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"""discrete_test.py - test discrete-time classes
RMM, 9 Sep 2012
"""
import numpy as np
import pytest
import cmath
import control as ct
from control import StateSpace, TransferFunction, bode, common_timebase, \
feedback, forced_response, impulse_response, isctime, isdtime, rss, \
c2d, sample_system, step_response, timebase
class TestDiscrete:
"""Tests for the system classes with discrete timebase."""
@pytest.fixture
def tsys(self):
"""Create some systems for testing"""
class Tsys:
pass
T = Tsys()
# Single input, single output continuous and discrete-time systems
sys = rss(3, 1, 1)
T.siso_ss1 = StateSpace(sys.A, sys.B, sys.C, sys.D, None)
T.siso_ss1c = StateSpace(sys.A, sys.B, sys.C, sys.D, 0.0)
dsys = ct.sample_system(sys, 1)
T.siso_ss1d = StateSpace(dsys.A, dsys.B, dsys.C, dsys.D, 0.1)
T.siso_ss2d = StateSpace(dsys.A, dsys.B, dsys.C, dsys.D, 0.2)
T.siso_ss3d = StateSpace(dsys.A, dsys.B, dsys.C, dsys.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.]]
T.mimo_ss1 = StateSpace(A, B, C, D, None)
T.mimo_ss1c = StateSpace(A, B, C, D, 0)
# Two input, two output discrete-time system
T.mimo_ss1d = ct.sample_system(T.mimo_ss1c, 0.1)
# Same system, but with a different sampling time
T.mimo_ss2d = StateSpace(
T.mimo_ss1d.A, T.mimo_ss1d.B, T.mimo_ss1d.C, T.mimo_ss1d.D, 0.2)
# Single input, single output continuus and discrete transfer function
T.siso_tf1 = TransferFunction([1, 1], [1, 2, 1], None)
T.siso_tf1c = TransferFunction([1, 1], [1, 0.2, 1], 0)
T.siso_tf1d = TransferFunction([1, 1], [1, 0.2, 0.1], 0.1)
T.siso_tf2d = TransferFunction([1, 1], [1, 0.2, 0.1], 0.2)
T.siso_tf3d = TransferFunction([1, 1], [1, 0.2, 0.1], True)
return T
def testCompatibleTimebases(self, tsys):
"""test that compatible timebases don't throw errors and vice versa"""
common_timebase(tsys.siso_ss1.dt, tsys.siso_tf1.dt)
common_timebase(tsys.siso_ss1.dt, tsys.siso_ss1c.dt)
common_timebase(tsys.siso_ss1d.dt, tsys.siso_ss1.dt)
common_timebase(tsys.siso_ss1.dt, tsys.siso_ss1d.dt)
common_timebase(tsys.siso_ss1.dt, tsys.siso_ss1d.dt)
common_timebase(tsys.siso_ss1d.dt, tsys.siso_ss3d.dt)
common_timebase(tsys.siso_ss3d.dt, tsys.siso_ss1d.dt)
with pytest.raises(ValueError):
# cont + discrete
common_timebase(tsys.siso_ss1d.dt, tsys.siso_ss1c.dt)
with pytest.raises(ValueError):
# incompatible discrete
common_timebase(tsys.siso_ss1d.dt, tsys.siso_ss2d.dt)
def testSystemInitialization(self, tsys):
# Check to make sure systems are discrete time with proper variables
assert tsys.siso_ss1.dt is None
assert tsys.siso_ss1c.dt == 0
assert tsys.siso_ss1d.dt == 0.1
assert tsys.siso_ss2d.dt == 0.2
assert tsys.siso_ss3d.dt is True
assert tsys.mimo_ss1c.dt == 0
assert tsys.mimo_ss1d.dt == 0.1
assert tsys.mimo_ss2d.dt == 0.2
assert tsys.siso_tf1.dt is None
assert tsys.siso_tf1c.dt == 0
assert tsys.siso_tf1d.dt == 0.1
assert tsys.siso_tf2d.dt == 0.2
assert tsys.siso_tf3d.dt is True
# keyword argument check
# dynamic systems
assert TransferFunction(1, [1, 1], dt=0.1).dt == 0.1
assert TransferFunction(1, [1, 1], 0.1).dt == 0.1
assert StateSpace(1,1,1,1, dt=0.1).dt == 0.1
assert StateSpace(1,1,1,1, 0.1).dt == 0.1
# static gain system, dt argument should still override default dt
assert TransferFunction(1, [1,], dt=0.1).dt == 0.1
