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1287 lines (1107 loc) · 50.3 KB
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"""xferfcn_test.py - test TransferFunction class
RMM, 30 Mar 2011 (based on TestXferFcn from v0.4a)
"""
import operator
import re
import numpy as np
import pytest
import control as ct
from control import (StateSpace, TransferFunction, defaults, evalfr, isctime,
isdtime, reset_defaults, rss, sample_system, set_defaults,
ss, ss2tf, tf, tf2ss, zpk)
from control.statesp import _convert_to_statespace
from control.tests.conftest import slycotonly
from control.xferfcn import _convert_to_transfer_function
class TestXferFcn:
"""Test functionality and correct reporting of the transfer function class.
Throughout these tests, we will give different input
formats to the xTranferFunction constructor, to try to break it. These
tests have been verified in MATLAB.
"""
# Tests for raising exceptions.
def test_constructor_bad_input_type(self):
"""Give the constructor invalid input types."""
# MIMO requires lists of lists of vectors (not lists of vectors)
with pytest.raises(TypeError):
TransferFunction([[0., 1.], [2., 3.]], [[5., 2.], [3., 0.]])
# good input
TransferFunction([[[0., 1.], [2., 3.]]],
[[[5., 2.], [3., 0.]]])
# Single argument of the wrong type
with pytest.raises(TypeError):
TransferFunction([1])
# Too many arguments
with pytest.raises(TypeError):
TransferFunction(1, 2, 3, 4)
# Different numbers of elements in numerator rows
with pytest.raises(ValueError):
TransferFunction([[[0, 1], [2, 3]],
[[4, 5]]],
[[[6, 7], [4, 5]],
[[2, 3], [0, 1]]])
with pytest.raises(ValueError):
TransferFunction([[[0, 1], [2, 3]],
[[4, 5], [6, 7]]],
[[[6, 7], [4, 5]],
[[2, 3]]])
# good input
TransferFunction([[[0, 1], [2, 3]],
[[4, 5], [6, 7]]],
[[[6, 7], [4, 5]],
[[2, 3], [0, 1]]])
def test_constructor_inconsistent_dimension(self):
"""Give constructor numerators, denominators of different sizes."""
with pytest.raises(ValueError):
TransferFunction([[[1.]]], [[[1.], [2., 3.]]])
with pytest.raises(ValueError):
TransferFunction([[[1.]]], [[[1.]], [[2., 3.]]])
with pytest.raises(ValueError):
TransferFunction([[[1.]]],
[[[1.], [1., 2.]], [[5., 2.], [2., 3.]]])
def test_constructor_inconsistent_columns(self):
"""Give the constructor inputs that do not have the same number of
columns in each row."""
with pytest.raises(ValueError):
TransferFunction(1., [[[1.]], [[2.], [3.]]])
with pytest.raises(ValueError):
TransferFunction([[[1.]], [[2.], [3.]]], 1.)
def test_constructor_zero_denominator(self):
"""Give the constructor a transfer function with a zero denominator."""
with pytest.raises(ValueError):
TransferFunction(1., 0.)
with pytest.raises(ValueError):
TransferFunction([[[1.], [2., 3.]], [[-1., 4.], [3., 2.]]],
[[[1., 0.], [0.]], [[0., 0.], [2.]]])
@pytest.mark.skip("outdated test")
def test_constructor_nodt(self):
"""Test the constructor when an object without dt is passed"""
sysin = TransferFunction([[[0., 1.], [2., 3.]]],
[[[5., 2.], [3., 0.]]])
del sysin.dt # this doesn't make sense and now breaks
sys = TransferFunction(sysin)
assert sys.dt == defaults['control.default_dt']
# test for static gain
sysin = TransferFunction([[[2.], [3.]]],
[[[1.], [.1]]])
del sysin.dt # this doesn't make sense and now breaks
sys = TransferFunction(sysin)
assert sys.dt is None
def test_constructor_double_dt(self):
"""Test that providing dt as arg and kwarg prefers arg with warning"""
with pytest.warns(UserWarning, match="received multiple dt.*"
"using positional arg"):
sys = TransferFunction(1, [1, 2, 3], 0.1, dt=0.2)
assert sys.dt == 0.1
def test_add_inconsistent_dimension(self):
"""Add two transfer function matrices of different sizes."""
sys1 = TransferFunction([[[1., 2.]]], [[[4., 5.]]])
sys2 = TransferFunction([[[4., 3.]], [[1., 2.]]],
[[[1., 6.]], [[2., 4.]]])
with pytest.raises(ValueError):
sys1.__add__(sys2)
with pytest.raises(ValueError):
sys1.__sub__(sys2)
with pytest.raises(ValueError):
sys1.__radd__(sys2)
with pytest.raises(ValueError):
sys1.__rsub__(sys2)
def test_mul_inconsistent_dimension(self):
"""Multiply two transfer function matrices of incompatible sizes."""
sys1 = TransferFunction([[[1., 2.], [4., 5.]], [[2., 5.], [4., 3.]]],
[[[6., 2.], [4., 1.]], [[6., 7.], [2., 4.]]])
sys2 = TransferFunction([[[1.]], [[2.]], [[3.]]],
[[[4.]], [[5.]], [[6.]]])
