#!/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 numpy as np 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 from control.tests.margin_test import assert_array_almost_equal import matplotlib.pyplot as plt 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() def suite(): return unittest.TestLoader().loadTestsFromTestCase(TestTimeresp) if __name__ == '__main__': unittest.main()