assert TransferFunction(1, [1,], 0.1).dt == 0.1
assert StateSpace(0,0,1,1, dt=0.1).dt == 0.1
assert StateSpace(0,0,1,1, 0.1).dt == 0.1
def testCopyConstructor(self, tsys):
for sys in (tsys.siso_ss1, tsys.siso_ss1c, tsys.siso_ss1d):
newsys = StateSpace(sys)
assert sys.dt == newsys.dt
for sys in (tsys.siso_tf1, tsys.siso_tf1c, tsys.siso_tf1d):
newsys = TransferFunction(sys)
assert sys.dt == newsys.dt
def test_timebase(self, tsys):
assert timebase(1) is None
with pytest.raises(ValueError):
timebase([1, 2])
assert timebase(tsys.siso_ss1, strict=False) is None
assert timebase(tsys.siso_ss1, strict=True) is None
assert timebase(tsys.siso_ss1c) == 0
assert timebase(tsys.siso_ss1d) == 0.1
assert timebase(tsys.siso_ss2d) == 0.2
assert timebase(tsys.siso_ss3d)
assert timebase(tsys.siso_ss3d, strict=False) == 1
assert timebase(tsys.siso_tf1, strict=False) is None
assert timebase(tsys.siso_tf1, strict=True) is None
assert timebase(tsys.siso_tf1c) == 0
assert timebase(tsys.siso_tf1d) == 0.1
assert timebase(tsys.siso_tf2d) == 0.2
assert timebase(tsys.siso_tf3d)
assert timebase(tsys.siso_tf3d, strict=False) == 1
def test_timebase_conversions(self, tsys):
'''Check to make sure timebases transfer properly'''
tf1 = TransferFunction([1, 1], [1, 2, 3], None) # 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
assert timebase(tf1*tf1) == timebase(tf1)
assert timebase(tf1*tf2) == timebase(tf2)
assert timebase(tf1*tf3) == timebase(tf3)
assert timebase(tf1*tf4) == timebase(tf4)
assert timebase(tf3*tf4) == timebase(tf4)
assert timebase(tf2*tf1) == timebase(tf2)
assert timebase(tf3*tf1) == timebase(tf3)
assert timebase(tf4*tf1) == timebase(tf4)
assert timebase(tf1+tf1) == timebase(tf1)
assert timebase(tf1+tf2) == timebase(tf2)
assert timebase(tf1+tf3) == timebase(tf3)
assert timebase(tf1+tf4) == timebase(tf4)
assert timebase(feedback(tf1, tf1)) == timebase(tf1)
assert timebase(feedback(tf1, tf2)) == timebase(tf2)
assert timebase(feedback(tf1, tf3)) == timebase(tf3)
assert timebase(feedback(tf1, tf4)) == timebase(tf4)
# Make sure discrete time without sampling is converted correctly
assert timebase(tf3*tf3) == timebase(tf3)
assert timebase(tf3*tf4) == timebase(tf4)
assert timebase(tf3+tf3) == timebase(tf3)
assert timebase(tf3+tf4) == timebase(tf4)
assert timebase(feedback(tf3, tf3)) == timebase(tf3)
assert timebase(feedback(tf3, tf4)) == timebase(tf4)
# Make sure all other combinations are errors
with pytest.raises(ValueError, match="incompatible timebases"):
tf2 * tf3
with pytest.raises(ValueError, match="incompatible timebases"):
tf3 * tf2
with pytest.raises(ValueError, match="incompatible timebases"):
tf2 * tf4
with pytest.raises(ValueError, match="incompatible timebases"):
tf4 * tf2
with pytest.raises(ValueError, match="incompatible timebases"):
tf2 + tf3
with pytest.raises(ValueError, match="incompatible timebases"):
tf3 + tf2
with pytest.raises(ValueError, match="incompatible timebases"):
tf2 + tf4
with pytest.raises(ValueError, match="incompatible timebases"):
tf4 + tf2
with pytest.raises(ValueError, match="incompatible timebases"):
feedback(tf2, tf3)
with pytest.raises(ValueError, match="incompatible timebases"):
feedback(tf3, tf2)
with pytest.raises(ValueError, match="incompatible timebases"):
feedback(tf2, tf4)
with pytest.raises(ValueError, match="incompatible timebases"):
