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#!/usr/bin/env python
#
# discrete_test.py - test discrete time classes
# RMM, 9 Sep 2012
import unittest
import numpy as np
from control import *
from control import matlab
class TestDiscrete(unittest.TestCase):
"""Tests for the DiscreteStateSpace class."""
def setUp(self):
"""Set up a SISO and MIMO system to test operations on."""
# Single input, single output continuous and discrete time systems
sys = matlab.rss(3, 1, 1)
self.siso_ss1 = StateSpace(sys.A, sys.B, sys.C, sys.D)
self.siso_ss1c = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.0)
self.siso_ss1d = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.1)
self.siso_ss2d = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.2)
self.siso_ss3d = StateSpace(sys.A, sys.B, sys.C, sys.D, True)
# Two input, two output continuous time system
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.]]
self.mimo_ss1 = StateSpace(A, B, C, D)
self.mimo_ss1c = StateSpace(A, B, C, D, 0)
# Two input, two output discrete time system
self.mimo_ss1d = StateSpace(A, B, C, D, 0.1)
# Same system, but with a different sampling time
self.mimo_ss2d = StateSpace(A, B, C, D, 0.2)
# Single input, single output continuus and discrete transfer function
self.siso_tf1 = TransferFunction([1, 1], [1, 2, 1])
self.siso_tf1c = TransferFunction([1, 1], [1, 2, 1], 0)
self.siso_tf1d = TransferFunction([1, 1], [1, 2, 1], 0.1)
self.siso_tf2d = TransferFunction([1, 1], [1, 2, 1], 0.2)
self.siso_tf3d = TransferFunction([1, 1], [1, 2, 1], True)
def testTimebaseEqual(self):
self.assertEqual(timebaseEqual(self.siso_ss1, self.siso_tf1), True)
self.assertEqual(timebaseEqual(self.siso_ss1, self.siso_ss1c), True)
self.assertEqual(timebaseEqual(self.siso_ss1, self.siso_ss1d), True)
self.assertEqual(timebaseEqual(self.siso_ss1d, self.siso_ss1c), False)
self.assertEqual(timebaseEqual(self.siso_ss1d, self.siso_ss2d), False)
self.assertEqual(timebaseEqual(self.siso_ss1d, self.siso_ss3d), False)
def testSystemInitialization(self):
# Check to make sure systems are discrete time with proper variables
self.assertEqual(self.siso_ss1.dt, None)
self.assertEqual(self.siso_ss1c.dt, 0)
self.assertEqual(self.siso_ss1d.dt, 0.1)
self.assertEqual(self.siso_ss2d.dt, 0.2)
self.assertEqual(self.siso_ss3d.dt, True)
self.assertEqual(self.mimo_ss1c.dt, 0)
self.assertEqual(self.mimo_ss1d.dt, 0.1)
self.assertEqual(self.mimo_ss2d.dt, 0.2)
self.assertEqual(self.siso_tf1.dt, None)
self.assertEqual(self.siso_tf1c.dt, 0)
self.assertEqual(self.siso_tf1d.dt, 0.1)
self.assertEqual(self.siso_tf2d.dt, 0.2)
self.assertEqual(self.siso_tf3d.dt, True)
def testCopyConstructor(self):
for sys in (self.siso_ss1, self.siso_ss1c, self.siso_ss1d):
newsys = StateSpace(sys);
self.assertEqual(sys.dt, newsys.dt)
for sys in (self.siso_tf1, self.siso_tf1c, self.siso_tf1d):
newsys = TransferFunction(sys);
self.assertEqual(sys.dt, newsys.dt)
def test_timebase(self):
self.assertEqual(timebase(1), None);
self.assertRaises(ValueError, timebase, [1, 2])
self.assertEqual(timebase(self.siso_ss1, strict=False), None);
self.assertEqual(timebase(self.siso_ss1, strict=True), None);
self.assertEqual(timebase(self.siso_ss1c), 0);
self.assertEqual(timebase(self.siso_ss1d), 0.1);
self.assertEqual(timebase(self.siso_ss2d), 0.2);
self.assertEqual(timebase(self.siso_ss3d), True);
self.assertEqual(timebase(self.siso_ss3d, strict=False), 1);
self.assertEqual(timebase(self.siso_tf1, strict=False), None);
self.assertEqual(timebase(self.siso_tf1, strict=True), None);
self.assertEqual(timebase(self.siso_tf1c), 0);
self.assertEqual(timebase(self.siso_tf1d), 0.1);
self.assertEqual(timebase(self.siso_tf2d), 0.2);