with pytest.raises(ValueError):
sys1.__mul__(sys2)
with pytest.raises(ValueError):
sys2.__mul__(sys1)
with pytest.raises(ValueError):
sys1.__rmul__(sys2)
with pytest.raises(ValueError):
sys2.__rmul__(sys1)
# Tests for TransferFunction._truncatecoeff
def test_truncate_coefficients_non_null_numerator(self):
"""Remove extraneous zeros in polynomial representations."""
sys1 = TransferFunction([0., 0., 1., 2.], [[[0., 0., 0., 3., 2., 1.]]])
np.testing.assert_allclose(sys1.num, [[[1., 2.]]])
np.testing.assert_allclose(sys1.den, [[[3., 2., 1.]]])
def test_truncate_coefficients_null_numerator(self):
"""Remove extraneous zeros in polynomial representations."""
sys1 = TransferFunction([0., 0., 0.], 1.)
np.testing.assert_allclose(sys1.num, [[[0.]]])
np.testing.assert_allclose(sys1.den, [[[1.]]])
# Tests for TransferFunction.__neg__
def test_reverse_sign_scalar(self):
"""Negate a direct feedthrough system."""
sys1 = TransferFunction(2., np.array([-3.]))
sys2 = - sys1
np.testing.assert_allclose(sys2.num, [[[-2.]]])
np.testing.assert_allclose(sys2.den, [[[-3.]]])
def test_reverse_sign_siso(self):
"""Negate a SISO system."""
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1.])
sys2 = - sys1
np.testing.assert_allclose(sys2.num, [[[-1., -3., -5.]]])
np.testing.assert_allclose(sys2.den, [[[1., 6., 2., -1.]]])
@slycotonly
def test_reverse_sign_mimo(self):
"""Negate a MIMO system."""
num1 = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
num3 = [[[-1., -2.], [0., -3.], [-2., 1.]],
[[-1.], [-4., 0.], [-1., 4., -3.]]]
den1 = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
sys1 = TransferFunction(num1, den1)
sys2 = - sys1
sys3 = TransferFunction(num3, den1)
for i in range(sys3.noutputs):
for j in range(sys3.ninputs):
np.testing.assert_allclose(sys2.num[i][j], sys3.num[i][j])
np.testing.assert_allclose(sys2.den[i][j], sys3.den[i][j])
# Tests for TransferFunction.__add__
def test_add_scalar(self):
"""Add two direct feedthrough systems."""
sys1 = TransferFunction(1., [[[1.]]])
sys2 = TransferFunction(np.array([2.]), [1.])
sys3 = sys1 + sys2
np.testing.assert_allclose(sys3.num, 3.)
np.testing.assert_allclose(sys3.den, 1.)
def test_add_siso(self):
"""Add two SISO systems."""
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1])
sys2 = TransferFunction([[np.array([-1., 3.])]], [[[1., 0., -1.]]])
sys3 = sys1 + sys2
# If sys3.num is [[[0., 20., 4., -8.]]], then this is wrong!
np.testing.assert_allclose(sys3.num, [[[20., 4., -8]]])
np.testing.assert_allclose(sys3.den, [[[1., 6., 1., -7., -2., 1.]]])
@slycotonly
def test_add_mimo(self):
"""Add two MIMO systems."""
num1 = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
den1 = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
num2 = [[[0., 0., -1], [2.], [-1., -1.]],
[[1., 2.], [-1., -2.], [4.]]]
den2 = [[[-1.], [1., 2., 3.], [-1., -1.]],
[[-4., -3., 2.], [0., 1.], [1., 0.]]]
num3 = [[[3., -3., -6], [5., 6., 9.], [-4., -2., 2]],
[[3., 2., -3., 2], [-2., -3., 7., 2.], [1., -4., 3., 4]]]
den3 = [[[3., -2., -4.], [1., 2., 3., 0., 0.], [-2., -1., 1.]],
[[-12., -9., 6., 0., 0.], [2., -1., -1.], [1., 0.]]]
sys1 = TransferFunction(num1, den1)
sys2 = TransferFunction(num2, den2)
sys3 = sys1 + sys2
for i in range(sys3.noutputs):
for j in range(sys3.ninputs):
np.testing.assert_allclose(sys3.num[i][j], num3[i][j])
np.testing.assert_allclose(sys3.den[i][j], den3[i][j])
# Tests for TransferFunction.__sub__
def test_subtract_scalar(self):
"""Subtract two direct feedthrough systems."""
sys1 = TransferFunction(1., [[[1.]]])
sys2 = TransferFunction(np.array([2.]), [1.])
sys3 = sys1 - sys2
np.testing.assert_allclose(sys3.num, -1.)
np.testing.assert_allclose(sys3.den, 1.)
def test_subtract_siso(self):
"""Subtract two SISO systems."""
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1])
sys2 = TransferFunction([[np.array([-1., 3.])]], [[[1., 0., -1.]]])
sys3 = sys1 - sys2
sys4 = sys2 - sys1
np.testing.assert_allclose(sys3.num, [[[2., 6., -12., -10., -2.]]])
np.testing.assert_allclose(sys3.den, [[[1., 6., 1., -7., -2., 1.]]])
np.testing.assert_allclose(sys4.num, [[[-2., -6., 12., 10., 2.]]])
np.testing.assert_allclose(sys4.den, [[[1., 6., 1., -7., -2., 1.]]])
