issue.
I'm going to open a separate issue about whether
indent_directionshould be used even when the poles are not exactly on the imaginary axis (it seems confusing in the case where you have small numerical errors, like this case).Hi @felipericardo-fe!
1. Why the indentation arc moves across these quadrants
When indenting to the right around a pole at
$s = j\omega_0$ in the$s$ -plane with$s = j\omega_0 + \epsilon e^{j\theta}$ where$\theta \in [-\pi/2, +\pi/2]$ :
$$G(s) \approx \frac{R}{s - j\omega_0} = \frac{|R|}{\epsilon} e^{j(\phi_R - \theta)}$$
where$R = |R| e^{j\phi_R}$ is the residue of$G(s)$ at that pole.For this transfer function, the pole is at
$s = +1j$ with residue:
$$R \approx 5.45 - 4.55j \implies \phi_R \approx -39.86^\circ$$ As
$\theta$ increases from$-90^\circ$ to$+90^\circ$ (tracing a clockwise detour in the$s$ -plane):- At the start (
$\theta = -90^\circ$ ):$\text{phase}(G(s)) = -39.86^\circ - (-90^\circ) = +50.14^\circ$ (Quadrant I) - At the end (
$\theta = +90^\circ$ ):$\text{phase}(G(s)) = -39.86^\circ - (+90^\circ) = -129.86^\circ$ (Quadrant III)
Because the phase decreases monotonically from
$+50.14^\circ$ to$-129.86^\circ$ , the large semicircular arc in the$G(s)$ -plane is mathematically rotating clockwise (angle decreasing by$180^\circ$ ). The non-zero phase of the residue$\phi_R$ rotates the starting and ending angles, which is why it connects Quadrant I to Quadrant III instead of the right-half plane.2. Left vs. Right Indentation
If you set
indent_direction='left',$s = j\omega_0 - \epsilon e^{j\theta}$ , the phase of$G(s)$ shifts by$180^\circ$ , starting at$-129.86^\circ$ (Quadrant III) and ending at$+50.14^\circ$ (Quadrant I) in counter-clockwise phase progression.- At the start (
Hi @felipericardo-fe!
This does not seem to be a user on this issue. @marko1olo, just to confirm, was your post written by an agent like Codex or Claude etc.?
Hi there!
As title says, I found a problem with the following transfer function
num [1,11,10]
den = [0.01,1,0.01,1]
When specified indent_direction = "right", the control Nyquist plot is as follows.
Also, changing indent_direction to "left" does not change the Nyquist diagram whatsoever.