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#!/usr/bin/env python
#
# freqresp_test.py - test frequency response functions
# RMM, 30 May 2016 (based on timeresp_test.py)
#
# This is a rudimentary set of tests for frequency response functions,
# including bode plots.
import unittest
import matplotlib.pyplot as plt
import numpy as np
from numpy.testing import assert_array_almost_equal
import control as ctrl
from control.statesp import StateSpace
from control.xferfcn import TransferFunction
from control.matlab import ss, tf, bode, rss
from control.exception import slycot_check
class TestFreqresp(unittest.TestCase):
def setUp(self):
self.A = np.matrix('1,1;0,1')
self.C = np.matrix('1,0')
self.omega = np.linspace(10e-2,10e2,1000)
def test_siso(self):
B = np.matrix('0;1')
D = 0
sys = StateSpace(self.A,B,self.C,D)
# test frequency response
frq=sys.freqresp(self.omega)
# test bode plot
bode(sys)
# Convert to transfer function and test bode
systf = tf(sys)
bode(systf)
def test_superimpose(self):
# Test to make sure that multiple calls to plots superimpose their
# data on the same axes unless told to do otherwise
# Generate two plots in a row; should be on the same axes
plt.figure(1); plt.clf()
ctrl.bode_plot(ctrl.tf([1], [1,2,1]))
ctrl.bode_plot(ctrl.tf([5], [1, 1]))
# Check to make sure there are two axes and that each axes has two lines
self.assertEqual(len(plt.gcf().axes), 2)
for ax in plt.gcf().axes:
# Make sure there are 2 lines in each subplot
assert len(ax.get_lines()) == 2
# Generate two plots as a list; should be on the same axes
plt.figure(2); plt.clf();
ctrl.bode_plot([ctrl.tf([1], [1,2,1]), ctrl.tf([5], [1, 1])])
# Check to make sure there are two axes and that each axes has two lines
self.assertEqual(len(plt.gcf().axes), 2)
for ax in plt.gcf().axes:
# Make sure there are 2 lines in each subplot
assert len(ax.get_lines()) == 2
# Generate two separate plots; only the second should appear
plt.figure(3); plt.clf();
ctrl.bode_plot(ctrl.tf([1], [1,2,1]))
plt.clf()
ctrl.bode_plot(ctrl.tf([5], [1, 1]))
# Check to make sure there are two axes and that each axes has one line
self.assertEqual(len(plt.gcf().axes), 2)
for ax in plt.gcf().axes:
# Make sure there is only 1 line in the subplot
assert len(ax.get_lines()) == 1
# Now add a line to the magnitude plot and make sure if is there
for ax in plt.gcf().axes:
if ax.get_label() == 'control-bode-magnitude':
break
ax.semilogx([1e-2, 1e1], 20 * np.log10([1, 1]), 'k-')
self.assertEqual(len(ax.get_lines()), 2)
def test_doubleint(self):
# 30 May 2016, RMM: added to replicate typecast bug in freqresp.py
A = np.matrix('0, 1; 0, 0');
B = np.matrix('0; 1');
C = np.matrix('1, 0');
D = 0;
sys = ss(A, B, C, D);
bode(sys);
@unittest.skipIf(not slycot_check(), "slycot not installed")
def test_mimo(self):
# MIMO
B = np.matrix('1,0;0,1')
D = np.matrix('0,0')
sysMIMO = ss(self.A,B,self.C,D)
frqMIMO = sysMIMO.freqresp(self.omega)
tfMIMO = tf(sysMIMO)
#bode(sysMIMO) # - should throw not implemented exception
#bode(tfMIMO) # - should throw not implemented exception
#plt.figure(3)
#plt.semilogx(self.omega,20*np.log10(np.squeeze(frq[0])))
#plt.figure(4)
#bode(sysMIMO,self.omega)
def test_bode_margin(self):
num = [1000]
den = [1, 25, 100, 0]
sys = ctrl.tf(num, den)
plt.figure()
ctrl.bode_plot(sys, margins=True,dB=False,deg = True, Hz=False)
fig = plt.gcf()
allaxes = fig.get_axes()
mag_to_infinity = (np.array([6.07828691, 6.07828691]),
np.array([1.00000000e+00, 1.00000000e-08]))
assert_array_almost_equal(mag_to_infinity, allaxes[0].lines[2].get_data())
gm_to_infinty = (np.array([10., 10.]), np.array([4.00000000e-01, 1.00000000e-08]))
assert_array_almost_equal(gm_to_infinty, allaxes[0].lines[3].get_data())
one_to_gm = (np.array([10., 10.]), np.array([1., 0.4]))
assert_array_almost_equal(one_to_gm, allaxes[0].lines[4].get_data())
pm_to_infinity = (np.array([6.07828691, 6.07828691]),
np.array([100000., -157.46405841]))
assert_array_almost_equal(pm_to_infinity, allaxes[1].lines[2].get_data())
pm_to_phase = (np.array([6.07828691, 6.07828691]), np.array([-157.46405841, -180.]))
