# Balanced model reduction examples¶

## Code¶

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55``` ```#!/usr/bin/env python import os import numpy as np import control.modelsimp as msimp import control.matlab as mt from control.statesp import StateSpace import matplotlib.pyplot as plt plt.close('all') # controllable canonical realization computed in MATLAB for the # transfer function: num = [1 11 45 32], den = [1 15 60 200 60] A = np.array([ [-15., -7.5, -6.25, -1.875], [8., 0., 0., 0.], [0., 4., 0., 0.], [0., 0., 1., 0.] ]) B = np.array([ [2.], [0.], [0.], [0.] ]) C = np.array([[0.5, 0.6875, 0.7031, 0.5]]) D = np.array([[0.]]) # The full system fsys = StateSpace(A, B, C, D) # The reduced system, truncating the order by 1 n = 3 rsys = msimp.balred(fsys, n, method='truncate') # Comparison of the step responses of the full and reduced systems plt.figure(1) y, t = mt.step(fsys) yr, tr = mt.step(rsys) plt.plot(t.T, y.T) plt.plot(tr.T, yr.T) # Repeat balanced reduction, now with 100-dimensional random state space sysrand = mt.rss(100, 1, 1) rsysrand = msimp.balred(sysrand, 10, method='truncate') # Comparison of the impulse responses of the full and reduced random systems plt.figure(2) yrand, trand = mt.impulse(sysrand) yrandr, trandr = mt.impulse(rsysrand) plt.plot(trand.T, yrand.T, trandr.T, yrandr.T) 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.