@slycotonly
def test_subtract_mimo(self):
"""Subtract two MIMO systems."""
num1 = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
den1 = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
num2 = [[[0., 0., -1], [2.], [-1., -1.]],
[[1., 2.], [-1., -2.], [4.]]]
den2 = [[[-1.], [1., 2., 3.], [-1., -1.]],
[[-4., -3., 2.], [0., 1.], [1., 0.]]]
num3 = [[[-3., 1., 2.], [1., 6., 9.], [0.]],
[[-3., -10., -3., 2], [2., 3., 1., -2], [1., -4., 3., -4]]]
den3 = [[[3., -2., -4], [1., 2., 3., 0., 0.], [1]],
[[-12., -9., 6., 0., 0.], [2., -1., -1], [1., 0.]]]
sys1 = TransferFunction(num1, den1)
sys2 = TransferFunction(num2, den2)
sys3 = sys1 - sys2
for i in range(sys3.noutputs):
for j in range(sys3.ninputs):
np.testing.assert_allclose(sys3.num[i][j], num3[i][j])
np.testing.assert_allclose(sys3.den[i][j], den3[i][j])
# Tests for TransferFunction.__mul__
def test_multiply_scalar(self):
"""Multiply two direct feedthrough systems."""
sys1 = TransferFunction(2., [1.])
sys2 = TransferFunction(1., 4.)
sys3 = sys1 * sys2
sys4 = sys1 * sys2
np.testing.assert_allclose(sys3.num, [[[2.]]])
np.testing.assert_allclose(sys3.den, [[[4.]]])
np.testing.assert_allclose(sys3.num, sys4.num)
np.testing.assert_allclose(sys3.den, sys4.den)
def test_multiply_siso(self):
"""Multiply two SISO systems."""
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1])
sys2 = TransferFunction([[[-1., 3.]]], [[[1., 0., -1.]]])
sys3 = sys1 * sys2
sys4 = sys2 * sys1
np.testing.assert_allclose(sys3.num, [[[-1., 0., 4., 15.]]])
np.testing.assert_allclose(sys3.den, [[[1., 6., 1., -7., -2., 1.]]])
np.testing.assert_allclose(sys3.num, sys4.num)
np.testing.assert_allclose(sys3.den, sys4.den)
@slycotonly
def test_multiply_mimo(self):
"""Multiply two MIMO systems."""
num1 = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
den1 = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
num2 = [[[0., 1., 2.]],
[[1., -5.]],
[[-2., 1., 4.]]]
den2 = [[[1., 0., 0., 0.]],
[[-2., 1., 3.]],
[[4., -1., -1., 0.]]]
num3 = [[[-24., 52., -14., 245., -490., -115., 467., -95., -56., 12.,
0., 0., 0.]],
[[24., -132., 138., 345., -768., -106., 510., 41., -79., -69.,
-23., 17., 6., 0.]]]
den3 = [[[48., -92., -84., 183., 44., -97., -2., 12., 0., 0., 0., 0.,
0., 0.]],
[[-48., 60., 84., -81., -45., 21., 9., 0., 0., 0., 0., 0., 0.]]]
sys1 = TransferFunction(num1, den1)
sys2 = TransferFunction(num2, den2)
sys3 = sys1 * sys2
for i in range(sys3.noutputs):
for j in range(sys3.ninputs):
np.testing.assert_allclose(sys3.num[i][j], num3[i][j])
np.testing.assert_allclose(sys3.den[i][j], den3[i][j])
# Tests for TransferFunction.__div__
def test_divide_scalar(self):
"""Divide two direct feedthrough systems."""
sys1 = TransferFunction(np.array([3.]), -4.)
sys2 = TransferFunction(5., 2.)
sys3 = sys1 / sys2
np.testing.assert_allclose(sys3.num, [[[6.]]])
np.testing.assert_allclose(sys3.den, [[[-20.]]])
def test_divide_siso(self):
"""Divide two SISO systems."""
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1])
sys2 = TransferFunction([[[-1., 3.]]], [[[1., 0., -1.]]])
sys3 = sys1 / sys2
sys4 = sys2 / sys1
np.testing.assert_allclose(sys3.num, [[[1., 3., 4., -3., -5.]]])
np.testing.assert_allclose(sys3.den, [[[-1., -3., 16., 7., -3.]]])