assert_array_almost_equal(pm_to_phase, allaxes[1].lines[3].get_data())
phase_to_infinity = (np.array([10., 10.]), np.array([1.00000000e-08, -1.80000000e+02]))
assert_array_almost_equal(phase_to_infinity, allaxes[1].lines[4].get_data())
def test_discrete(self):
# Test discrete time frequency response
# SISO state space systems with either fixed or unspecified sampling times
sys = rss(3, 1, 1)
siso_ss1d = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.1)
siso_ss2d = StateSpace(sys.A, sys.B, sys.C, sys.D, True)
# MIMO state space systems with either fixed or unspecified sampling times
A = [[-3., 4., 2.], [-1., -3., 0.], [2., 5., 3.]]
B = [[1., 4.], [-3., -3.], [-2., 1.]]
C = [[4., 2., -3.], [1., 4., 3.]]
D = [[-2., 4.], [0., 1.]]
mimo_ss1d = StateSpace(A, B, C, D, 0.1)
mimo_ss2d = StateSpace(A, B, C, D, True)
# SISO transfer functions
siso_tf1d = TransferFunction([1, 1], [1, 2, 1], 0.1)
siso_tf2d = TransferFunction([1, 1], [1, 2, 1], True)
# Go through each system and call the code, checking return types
for sys in (siso_ss1d, siso_ss2d, mimo_ss1d, mimo_ss2d,
siso_tf1d, siso_tf2d):
# Set frequency range to just below Nyquist freq (for Bode)
omega_ok = np.linspace(10e-4,0.99,100) * np.pi/sys.dt
# Test frequency response
ret = sys.freqresp(omega_ok)
# Check for warning if frequency is out of range
import warnings
warnings.simplefilter('always', UserWarning) # don't supress
with warnings.catch_warnings(record=True) as w:
# Set up warnings filter to only show warnings in control module
warnings.filterwarnings("ignore")
warnings.filterwarnings("always", module="control")
# Look for a warning about sampling above Nyquist frequency
omega_bad = np.linspace(10e-4,1.1,10) * np.pi/sys.dt
ret = sys.freqresp(omega_bad)
print("len(w) =", len(w))
self.assertEqual(len(w), 1)
self.assertIn("above", str(w[-1].message))
self.assertIn("Nyquist", str(w[-1].message))
# Test bode plots (currently only implemented for SISO)
if (sys.inputs == 1 and sys.outputs == 1):
# Generic call (frequency range calculated automatically)
ret_ss = bode(sys)
# Convert to transfer function and test bode again
systf = tf(sys);
ret_tf = bode(systf)
# Make sure we can pass a frequency range
bode(sys, omega_ok)
else:
# Calling bode should generate a not implemented error
self.assertRaises(NotImplementedError, bode, (sys,))
def test_options(self):
"""Test ability to set parameter values"""
# Generate a Bode plot of a transfer function
sys = ctrl.tf([1000], [1, 25, 100, 0])
fig1 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg = True, Hz=False)
# Save the parameter values
left1, right1 = fig1.axes[0].xaxis.get_data_interval()
numpoints1 = len(fig1.axes[0].lines[0].get_data()[0])
# Same transfer function, but add a decade on each end
ctrl.config.set_defaults('freqplot', feature_periphery_decades=2)
fig2 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg = True, Hz=False)
left2, right2 = fig2.axes[0].xaxis.get_data_interval()
# Make sure we got an extra decade on each end
self.assertAlmostEqual(left2, 0.1 * left1)
self.assertAlmostEqual(right2, 10 * right1)
# Same transfer function, but add more points to the plot
ctrl.config.set_defaults(
'freqplot', feature_periphery_decades=2, number_of_samples=13)
fig3 = plt.figure()
ctrl.bode_plot(sys, dB=False, deg = True, Hz=False)
numpoints3 = len(fig3.axes[0].lines[0].get_data()[0])
# Make sure we got the right number of points
self.assertNotEqual(numpoints1, numpoints3)
self.assertEqual(numpoints3, 13)
# Reset default parameters to avoid contamination
ctrl.config.reset_defaults()
if __name__ == '__main__':
unittest.main()