self.assertEqual(timebase(self.siso_tf3d), True);
self.assertEqual(timebase(self.siso_tf3d, strict=False), 1);
def test_timebase_conversions(self):
'''Check to make sure timebases transfer properly'''
tf1 = TransferFunction([1,1],[1,2,3]) # unspecified
tf2 = TransferFunction([1,1],[1,2,3], 0) # cont time
tf3 = TransferFunction([1,1],[1,2,3], True) # dtime, unspec
tf4 = TransferFunction([1,1],[1,2,3], 1) # dtime, dt=1
# Make sure unspecified timebase is converted correctly
self.assertEqual(timebase(tf1*tf1), timebase(tf1))
self.assertEqual(timebase(tf1*tf2), timebase(tf2))
self.assertEqual(timebase(tf1*tf3), timebase(tf3))
self.assertEqual(timebase(tf1*tf4), timebase(tf4))
self.assertEqual(timebase(tf2*tf1), timebase(tf2))
self.assertEqual(timebase(tf3*tf1), timebase(tf3))
self.assertEqual(timebase(tf4*tf1), timebase(tf4))
self.assertEqual(timebase(tf1+tf1), timebase(tf1))
self.assertEqual(timebase(tf1+tf2), timebase(tf2))
self.assertEqual(timebase(tf1+tf3), timebase(tf3))
self.assertEqual(timebase(tf1+tf4), timebase(tf4))
self.assertEqual(timebase(feedback(tf1, tf1)), timebase(tf1))
self.assertEqual(timebase(feedback(tf1, tf2)), timebase(tf2))
self.assertEqual(timebase(feedback(tf1, tf3)), timebase(tf3))
self.assertEqual(timebase(feedback(tf1, tf4)), timebase(tf4))
# Make sure discrete time without sampling is converted correctly
self.assertEqual(timebase(tf3*tf3), timebase(tf3))
self.assertEqual(timebase(tf3*tf4), timebase(tf4))
self.assertEqual(timebase(tf3+tf3), timebase(tf3))
self.assertEqual(timebase(tf3+tf3), timebase(tf4))
self.assertEqual(timebase(feedback(tf3, tf3)), timebase(tf3))
self.assertEqual(timebase(feedback(tf3, tf4)), timebase(tf4))
# Make sure all other combinations are errors
try:
tf2*tf3 # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
try:
tf2*tf4 # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
try:
tf2+tf3 # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
try:
tf2+tf4 # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
try:
feedback(tf2, tf3) # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
try:
feedback(tf2, tf4) # Error; incompatible timebases
raise ValueError("incompatible operation allowed")
except ValueError:
pass
def testisdtime(self):
# Constant
self.assertEqual(isdtime(1), True);
self.assertEqual(isdtime(1, strict=True), False);
# State space
self.assertEqual(isdtime(self.siso_ss1), True);
self.assertEqual(isdtime(self.siso_ss1, strict=True), False);
self.assertEqual(isdtime(self.siso_ss1c), False);
self.assertEqual(isdtime(self.siso_ss1c, strict=True), False);
self.assertEqual(isdtime(self.siso_ss1d), True);
self.assertEqual(isdtime(self.siso_ss1d, strict=True), True);
self.assertEqual(isdtime(self.siso_ss3d, strict=True), True);
# Transfer function
self.assertEqual(isdtime(self.siso_tf1), True);
self.assertEqual(isdtime(self.siso_tf1, strict=True), False);
self.assertEqual(isdtime(self.siso_tf1c), False);
self.assertEqual(isdtime(self.siso_tf1c, strict=True), False);
self.assertEqual(isdtime(self.siso_tf1d), True);
self.assertEqual(isdtime(self.siso_tf1d, strict=True), True);
self.assertEqual(isdtime(self.siso_tf3d, strict=True), True);
def testisctime(self):
# Constant
self.assertEqual(isctime(1), True);
self.assertEqual(isctime(1, strict=True), False);
# State Space
self.assertEqual(isctime(self.siso_ss1), True);
self.assertEqual(isctime(self.siso_ss1, strict=True), False);
self.assertEqual(isctime(self.siso_ss1c), True);
self.assertEqual(isctime(self.siso_ss1c, strict=True), True);
self.assertEqual(isctime(self.siso_ss1d), False);
self.assertEqual(isctime(self.siso_ss1d, strict=True), False);