np.testing.assert_allclose(sys4.num, sys3.den)
np.testing.assert_allclose(sys4.den, sys3.num)
def test_div(self):
# Make sure that sampling times work correctly
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1], None)
sys2 = TransferFunction([[[-1., 3.]]], [[[1., 0., -1.]]], True)
sys3 = sys1 / sys2
assert sys3.dt is True
sys2 = TransferFunction([[[-1., 3.]]], [[[1., 0., -1.]]], 0.5)
sys3 = sys1 / sys2
assert sys3.dt == 0.5
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1], 0.1)
with pytest.raises(ValueError):
TransferFunction.__truediv__(sys1, sys2)
sys1 = sample_system(rss(4, 1, 1), 0.5)
sys3 = TransferFunction.__rtruediv__(sys2, sys1)
assert sys3.dt == 0.5
def test_pow(self):
sys1 = TransferFunction([1., 3., 5], [1., 6., 2., -1])
with pytest.raises(ValueError):
TransferFunction.__pow__(sys1, 0.5)
def test_slice(self):
sys = TransferFunction(
[ [ [1], [2], [3]], [ [3], [4], [5]] ],
[ [[1, 2], [1, 3], [1, 4]], [[1, 4], [1, 5], [1, 6]] ],
inputs=['u0', 'u1', 'u2'], outputs=['y0', 'y1'], name='sys')
sys1 = sys[1:, 1:]
assert (sys1.ninputs, sys1.noutputs) == (2, 1)
assert sys1.input_labels == ['u1', 'u2']
assert sys1.output_labels == ['y1']
assert sys1.name == 'sys$indexed'
sys2 = sys[:2, :2]
assert (sys2.ninputs, sys2.noutputs) == (2, 2)
assert sys2.input_labels == ['u0', 'u1']
assert sys2.output_labels == ['y0', 'y1']
assert sys2.name == 'sys$indexed'
sys = TransferFunction(
[ [ [1], [2], [3]], [ [3], [4], [5]] ],
[ [[1, 2], [1, 3], [1, 4]], [[1, 4], [1, 5], [1, 6]] ], 0.5)
sys1 = sys[1:, 1:]
assert (sys1.ninputs, sys1.noutputs) == (2, 1)
assert sys1.dt == 0.5
assert sys1.input_labels == ['u[1]', 'u[2]']
assert sys1.output_labels == ['y[1]']
assert sys1.name == sys.name + '$indexed'
def test__isstatic(self):
numstatic = 1.1
denstatic = 1.2
numdynamic = [1, 1]
dendynamic = [2, 1]
numstaticmimo = [[[1.1,], [1.2,]], [[1.2,], [0.8,]]]
denstaticmimo = [[[1.9,], [1.2,]], [[1.2,], [0.8,]]]
numdynamicmimo = [[[1.1, 0.9], [1.2]], [[1.2], [0.8]]]
dendynamicmimo = [[[1.1, 0.7], [0.2]], [[1.2], [0.8]]]
assert TransferFunction(numstatic, denstatic)._isstatic()
assert TransferFunction(numstaticmimo, denstaticmimo)._isstatic()
assert not TransferFunction(numstatic, dendynamic)._isstatic()
assert not TransferFunction(numdynamic, dendynamic)._isstatic()
assert not TransferFunction(numdynamic, denstatic)._isstatic()
assert not TransferFunction(numstatic, dendynamic)._isstatic()
assert not TransferFunction(numstaticmimo,
dendynamicmimo)._isstatic()
assert not TransferFunction(numdynamicmimo,
denstaticmimo)._isstatic()
@pytest.mark.parametrize("omega, resp",
[(1, np.array([[-0.5 - 0.5j]])),
(32, np.array([[0.002819593 - 0.03062847j]]))])
@pytest.mark.parametrize("dt", [None, 0, 1e-3])
def test_call_siso(self, dt, omega, resp):
"""Evaluate the frequency response of a SISO system at one frequency."""
sys = TransferFunction([1., 3., 5], [1., 6., 2., -1])
if dt:
sys = sample_system(sys, dt)
s = np.exp(omega * 1j * dt)
else:
s = omega * 1j
# Correct versions of the call
np.testing.assert_allclose(evalfr(sys, s), resp, atol=1e-3)
np.testing.assert_allclose(sys(s), resp, atol=1e-3)
# Deprecated version of the call (should generate exception)
with pytest.raises(AttributeError):
np.testing.assert_allclose(sys.evalfr(omega), resp, atol=1e-3)
def test_call_dtime(self):
sys = TransferFunction([1., 3., 5], [1., 6., 2., -1], 0.1)
np.testing.assert_array_almost_equal(sys(1j), -0.5 - 0.5j)
@slycotonly
def test_call_mimo(self):
"""Evaluate the frequency response of a MIMO system at one frequency."""
num = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
den = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
sys = TransferFunction(num, den)
resp = [[0.147058823529412 + 0.0882352941176471j, -0.75, 1.],
[-0.083333333333333, -0.188235294117647 - 0.847058823529412j,
-1. - 8.j]]
np.testing.assert_array_almost_equal(evalfr(sys, 2j), resp)
# Test call version as well
np.testing.assert_array_almost_equal(sys(2.j), resp)
def test_freqresp_deprecated(self):
sys = TransferFunction([1., 3., 5], [1., 6., 2., -1.])
# Deprecated version of the call (should generate warning)
with pytest.warns(DeprecationWarning):
sys.freqresp(1.)
def test_frequency_response_siso(self):
"""Evaluate the magnitude and phase of a SISO system at
multiple frequencies."""
sys = TransferFunction([1., 3., 5], [1., 6., 2., -1])
truemag = [[[4.63507337473906, 0.707106781186548, 0.0866592803995351]]]
truephase = [[[-2.89596891081488, -2.35619449019234,
-1.32655885133871]]]
trueomega = [0.1, 1., 10.]
mag, phase, omega = sys.frequency_response(trueomega, squeeze=False)
np.testing.assert_array_almost_equal(mag, truemag)
np.testing.assert_array_almost_equal(phase, truephase)
np.testing.assert_array_almost_equal(omega, trueomega)
@slycotonly
def test_freqresp_mimo(self):
"""Evaluate the MIMO magnitude and phase at multiple frequencies."""
