import control as ct
import matplotlib.pyplot as plt
import numpy as np

# Define the open-loop transfer function G(s) = 4 / (s + 2)(s + 4)
# Numerator coefficients
num = [1]
# Denominator coefficients
den = [1, 1, 0]  # (s + 2)(s + 4) = s^2 + 6s + 8

# Create the transfer function object
sys = ct.TransferFunction(num, den)

# Generate the Nyquist plot (which is a polar-style plot of the frequency response)
# We need to vary omega from 0 to infinity, but we use a practical range
# Note: The 'nyquist_plot' is typically used for stability analysis (encirclements of -1),
# but it inherently uses polar coordinates for visualization of magnitude and phase.
# The 'freqresp' function can also be used to get magnitude and phase data.

# Get frequency response data
omega = np.logspace(-2, 2, 500) # Frequencies from 0.01 to 100 rad/s
magnitude, phase_rad, omega = ct.freqresp(sys, omega)

# Convert phase to degrees for easier interpretation (optional)
phase_deg = np.degrees(phase_rad)

# Plot using matplotlib with polar projection
fig = plt.figure()
ax = fig.add_subplot(111, polar=True)

# Plot the magnitude vs angle
# Note: matplotlib expects angles in radians
ax.plot(phase_rad, magnitude.squeeze())
ax.set_title("Open Loop Polar Plot (Nyquist style)")
ax.grid(True)

plt.show()