self.assertEqual(isctime(self.siso_ss3d, strict=True), False);
# Transfer Function
self.assertEqual(isctime(self.siso_tf1), True);
self.assertEqual(isctime(self.siso_tf1, strict=True), False);
self.assertEqual(isctime(self.siso_tf1c), True);
self.assertEqual(isctime(self.siso_tf1c, strict=True), True);
self.assertEqual(isctime(self.siso_tf1d), False);
self.assertEqual(isctime(self.siso_tf1d, strict=True), False);
self.assertEqual(isctime(self.siso_tf3d, strict=True), False);
def testAddition(self):
# State space addition
sys = self.siso_ss1 + self.siso_ss1d
sys = self.siso_ss1 + self.siso_ss1c
sys = self.siso_ss1c + self.siso_ss1
sys = self.siso_ss1d + self.siso_ss1
sys = self.siso_ss1c + self.siso_ss1c
sys = self.siso_ss1d + self.siso_ss1d
sys = self.siso_ss3d + self.siso_ss3d
self.assertRaises(ValueError, StateSpace.__add__, self.mimo_ss1c,
self.mimo_ss1d)
self.assertRaises(ValueError, StateSpace.__add__, self.mimo_ss1d,
self.mimo_ss2d)
self.assertRaises(ValueError, StateSpace.__add__, self.siso_ss1d,
self.siso_ss3d)
# Transfer function addition
sys = self.siso_tf1 + self.siso_tf1d
sys = self.siso_tf1 + self.siso_tf1c
sys = self.siso_tf1c + self.siso_tf1
sys = self.siso_tf1d + self.siso_tf1
sys = self.siso_tf1c + self.siso_tf1c
sys = self.siso_tf1d + self.siso_tf1d
sys = self.siso_tf2d + self.siso_tf2d
self.assertRaises(ValueError, TransferFunction.__add__, self.siso_tf1c,
self.siso_tf1d)
self.assertRaises(ValueError, TransferFunction.__add__, self.siso_tf1d,
self.siso_tf2d)
self.assertRaises(ValueError, TransferFunction.__add__, self.siso_tf1d,
self.siso_tf3d)
# State space + transfer function
sys = self.siso_ss1c + self.siso_tf1c
sys = self.siso_tf1c + self.siso_ss1c
sys = self.siso_ss1d + self.siso_tf1d
sys = self.siso_tf1d + self.siso_ss1d
self.assertRaises(ValueError, TransferFunction.__add__, self.siso_tf1c,
self.siso_ss1d)
def testMultiplication(self):
# State space addition
sys = self.siso_ss1 * self.siso_ss1d
sys = self.siso_ss1 * self.siso_ss1c
sys = self.siso_ss1c * self.siso_ss1
sys = self.siso_ss1d * self.siso_ss1
sys = self.siso_ss1c * self.siso_ss1c
sys = self.siso_ss1d * self.siso_ss1d
self.assertRaises(ValueError, StateSpace.__mul__, self.mimo_ss1c,
self.mimo_ss1d)
self.assertRaises(ValueError, StateSpace.__mul__, self.mimo_ss1d,
self.mimo_ss2d)
self.assertRaises(ValueError, StateSpace.__mul__, self.siso_ss1d,
self.siso_ss3d)
# Transfer function addition
sys = self.siso_tf1 * self.siso_tf1d
sys = self.siso_tf1 * self.siso_tf1c
sys = self.siso_tf1c * self.siso_tf1
sys = self.siso_tf1d * self.siso_tf1
sys = self.siso_tf1c * self.siso_tf1c
sys = self.siso_tf1d * self.siso_tf1d
self.assertRaises(ValueError, TransferFunction.__mul__, self.siso_tf1c,
self.siso_tf1d)
self.assertRaises(ValueError, TransferFunction.__mul__, self.siso_tf1d,
self.siso_tf2d)
self.assertRaises(ValueError, TransferFunction.__mul__, self.siso_tf1d,
self.siso_tf3d)
# State space * transfer function
sys = self.siso_ss1c * self.siso_tf1c
sys = self.siso_tf1c * self.siso_ss1c
sys = self.siso_ss1d * self.siso_tf1d
sys = self.siso_tf1d * self.siso_ss1d
self.assertRaises(ValueError, TransferFunction.__mul__, self.siso_tf1c,
self.siso_ss1d)
def testFeedback(self):
# State space addition
sys = feedback(self.siso_ss1, self.siso_ss1d)
sys = feedback(self.siso_ss1, self.siso_ss1c)
sys = feedback(self.siso_ss1c, self.siso_ss1)
sys = feedback(self.siso_ss1d, self.siso_ss1)
sys = feedback(self.siso_ss1c, self.siso_ss1c)
sys = feedback(self.siso_ss1d, self.siso_ss1d)
self.assertRaises(ValueError, feedback, self.mimo_ss1c, self.mimo_ss1d)
self.assertRaises(ValueError, feedback, self.mimo_ss1d, self.mimo_ss2d)