num = [[[1., 2.], [0., 3.], [2., -1.]],
[[1.], [4., 0.], [1., -4., 3.]]]
den = [[[-3., 2., 4.], [1., 0., 0.], [2., -1.]],
[[3., 0., .0], [2., -1., -1.], [1.]]]
sys = TransferFunction(num, den)
true_omega = [0.1, 1., 10.]
true_mag = [[[0.49628709, 0.30714755, 0.03347381],
[300., 3., 0.03], [1., 1., 1.]],
[[33.333333, 0.33333333, 0.00333333],
[0.39028569, 1.26491106, 0.19875914],
[3.01663720, 4.47213595, 104.92378186]]]
true_phase = [[[3.7128711e-4, 0.18534794,
1.30770596], [-np.pi, -np.pi, -np.pi],
[0., 0., 0.]],
[[-np.pi, -np.pi, -np.pi],
[-1.66852323, -1.89254688, -1.62050658],
[-0.13298964, -1.10714871, -2.75046720]]]
mag, phase, omega = sys.frequency_response(true_omega)
np.testing.assert_array_almost_equal(mag, true_mag)
np.testing.assert_array_almost_equal(phase, true_phase)
np.testing.assert_allclose(omega, true_omega)
# Tests for TransferFunction.pole and TransferFunction.zero.
def test_common_den(self):
""" Test the helper function to compute common denomitators."""
# _common_den() computes the common denominator per input/column.
# The testing columns are:
# 0: no common poles
# 1: regular common poles
# 2: poles with multiplicity,
# 3: complex poles
# 4: complex poles below threshold
eps = np.finfo(float).eps
tol_imag = np.sqrt(eps*5*2*2)*0.9
numin = [[[1.], [1.], [1.], [1.], [1.]],
[[1.], [1.], [1.], [1.], [1.]]]
denin = [[[1., 3., 2.], # 0: poles: [-1, -2]
[1., 6., 11., 6.], # 1: poles: [-1, -2, -3]
[1., 6., 11., 6.], # 2: poles: [-1, -2, -3]
[1., 6., 11., 6.], # 3: poles: [-1, -2, -3]
[1., 6., 11., 6.]], # 4: poles: [-1, -2, -3],
[[1., 12., 47., 60.], # 0: poles: [-3, -4, -5]
[1., 9., 26., 24.], # 1: poles: [-2, -3, -4]
[1., 7., 16., 12.], # 2: poles: [-2, -2, -3]
[1., 7., 17., 15.], # 3: poles: [-2+1J, -2-1J, -3],
np.poly([-2 + tol_imag * 1J, -2 - tol_imag * 1J, -3])]]
numref = np.array([
[[0., 0., 1., 12., 47., 60.],
[0., 0., 0., 1., 4., 0.],
[0., 0., 0., 1., 2., 0.],
[0., 0., 0., 1., 4., 5.],
[0., 0., 0., 1., 2., 0.]],
[[0., 0., 0., 1., 3., 2.],
[0., 0., 0., 1., 1., 0.],
[0., 0., 0., 1., 1., 0.],
[0., 0., 0., 1., 3., 2.],
[0., 0., 0., 1., 1., 0.]]])
denref = np.array(
[[1., 15., 85., 225., 274., 120.],
[1., 10., 35., 50., 24., 0.],
[1., 8., 23., 28., 12., 0.],
[1., 10., 40., 80., 79., 30.],
[1., 8., 23., 28., 12., 0.]])
sys = TransferFunction(numin, denin)
num, den, denorder = sys._common_den()
np.testing.assert_array_almost_equal(num[:2, :, :], numref)
np.testing.assert_array_almost_equal(num[2:, :, :],
np.zeros((3, 5, 6)))
np.testing.assert_array_almost_equal(den, denref)
def test_common_den_nonproper(self):
""" Test _common_den with order(num)>order(den) """
tf1 = TransferFunction(
[[[1., 2., 3.]], [[1., 2.]]],
[[[1., -2.]], [[1., -3.]]])
tf2 = TransferFunction(
[[[1., 2.]], [[1., 2., 3.]]],
[[[1., -2.]], [[1., -3.]]])
common_den_ref = np.array([[1., -5., 6.]])
np.testing.assert_raises(ValueError, tf1._common_den)
np.testing.assert_raises(ValueError, tf2._common_den)
_, den1, _ = tf1._common_den(allow_nonproper=True)
np.testing.assert_array_almost_equal(den1, common_den_ref)
_, den2, _ = tf2._common_den(allow_nonproper=True)
np.testing.assert_array_almost_equal(den2, common_den_ref)
@slycotonly
def test_pole_mimo(self):
"""Test for correct MIMO poles."""
sys = TransferFunction(
[[[1.], [1.]], [[1.], [1.]]],
[[[1., 2.], [1., 3.]], [[1., 4., 4.], [1., 9., 14.]]])
p = sys.poles()
np.testing.assert_array_almost_equal(p, [-2., -2., -7., -3., -2.])
