Hello,

I plotted the following open-loop L(s) transfer function:

Solving the equation after plugging in s = jw, we have:

When I plug in K = 1 / 2, the following warning is generated (any value above or below, all is well):

UserWarning: number of encirclements does not match Nyquist criterion; check frequency range and indent radius/direction
  nyquist_responses = nyquist_response(

Using this test script:

import matplotlib.pyplot as plt
import control as ct

K1 = 0.5

Gc = ct.TransferFunction([K1, -2*K1], [1, 2, 1]) 

plt.style.use('dark_background')

print(Gc)

# ct.nyquist_plot([Gc], max_curve_magnitude=np.inf)
ct.nyquist_plot([Gc])

# Increase size of red marker
ax = plt.gca()
ax.plot(-1, 0, 'x', color = 'red', markersize=7)
plt.axis('equal')
plt.show()

Why is a warning generated. I do understand that this is the boundary limit for stability. If K is less than or equal to 0.5, the system is stable, else if greater then it is unstable since this would make the Nyquist plot encircle the -1 + 0j value.

Any insight would be appreciated.