self.assertRaises(ValueError, feedback, self.siso_ss1d, self.siso_ss3d)
# Transfer function addition
sys = feedback(self.siso_tf1, self.siso_tf1d)
sys = feedback(self.siso_tf1, self.siso_tf1c)
sys = feedback(self.siso_tf1c, self.siso_tf1)
sys = feedback(self.siso_tf1d, self.siso_tf1)
sys = feedback(self.siso_tf1c, self.siso_tf1c)
sys = feedback(self.siso_tf1d, self.siso_tf1d)
self.assertRaises(ValueError, feedback, self.siso_tf1c, self.siso_tf1d)
self.assertRaises(ValueError, feedback, self.siso_tf1d, self.siso_tf2d)
self.assertRaises(ValueError, feedback, self.siso_tf1d, self.siso_tf3d)
# State space, transfer function
sys = feedback(self.siso_ss1c, self.siso_tf1c)
sys = feedback(self.siso_tf1c, self.siso_ss1c)
sys = feedback(self.siso_ss1d, self.siso_tf1d)
sys = feedback(self.siso_tf1d, self.siso_ss1d)
self.assertRaises(ValueError, feedback, self.siso_tf1c, self.siso_ss1d)
def testSimulation(self):
T = range(100)
U = np.sin(T)
# For now, just check calling syntax
# TODO: add checks on output of simulations
tout, yout = step_response(self.siso_ss1d)
tout, yout = step_response(self.siso_ss1d, T)
tout, yout = impulse_response(self.siso_ss1d, T)
tout, yout = impulse_response(self.siso_ss1d)
tout, yout, xout = forced_response(self.siso_ss1d, T, U, 0)
tout, yout, xout = forced_response(self.siso_ss2d, T, U, 0)
tout, yout, xout = forced_response(self.siso_ss3d, T, U, 0)
def test_sample_system(self):
# Make sure we can convert various types of systems
for sysc in (self.siso_tf1, self.siso_tf1c,
self.siso_ss1, self.siso_ss1c,
self.mimo_ss1, self.mimo_ss1c):
for method in ("zoh", "bilinear", "euler", "backward_diff"):
sysd = sample_system(sysc, 1, method=method)
self.assertEqual(sysd.dt, 1)
# Check "matched", defined only for SISO transfer functions
for sysc in (self.siso_tf1, self.siso_tf1c):
sysd = sample_system(sysc, 1, method="matched")
self.assertEqual(sysd.dt, 1)
# Check errors
self.assertRaises(ValueError, sample_system, self.siso_ss1d, 1)
self.assertRaises(ValueError, sample_system, self.siso_ss1, 1, 'unknown')
def test_sample_ss(self):
# double integrators, two different ways
sys1 = StateSpace([[0.,1.],[0.,0.]], [[0.],[1.]], [[1.,0.]], 0.)
sys2 = StateSpace([[0.,0.],[1.,0.]], [[1.],[0.]], [[0.,1.]], 0.)
I = np.eye(2)
for sys in (sys1, sys2):
for h in (0.1, 0.5, 1, 2):
Ad = I + h * sys.A
Bd = h * sys.B + 0.5 * h**2 * (sys.A * sys.B)
sysd = sample_system(sys, h, method='zoh')
np.testing.assert_array_almost_equal(sysd.A, Ad)
np.testing.assert_array_almost_equal(sysd.B, Bd)
np.testing.assert_array_almost_equal(sysd.C, sys.C)
np.testing.assert_array_almost_equal(sysd.D, sys.D)
self.assertEqual(sysd.dt, h)
def test_sample_tf(self):
# double integrator
sys = TransferFunction(1, [1,0,0])
for h in (0.1, 0.5, 1, 2):
numd_expected = 0.5 * h**2 * np.array([1.,1.])
dend_expected = np.array([1.,-2.,1.])
sysd = sample_system(sys, h, method='zoh')
self.assertEqual(sysd.dt, h)
numd = sysd.num[0][0]
dend = sysd.den[0][0]
np.testing.assert_array_almost_equal(numd, numd_expected)
np.testing.assert_array_almost_equal(dend, dend_expected)
def test_discrete_bode(self):
# Create a simple discrete time system and check the calculation
sys = TransferFunction([1], [1, 0.5], 1)
omega = [1, 2, 3]
mag_out, phase_out, omega_out = bode(sys, omega)
H_z = list(map(lambda w: 1./(np.exp(1.j * w) + 0.5), omega))
np.testing.assert_array_almost_equal(omega, omega_out)
np.testing.assert_array_almost_equal(mag_out, np.absolute(H_z))
np.testing.assert_array_almost_equal(phase_out, np.angle(H_z))
def suite():
return unittest.TestLoader().loadTestsFromTestCase(TestDiscrete)
if __name__ == "__main__":
unittest.main()