# non proper transfer function
sys2 = TransferFunction(
[[[1., 2., 3., 4.], [1.]], [[1.], [1.]]],
[[[1., 2.], [1., 3.]], [[1., 4., 4.], [1., 9., 14.]]])
p2 = sys2.poles()
np.testing.assert_array_almost_equal(p2, [-2., -2., -7., -3., -2.])
def test_double_cancelling_poles_siso(self):
H = TransferFunction([1, 1], [1, 2, 1])
p = H.poles()
np.testing.assert_array_almost_equal(p, [-1, -1])
# Tests for TransferFunction.feedback
def test_feedback_siso(self):
"""Test for correct SISO transfer function feedback."""
sys1 = TransferFunction([-1., 4.], [1., 3., 5.])
sys2 = TransferFunction([2., 3., 0.], [1., -3., 4., 0])
sys3 = sys1.feedback(sys2)
sys4 = sys1.feedback(sys2, 1)
np.testing.assert_allclose(sys3.num, [[[-1., 7., -16., 16., 0.]]])
np.testing.assert_allclose(sys3.den, [[[1., 0., -2., 2., 32., 0.]]])
np.testing.assert_allclose(sys4.num, [[[-1., 7., -16., 16., 0.]]])
np.testing.assert_allclose(sys4.den, [[[1., 0., 2., -8., 8., 0.]]])
@slycotonly
def test_convert_to_transfer_function(self):
"""Test for correct state space to transfer function conversion."""
A = [[1., -2.], [-3., 4.]]
B = [[6., 5.], [4., 3.]]
C = [[1., -2.], [3., -4.], [5., -6.]]
D = [[1., 0.], [0., 1.], [1., 0.]]
sys = StateSpace(A, B, C, D)
tfsys = _convert_to_transfer_function(sys)
num = [[np.array([1., -7., 10.]), np.array([-1., 10.])],
[np.array([2., -8.]), np.array([1., -2., -8.])],
[np.array([1., 1., -30.]), np.array([7., -22.])]]
den = [[np.array([1., -5., -2.]) for _ in range(sys.ninputs)]
for _ in range(sys.noutputs)]
for i in range(sys.noutputs):
for j in range(sys.ninputs):
np.testing.assert_array_almost_equal(tfsys.num[i][j],
num[i][j])
np.testing.assert_array_almost_equal(tfsys.den[i][j],
den[i][j])
def test_minreal(self):
"""Try the minreal function, and also test easy entry by creation
of a Laplace variable s"""
s = TransferFunction([1, 0], [1])
h = (s + 1) * (s + 2.00000000001) / (s + 2) / (s**2 + s + 1)
hm = h.minreal()
hr = (s + 1) / (s**2 + s + 1)
np.testing.assert_array_almost_equal(hm.num[0][0], hr.num[0][0])
np.testing.assert_array_almost_equal(hm.den[0][0], hr.den[0][0])
np.testing.assert_equal(hm.dt, hr.dt)
def test_minreal_2(self):
"""This one gave a problem, due to poly([]) giving simply 1
instead of numpy.array([1])"""
s = TransferFunction([1, 0], [1])
G = 6205/(s*(s**2 + 13*s + 1281))
Heq = G.feedback(1)
H1 = 1/(s+5)
H2a = Heq/H1
H2b = H2a.minreal()
hr = 6205/(s**2+8*s+1241)
np.testing.assert_array_almost_equal(H2b.num[0][0], hr.num[0][0])
np.testing.assert_array_almost_equal(H2b.den[0][0], hr.den[0][0])
np.testing.assert_equal(H2b.dt, hr.dt)
def test_minreal_3(self):
"""Regression test for minreal of tf([1,1],[1,1])"""
g = TransferFunction([1,1],[1,1]).minreal()
np.testing.assert_array_almost_equal(1.0, g.num[0][0])
np.testing.assert_array_almost_equal(1.0, g.den[0][0])
def test_minreal_4(self):
"""Check minreal on discrete TFs."""