feedback(tf4, tf2)
def testisdtime(self, tsys):
# Constant
assert isdtime(1)
assert not isdtime(1, strict=True)
# State space
assert isdtime(tsys.siso_ss1)
assert not isdtime(tsys.siso_ss1, strict=True)
assert not isdtime(tsys.siso_ss1c)
assert not isdtime(tsys.siso_ss1c, strict=True)
assert isdtime(tsys.siso_ss1d)
assert isdtime(tsys.siso_ss1d, strict=True)
assert isdtime(tsys.siso_ss3d, strict=True)
# Transfer function
assert isdtime(tsys.siso_tf1)
assert not isdtime(tsys.siso_tf1, strict=True)
assert not isdtime(tsys.siso_tf1c)
assert not isdtime(tsys.siso_tf1c, strict=True)
assert isdtime(tsys.siso_tf1d)
assert isdtime(tsys.siso_tf1d, strict=True)
assert isdtime(tsys.siso_tf3d, strict=True)
def testisctime(self, tsys):
# Constant
assert isctime(1)
assert not isctime(1, strict=True)
# State Space
assert isctime(tsys.siso_ss1)
assert not isctime(tsys.siso_ss1, strict=True)
assert isctime(tsys.siso_ss1c)
assert isctime(tsys.siso_ss1c, strict=True)
assert not isctime(tsys.siso_ss1d)
assert not isctime(tsys.siso_ss1d, strict=True)
assert not isctime(tsys.siso_ss3d, strict=True)
# Transfer Function
assert isctime(tsys.siso_tf1)
assert not isctime(tsys.siso_tf1, strict=True)
assert isctime(tsys.siso_tf1c)
assert isctime(tsys.siso_tf1c, strict=True)
assert not isctime(tsys.siso_tf1d)
assert not isctime(tsys.siso_tf1d, strict=True)
assert not isctime(tsys.siso_tf3d, strict=True)
def testAddition(self, tsys):
# State space addition
_sys = tsys.siso_ss1 + tsys.siso_ss1d
_sys = tsys.siso_ss1 + tsys.siso_ss1c
_sys = tsys.siso_ss1c + tsys.siso_ss1
_sys = tsys.siso_ss1d + tsys.siso_ss1
_sys = tsys.siso_ss1c + tsys.siso_ss1c
_sys = tsys.siso_ss1d + tsys.siso_ss1d
_sys = tsys.siso_ss3d + tsys.siso_ss3d
_sys = tsys.siso_ss1d + tsys.siso_ss3d
with pytest.raises(ValueError):
StateSpace.__add__(tsys.mimo_ss1c, tsys.mimo_ss1d)
with pytest.raises(ValueError):
StateSpace.__add__(tsys.mimo_ss1d, tsys.mimo_ss2d)
# Transfer function addition
_sys = tsys.siso_tf1 + tsys.siso_tf1d
_sys = tsys.siso_tf1 + tsys.siso_tf1c
_sys = tsys.siso_tf1c + tsys.siso_tf1
_sys = tsys.siso_tf1d + tsys.siso_tf1
_sys = tsys.siso_tf1c + tsys.siso_tf1c
_sys = tsys.siso_tf1d + tsys.siso_tf1d
_sys = tsys.siso_tf2d + tsys.siso_tf2d
_sys = tsys.siso_tf1d + tsys.siso_tf3d
with pytest.raises(ValueError):
TransferFunction.__add__(tsys.siso_tf1c, tsys.siso_tf1d)
with pytest.raises(ValueError):
TransferFunction.__add__(tsys.siso_tf1d, tsys.siso_tf2d)
# State space + transfer function
_sys = tsys.siso_ss1c + tsys.siso_tf1c
_sys = tsys.siso_tf1c + tsys.siso_ss1c
_sys = tsys.siso_ss1d + tsys.siso_tf1d
_sys = tsys.siso_tf1d + tsys.siso_ss1d
with pytest.raises(ValueError):
TransferFunction.__add__(tsys.siso_tf1c, tsys.siso_ss1d)
def testMultiplication(self, tsys):
# State space multiplication
_sys = tsys.siso_ss1 * tsys.siso_ss1d
_sys = tsys.siso_ss1 * tsys.siso_ss1c
_sys = tsys.siso_ss1c * tsys.siso_ss1
_sys = tsys.siso_ss1d * tsys.siso_ss1
_sys = tsys.siso_ss1c * tsys.siso_ss1c
_sys = tsys.siso_ss1d * tsys.siso_ss1d
_sys = tsys.siso_ss1d * tsys.siso_ss3d
with pytest.raises(ValueError):
StateSpace.__mul__(tsys.mimo_ss1c, tsys.mimo_ss1d)
with pytest.raises(ValueError):
StateSpace.__mul__(tsys.mimo_ss1d, tsys.mimo_ss2d)
# Transfer function multiplication
_sys = tsys.siso_tf1 * tsys.siso_tf1d
