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#!/usr/bin/env python
#
# timeresp_test.py - test time response functions
# RMM, 17 Jun 2011 (based on TestMatlab from v0.4c)
#
# This test suite just goes through and calls all of the MATLAB
# functions using different systems and arguments to make sure that
# nothing crashes. It doesn't test actual functionality; the module
# specific unit tests will do that.
import unittest
import numpy as np
import scipy as sp
from control.timeresp import *
from control.statesp import *
from control.xferfcn import TransferFunction, _convertToTransferFunction
class TestTimeresp(unittest.TestCase):
def setUp(self):
"""Set up some systems for testing out MATLAB functions"""
A = np.matrix("1. -2.; 3. -4.")
B = np.matrix("5.; 7.")
C = np.matrix("6. 8.")
D = np.matrix("9.")
self.siso_ss1 = StateSpace(A,B,C,D)
# Create some transfer functions
self.siso_tf1 = TransferFunction([1], [1, 2, 1]);
self.siso_tf2 = _convertToTransferFunction(self.siso_ss1);
#Create MIMO system, contains ``siso_ss1`` twice
A = np.matrix("1. -2. 0. 0.;"
"3. -4. 0. 0.;"
"0. 0. 1. -2.;"
"0. 0. 3. -4. ")
B = np.matrix("5. 0.;"
"7. 0.;"
"0. 5.;"
"0. 7. ")
C = np.matrix("6. 8. 0. 0.;"
"0. 0. 6. 8. ")
D = np.matrix("9. 0.;"
"0. 9. ")
self.mimo_ss1 = StateSpace(A, B, C, D)
def test_step_response(self):
#Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
# SISO call
tout, yout = step_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Play with arguments
tout, yout = step_response(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
X0 = np.array([0, 0]);
tout, yout = step_response(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = step_response(sys, T=t, input=0, output=0)
_t, y_11 = step_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
def test_impulse_response(self):
#Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
youttrue = np.array([86., 70.1808, 57.3753, 46.9975, 38.5766, 31.7344,
26.1668, 21.6292, 17.9245, 14.8945])
tout, yout = impulse_response(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
#Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
_t, y_00 = impulse_response(sys, T=t, input=0, output=0)
_t, y_11 = impulse_response(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
#Test MIMO system, as mimo, and don't trim outputs
sys = self.mimo_ss1
_t, yy = impulse_response(sys, T=t, input=0)
np.testing.assert_array_almost_equal(
yy, np.vstack((youttrue, np.zeros_like(youttrue))), decimal=4)
def test_initial_response(self):
#Test SISO system
sys = self.siso_ss1
t = np.linspace(0, 1, 10)
x0 = np.array([[0.5], [1]]);
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
tout, yout = initial_response(sys, T=t, X0=x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
#Test MIMO system, which contains ``siso_ss1`` twice
sys = self.mimo_ss1
x0 = np.matrix(".5; 1.; .5; 1.")
_t, y_00 = initial_response(sys, T=t, X0=x0, input=0, output=0)
_t, y_11 = initial_response(sys, T=t, X0=x0, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
# test MIMO system without trimming
_t, yy = initial_response(sys, T=t, X0=x0)
np.testing.assert_array_almost_equal(yy, np.vstack((y_00, y_11)),
decimal=4)
def test_forced_response(self):
t = np.linspace(0, 1, 10)
#compute step response - test with state space, and transfer function
#objects
u = np.array([1., 1, 1, 1, 1, 1, 1, 1, 1, 1])
youttrue = np.array([9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776])
tout, yout, _xout = forced_response(self.siso_ss1, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
_t, yout, _xout = forced_response(self.siso_tf2, t, u)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
#test with initial value and special algorithm for ``U=0``
u=0
x0 = np.matrix(".5; 1.")
youttrue = np.array([11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391])
_t, yout, _xout = forced_response(self.siso_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
#Test MIMO system, which contains ``siso_ss1`` twice
#first system: initial value, second system: step response
u = np.array([[0., 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1., 1, 1, 1, 1, 1, 1, 1, 1, 1]])
x0 = np.matrix(".5; 1; 0; 0")
youttrue = np.array([[11., 8.1494, 5.9361, 4.2258, 2.9118, 1.9092,
1.1508, 0.5833, 0.1645, -0.1391],
[9., 17.6457, 24.7072, 30.4855, 35.2234, 39.1165,
42.3227, 44.9694, 47.1599, 48.9776]])
_t, yout, _xout = forced_response(self.mimo_ss1, t, u, x0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
def suite():
return unittest.TestLoader().loadTestsFromTestCase(TestTimeresp)
if __name__ == '__main__':
unittest.main()