T = 0.01
z = TransferFunction([1, 0], [1], T)
h = (z - 1.00000000001) * (z + 1.0000000001) / (z**2 - 1)
hm = h.minreal()
hr = TransferFunction([1], [1], T)
np.testing.assert_allclose(hm.num[0][0], hr.num[0][0])
np.testing.assert_allclose(hr.dt, hm.dt)
@slycotonly
def test_state_space_conversion_mimo(self):
"""Test conversion of a single input, two-output state-space
system against the same TF"""
s = TransferFunction([1, 0], [1])
b0 = 0.2
b1 = 0.1
b2 = 0.5
a0 = 2.3
a1 = 6.3
a2 = 3.6
a3 = 1.0
h = (b0 + b1*s + b2*s**2)/(a0 + a1*s + a2*s**2 + a3*s**3)
H = TransferFunction([[h.num[0][0]], [(h*s).num[0][0]]],
[[h.den[0][0]], [h.den[0][0]]])
sys = _convert_to_statespace(H)
H2 = _convert_to_transfer_function(sys)
np.testing.assert_array_almost_equal(H.num[0][0], H2.num[0][0])
np.testing.assert_array_almost_equal(H.den[0][0], H2.den[0][0])
np.testing.assert_array_almost_equal(H.num[1][0], H2.num[1][0])
np.testing.assert_array_almost_equal(H.den[1][0], H2.den[1][0])
@slycotonly
def test_indexing(self):
"""Test TF scalar indexing and slice"""
tm = ss2tf(rss(5, 3, 3))
# scalar indexing
sys01 = tm[0, 1]
np.testing.assert_array_almost_equal(sys01.num[0][0], tm.num[0][1])
np.testing.assert_array_almost_equal(sys01.den[0][0], tm.den[0][1])
# slice indexing
sys = tm[:2, 1:3]
np.testing.assert_array_almost_equal(sys.num[0][0], tm.num[0][1])
np.testing.assert_array_almost_equal(sys.den[0][0], tm.den[0][1])
np.testing.assert_array_almost_equal(sys.num[0][1], tm.num[0][2])
np.testing.assert_array_almost_equal(sys.den[0][1], tm.den[0][2])
np.testing.assert_array_almost_equal(sys.num[1][0], tm.num[1][1])
np.testing.assert_array_almost_equal(sys.den[1][0], tm.den[1][1])
np.testing.assert_array_almost_equal(sys.num[1][1], tm.num[1][2])
np.testing.assert_array_almost_equal(sys.den[1][1], tm.den[1][2])
@pytest.mark.parametrize("op", [
pytest.param('mul'),
pytest.param(
'matmul', marks=pytest.mark.skip(".__matmul__ not implemented")),
])
@pytest.mark.parametrize("X, ij",
[(np.array([[2., 0., ]]), 0),
(np.array([[0., 2., ]]), 1)])
def test_matrix_array_multiply(self, op, X, ij):
"""Test mulitplication of MIMO TF with matrix"""
# 2 inputs, 2 outputs with prime zeros so they do not cancel
n = 2
p = [3, 5, 7, 11, 13, 17, 19, 23]
H = TransferFunction(
[[np.poly(p[2 * i + j:2 * i + j + 1]) for j in range(n)]
for i in range(n)],
[[[1, -1]] * n] * n)
if op == 'matmul':
XH = X @ H
elif op == 'mul':
XH = X * H
else:
assert NotImplemented(f"unknown operator '{op}'")
XH = XH.minreal()
assert XH.ninputs == n
assert XH.noutputs == X.shape[0]
assert len(XH.num) == XH.noutputs
assert len(XH.den) == XH.noutputs
assert len(XH.num[0]) == n
assert len(XH.den[0]) == n
np.testing.assert_allclose(2. * H.num[ij][0], XH.num[0][0], rtol=1e-4)
np.testing.assert_allclose( H.den[ij][0], XH.den[0][0], rtol=1e-4)
np.testing.assert_allclose(2. * H.num[ij][1], XH.num[0][1], rtol=1e-4)
np.testing.assert_allclose( H.den[ij][1], XH.den[0][1], rtol=1e-4)
if op == 'matmul':
HXt = H @ X.T
elif op == 'mul':
HXt = H * X.T
else:
assert NotImplemented(f"unknown operator '{op}'")
HXt = HXt.minreal()
assert HXt.ninputs == X.T.shape[1]
assert HXt.noutputs == n
assert len(HXt.num) == n
assert len(HXt.den) == n
assert len(HXt.num[0]) == HXt.ninputs
assert len(HXt.den[0]) == HXt.ninputs
np.testing.assert_allclose(2. * H.num[0][ij], HXt.num[0][0], rtol=1e-4)
np.testing.assert_allclose( H.den[0][ij], HXt.den[0][0], rtol=1e-4)
np.testing.assert_allclose(2. * H.num[1][ij], HXt.num[1][0], rtol=1e-4)
np.testing.assert_allclose( H.den[1][ij], HXt.den[1][0], rtol=1e-4)
def test_dcgain_cont(self):
"""Test DC gain for continuous-time transfer functions"""
sys = TransferFunction(6, 3)
np.testing.assert_allclose(sys.dcgain(), 2)
sys2 = TransferFunction(6, [1, 3])
np.testing.assert_allclose(sys2.dcgain(), 2)
sys3 = TransferFunction(6, [1, 0])
np.testing.assert_equal(sys3.dcgain(), np.inf)
num = [[[15], [21], [33]], [[10], [14], [22]]]
den = [[[1, 3], [2, 3], [3, 3]], [[1, 5], [2, 7], [3, 11]]]
sys4 = TransferFunction(num, den)
expected = [[5, 7, 11], [2, 2, 2]]
np.testing.assert_allclose(sys4.dcgain(), expected)
def test_dcgain_discr(self):
"""Test DC gain for discrete-time transfer functions"""
# static gain
sys = TransferFunction(6, 3, True)
np.testing.assert_allclose(sys.dcgain(), 2)
# averaging filter
sys = TransferFunction(0.5, [1, -0.5], True)
np.testing.assert_almost_equal(sys.dcgain(), 1)
# differencer
sys = TransferFunction(1, [1, -1], True)
np.testing.assert_equal(sys.dcgain(), np.inf)
# differencer, with warning
sys = TransferFunction(1, [1, -1], True)
with pytest.warns() as record:
np.testing.assert_equal(
sys.dcgain(warn_infinite=True), np.inf)
assert len(record) == 2 # generates two RuntimeWarnings
assert record[0].category is RuntimeWarning
assert re.search("divide by zero", str(record[0].message))
assert record[1].category is RuntimeWarning
assert re.search("invalid value", str(record[1].message))
# summer
sys = TransferFunction([1, -1], [1], True)
np.testing.assert_allclose(sys.dcgain(), 0)
def test_ss2tf(self):
"""Test SISO ss2tf"""
A = np.array([[-4, -1], [-1, -4]])
B = np.array([[1], [3]])
C = np.array([[3, 1]])
D = 0
sys = ss2tf(A, B, C, D)
true_sys = TransferFunction([6., 14.], [1., 8., 15.])