_sys = tsys.siso_tf1 * tsys.siso_tf1c
_sys = tsys.siso_tf1c * tsys.siso_tf1
_sys = tsys.siso_tf1d * tsys.siso_tf1
_sys = tsys.siso_tf1c * tsys.siso_tf1c
_sys = tsys.siso_tf1d * tsys.siso_tf1d
_sys = tsys.siso_tf1d * tsys.siso_tf3d
with pytest.raises(ValueError):
TransferFunction.__mul__(tsys.siso_tf1c, tsys.siso_tf1d)
with pytest.raises(ValueError):
TransferFunction.__mul__(tsys.siso_tf1d, tsys.siso_tf2d)
# State space * transfer function
_sys = tsys.siso_ss1c * tsys.siso_tf1c
_sys = tsys.siso_tf1c * tsys.siso_ss1c
_sys = tsys.siso_ss1d * tsys.siso_tf1d
_sys = tsys.siso_tf1d * tsys.siso_ss1d
with pytest.raises(ValueError):
TransferFunction.__mul__(tsys.siso_tf1c,
tsys.siso_ss1d)
def testFeedback(self, tsys):
# State space feedback
_sys = feedback(tsys.siso_ss1, tsys.siso_ss1d)
_sys = feedback(tsys.siso_ss1, tsys.siso_ss1c)
_sys = feedback(tsys.siso_ss1c, tsys.siso_ss1)
_sys = feedback(tsys.siso_ss1d, tsys.siso_ss1)
_sys = feedback(tsys.siso_ss1c, tsys.siso_ss1c)
_sys = feedback(tsys.siso_ss1d, tsys.siso_ss1d)
_sys = feedback(tsys.siso_ss1d, tsys.siso_ss3d)
with pytest.raises(ValueError):
feedback(tsys.mimo_ss1c, tsys.mimo_ss1d)
with pytest.raises(ValueError):
feedback(tsys.mimo_ss1d, tsys.mimo_ss2d)
# Transfer function feedback
_sys = feedback(tsys.siso_tf1, tsys.siso_tf1d)
_sys = feedback(tsys.siso_tf1, tsys.siso_tf1c)
_sys = feedback(tsys.siso_tf1c, tsys.siso_tf1)
_sys = feedback(tsys.siso_tf1d, tsys.siso_tf1)
_sys = feedback(tsys.siso_tf1c, tsys.siso_tf1c)
_sys = feedback(tsys.siso_tf1d, tsys.siso_tf1d)
_sys = feedback(tsys.siso_tf1d, tsys.siso_tf3d)
with pytest.raises(ValueError):
feedback(tsys.siso_tf1c, tsys.siso_tf1d)
with pytest.raises(ValueError):
feedback(tsys.siso_tf1d, tsys.siso_tf2d)
# State space, transfer function
_sys = feedback(tsys.siso_ss1c, tsys.siso_tf1c)
_sys = feedback(tsys.siso_tf1c, tsys.siso_ss1c)
_sys = feedback(tsys.siso_ss1d, tsys.siso_tf1d)
_sys = feedback(tsys.siso_tf1d, tsys.siso_ss1d)
with pytest.raises(ValueError):
feedback(tsys.siso_tf1c, tsys.siso_ss1d)
def testSimulation(self, tsys):
T = range(100)
U = np.sin(T)
# For now, just check calling syntax
# TODO: add checks on output of simulations
tout, yout = step_response(tsys.siso_ss1d)
tout, yout = step_response(tsys.siso_ss1d, T)
tout, yout = impulse_response(tsys.siso_ss1d)
tout, yout = impulse_response(tsys.siso_ss1d, T)
tout, yout = forced_response(tsys.siso_ss1d, T, U, 0)
tout, yout = forced_response(tsys.siso_ss2d, T, U, 0)
tout, yout = forced_response(tsys.siso_ss3d, T, U, 0)
tout, yout, xout = forced_response(tsys.siso_ss1d, T, U, 0,
return_x=True)
def test_sample_system(self, tsys):
# Make sure we can convert various types of systems
for sysc in (tsys.siso_tf1, tsys.siso_tf1c,
tsys.siso_ss1, tsys.siso_ss1c,
tsys.mimo_ss1, tsys.mimo_ss1c):
for method in ("zoh", "bilinear", "euler", "backward_diff"):
sysd = sample_system(sysc, 1, method=method)
assert sysd.dt == 1
# Check "matched", defined only for SISO transfer functions
for sysc in (tsys.siso_tf1, tsys.siso_tf1c):
sysd = sample_system(sysc, 1, method="matched")
assert sysd.dt == 1
@pytest.mark.parametrize("plantname",
["siso_ss1c",
"siso_tf1c"])
@pytest.mark.parametrize("wwarp",
[.1, 1, 3])
@pytest.mark.parametrize("Ts",
[.1, 1])
@pytest.mark.parametrize("discretization_type",
