figure-5.3-phase_portraits.py

# phase_portraits.py - phase portrait examples
# RMM, 6 Apr 2024

import matplotlib.pyplot as plt
import numpy as np
import control as ct
import fbs                      # FBS plotting customizations

# Oscillator parameters
damposc_params = {'m': 1, 'b': 1, 'k': 1}

# System model (as ODE)
def damposc_update(t, x, u, params):
    m, b, k = params['m'], params['b'], params['k']
    return np.array([x[1], -k/m * x[0] - b/m * x[1]])
damposc = ct.nlsys(damposc_update, states=2, params=damposc_params)

# Set the limits for the plot
limits = [-1, 1, -1, 1]

# Vector field
fbs.figure('mlh')
ct.phase_plane_plot(
    damposc, limits, plot_streamlines=False,
    plot_vectorfield=True, gridspec=[15, 12])
plt.suptitle(""); plt.title("Vector field")
fbs.savefig('figure-5.3-phase_portraits-vf.png')

# Streamlines
fbs.figure('mlh')
ct.phase_plane_plot(damposc, limits, 8)
plt.suptitle(""); plt.title("Phase portrait")
fbs.savefig('figure-5.3-phase_portraits-sl.png')