np.testing.assert_almost_equal(sys.num, true_sys.num)
np.testing.assert_almost_equal(sys.den, true_sys.den)
def test_class_constants_s(self):
"""Make sure that the 's' variable is defined properly"""
s = TransferFunction.s
G = (s + 1)/(s**2 + 2*s + 1)
np.testing.assert_array_almost_equal(G.num, [[[1, 1]]])
np.testing.assert_array_almost_equal(G.den, [[[1, 2, 1]]])
assert isctime(G, strict=True)
def test_class_constants_z(self):
"""Make sure that the 'z' variable is defined properly"""
z = TransferFunction.z
G = (z + 1)/(z**2 + 2*z + 1)
np.testing.assert_array_almost_equal(G.num, [[[1, 1]]])
np.testing.assert_array_almost_equal(G.den, [[[1, 2, 1]]])
assert isdtime(G, strict=True)
def test_printing(self):
"""Print SISO"""
sys = ss2tf(rss(4, 1, 1))
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
# SISO, discrete time
sys = sample_system(sys, 1)
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
@pytest.mark.parametrize(
"args, output",
[(([0], [1]), "\n0\n-\n1\n"),
(([1.0001], [-1.1111]), "\n 1\n------\n-1.111\n"),
(([0, 1], [0, 1.]), "\n1\n-\n1\n"),
])
def test_printing_polynomial_const(self, args, output):
"""Test _tf_polynomial_to_string for constant systems"""
assert str(TransferFunction(*args)).partition('\n\n')[2] == output
@pytest.mark.parametrize(
"args, outputfmt",
[(([1, 0], [2, 1]),
"\n {var}\n-------\n2 {var} + 1\n{dtstring}"),
(([2, 0, -1], [1, 0, 0, 1.2]),
"\n2 {var}^2 - 1\n---------\n{var}^3 + 1.2\n{dtstring}")])
@pytest.mark.parametrize("var, dt, dtstring",
[("s", None, ''),
("z", True, ''),
("z", 1, '\ndt = 1\n')])
def test_printing_polynomial(self, args, outputfmt, var, dt, dtstring):
"""Test _tf_polynomial_to_string for all other code branches"""
assert str(TransferFunction(*(args + (dt,)))).partition('\n\n')[2] == \
outputfmt.format(var=var, dtstring=dtstring)
@slycotonly
def test_printing_mimo(self):
"""Print MIMO, continuous time"""
sys = ss2tf(rss(4, 2, 3))
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
@pytest.mark.parametrize(
"zeros, poles, gain, output",
[([0], [-1], 1,
'\n'
' s\n'
'-----\n'
's + 1\n'),
([-1], [-1], 1,
'\n'
's + 1\n'
'-----\n'
's + 1\n'),
([-1], [1], 1,
'\n'
's + 1\n'
'-----\n'
's - 1\n'),
([1], [-1], 1,
'\n'
's - 1\n'
'-----\n'
's + 1\n'),
([-1], [-1], 2,
'\n'
'2 (s + 1)\n'
'---------\n'
' s + 1\n'),
([-1], [-1], 0,
'\n'
'0\n'
'-\n'
'1\n'),
([-1], [1j, -1j], 1,
'\n'
' s + 1\n'
'-----------------\n'
'(s - 1j) (s + 1j)\n'),
([4j, -4j], [2j, -2j], 2,
'\n'
'2 (s - 4j) (s + 4j)\n'
'-------------------\n'
' (s - 2j) (s + 2j)\n'),
([1j, -1j], [-1, -4], 2,
'\n'
'2 (s - 1j) (s + 1j)\n'
'-------------------\n'
' (s + 1) (s + 4)\n'),
([1], [-1 + 1j, -1 - 1j], 1,
'\n'
' s - 1\n'
'-------------------------\n'
'(s + (1-1j)) (s + (1+1j))\n'),
([1], [1 + 1j, 1 - 1j], 1,
'\n'
' s - 1\n'
'-------------------------\n'
'(s - (1+1j)) (s - (1-1j))\n'),
])
def test_printing_zpk(self, zeros, poles, gain, output):
"""Test _tf_polynomial_to_string for constant systems"""
G = zpk(zeros, poles, gain, display_format='zpk')
res = str(G)
assert res.partition('\n\n')[2] == output
@pytest.mark.parametrize(
"zeros, poles, gain, format, output",
[([1], [1 + 1j, 1 - 1j], 1, ".2f",
'\n'
' 1.00\n'
'-------------------------------------\n'
'(s + (1.00-1.41j)) (s + (1.00+1.41j))\n'),
([1], [1 + 1j, 1 - 1j], 1, ".3f",
'\n'
' 1.000\n'
'-----------------------------------------\n'
'(s + (1.000-1.414j)) (s + (1.000+1.414j))\n'),
([1], [1 + 1j, 1 - 1j], 1, ".6g",
'\n'