['bilinear', 'tustin', 'gbt'])
def test_sample_system_prewarp(self, tsys, plantname, discretization_type, wwarp, Ts):
"""bilinear approximation with prewarping test"""
# test state space version
plant = getattr(tsys, plantname)
plant_fr = plant(wwarp * 1j)
alpha = 0.5 if discretization_type == 'gbt' else None
plant_d_warped = plant.sample(Ts, discretization_type,
prewarp_frequency=wwarp, alpha=alpha)
dt = plant_d_warped.dt
plant_d_fr = plant_d_warped(np.exp(wwarp * 1.j * dt))
np.testing.assert_array_almost_equal(plant_fr, plant_d_fr)
plant_d_warped = sample_system(plant, Ts, discretization_type,
prewarp_frequency=wwarp, alpha=alpha)
plant_d_fr = plant_d_warped(np.exp(wwarp * 1.j * dt))
np.testing.assert_array_almost_equal(plant_fr, plant_d_fr)
plant_d_warped = c2d(plant, Ts, discretization_type,
prewarp_frequency=wwarp, alpha=alpha)
plant_d_fr = plant_d_warped(np.exp(wwarp * 1.j * dt))
np.testing.assert_array_almost_equal(plant_fr, plant_d_fr)
@pytest.mark.parametrize("plantname",
["siso_ss1c",
"siso_tf1c"])
@pytest.mark.parametrize("discretization_type",
['euler', 'backward_diff', 'zoh'])
def test_sample_system_prewarp_warning(self, tsys, plantname, discretization_type):
plant = getattr(tsys, plantname)
wwarp = 1
Ts = 0.1
with pytest.warns(UserWarning, match="prewarp_frequency ignored: incompatible conversion"):
plant.sample(Ts, discretization_type, prewarp_frequency=wwarp)
with pytest.warns(UserWarning, match="prewarp_frequency ignored: incompatible conversion"):
sample_system(plant, Ts, discretization_type, prewarp_frequency=wwarp)
with pytest.warns(UserWarning, match="prewarp_frequency ignored: incompatible conversion"):
c2d(plant, Ts, discretization_type, prewarp_frequency=wwarp)
def test_sample_system_errors(self, tsys):
# Check errors
with pytest.raises(ValueError):
sample_system(tsys.siso_ss1d, 1)
with pytest.raises(ValueError):
sample_system(tsys.siso_tf1d, 1)
with pytest.raises(ValueError):
sample_system(tsys.siso_ss1, 1, 'unknown')
def test_sample_ss(self, tsys):
# 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)
assert sysd.dt == h
def test_sample_tf(self, tsys):
# 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')
assert 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)
@pytest.mark.usefixtures("legacy_plot_signature")
def test_discrete_bode(self, tsys):
# 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, plot=True)
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 test_signal_names(self, tsys):
"test that signal names are preserved in conversion to discrete time"
ssc = StateSpace(tsys.siso_ss1c,
inputs='u', outputs='y', states=['a', 'b', 'c'])
ssd = ssc.sample(0.1)
tfc = TransferFunction(tsys.siso_tf1c, inputs='u', outputs='y')
tfd = tfc.sample(0.1)
assert ssd.input_labels == ['u']
assert ssd.state_labels == ['a', 'b', 'c']
assert ssd.output_labels == ['y']
assert tfd.input_labels == ['u']
assert tfd.output_labels == ['y']
ssd = sample_system(ssc, 0.1)
tfd = sample_system(tfc, 0.1)
assert ssd.input_labels == ['u']
assert ssd.state_labels == ['a', 'b', 'c']
assert ssd.output_labels == ['y']
assert tfd.input_labels == ['u']
assert tfd.output_labels == ['y']
# system names and signal name override
sysc = StateSpace(1.1, 1, 1, 1, inputs='u', outputs='y', states='a')
