Secord order system (MATLAB module example)

This example computes time and frequency responses for a second-order system using the MATLAB compatibility module.

Code

# secord.py - demonstrate some standard MATLAB commands
# RMM, 25 May 09

import os
import matplotlib.pyplot as plt   # MATLAB plotting functions
import numpy as np
from control.matlab import ss, step, bode, nyquist, rlocus # MATLAB-like functions

# Parameters defining the system
m = 250.0           # system mass
k = 40.0            # spring constant
b = 60.0            # damping constant

# System matrices
A = [[0, 1.], [-k/m, -b/m]]
B = [[0], [1/m]]
C = [[1., 0]]
sys = ss(A, B, C, 0)

# Step response for the system
plt.figure(1)
yout, T = step(sys)
plt.plot(T.T, yout.T)
plt.show(block=False)

# Bode plot for the system
plt.figure(2)
mag, phase, om = bode(sys, np.logspace(-2, 2), plot=True)
plt.show(block=False)

# Nyquist plot for the system
plt.figure(3)
nyquist(sys)
plt.show(block=False)

# Root locus plot for the system
rlocus(sys)

if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:
    plt.show()

Notes

1. The environment variable PYCONTROL_TEST_EXAMPLES is used for testing to turn off plotting of the outputs.