sysd = sample_system(sysc, 0.1, name='sampled')
assert sysd.name == 'sampled'
assert sysd.find_input('u') == 0
assert sysd.find_output('y') == 0
assert sysd.find_state('a') == 0
# If we copy signal names w/out a system name, append '$sampled'
sysd = sample_system(sysc, 0.1)
assert sysd.name == sysc.name + '$sampled'
# If copy is False, signal names should not be copied
sysd_nocopy = sample_system(sysc, 0.1, copy_names=False)
assert sysd_nocopy.find_input('u') is None
assert sysd_nocopy.find_output('y') is None
assert sysd_nocopy.find_state('a') is None
# if signal names are provided, they should override those of sysc
sysd_newnames = sample_system(sysc, 0.1,
inputs='v', outputs='x', states='b')
assert sysd_newnames.find_input('v') == 0
assert sysd_newnames.find_input('u') is None
assert sysd_newnames.find_output('x') == 0
assert sysd_newnames.find_output('y') is None
assert sysd_newnames.find_state('b') == 0
assert sysd_newnames.find_state('a') is None
# test just one name
sysd_newnames = sample_system(sysc, 0.1, inputs='v')
assert sysd_newnames.find_input('v') == 0
assert sysd_newnames.find_input('u') is None
assert sysd_newnames.find_output('y') == 0
assert sysd_newnames.find_output('x') is None
@pytest.mark.parametrize("num, den", [
([1], [1, 1]),
([1, 2], [1, 3]),
([1, 2], [3, 4, 5])
])
@pytest.mark.parametrize("dt", [True, 0.1, 2])
@pytest.mark.parametrize("method", ['zoh', 'bilinear', 'matched'])
def test_c2d_matched(num, den, dt, method):
sys_ct = ct.tf(num, den)
sys_dt = ct.sample_system(sys_ct, dt, method=method)
assert sys_dt.dt == dt # make sure sampling time is OK
assert cmath.isclose(sys_ct(0), sys_dt(1)) # check zero frequency gain
assert cmath.isclose(
sys_ct.dcgain(), sys_dt.dcgain()) # another way to check
if method in ['zoh', 'matched']:
# Make sure that poles were properly matched
zpoles = sys_dt.poles()
for cpole in sys_ct.poles():
zpole = zpoles[(np.abs(zpoles - cmath.exp(cpole * dt))).argmin()]
assert cmath.isclose(cmath.exp(cpole * dt), zpole)
if method in ['matched']:
# Make sure that zeros were properly matched
zzeros = sys_dt.zeros()
for czero in sys_ct.zeros():
zzero = zzeros[(np.abs(zzeros - cmath.exp(czero * dt))).argmin()]
assert cmath.isclose(cmath.exp(czero * dt), zzero)
@pytest.mark.parametrize("num, den", [
([1.], [1., 0.]), # integrator (pole at s = 0)
([1.], [1., 0., 0.]), # double integrator
([2., 5.], [1., 0.]), # PI controller
([1.], [1., 1., 0.]), # type 1 plant, 1/(s(s+1))
([1., 0.], [1., 2., 5.]), # differentiator (zero at s = 0)
([2., 0., 0.], [1., 3., 3., 1.]), # double zero at s = 0
([1., 0.], [1., 0., 0.]), # zero and pole at s = 0
])
@pytest.mark.parametrize("dt", [0.1, 0.5])
def test_c2d_matched_origin(num, den, dt):
# A pole or zero at s = 0 (integrators, PI/PID, type-1/2 plants) used to
# give an all-NaN numerator: the DC-gain match divides by the vanishing
# 1 - z factor of the origin pole/zero (#950, #951).
sys_ct = ct.tf(num, den)
sys_dt = ct.sample_system(sys_ct, dt, method='matched')
assert np.all(np.isfinite(sys_dt.num[0][0]))
assert np.all(np.isfinite(sys_dt.den[0][0]))
# the gain is matched just off the origin, so |G_d(e^jwT)| -> |G_c(jw)|
w = 1e-3 / dt
assert np.isclose(abs(sys_ct(1j * w)),
abs(sys_dt(cmath.exp(1j * w * dt))), rtol=1e-4)
@pytest.mark.parametrize("dt", [0.1, 0.5, 2])
@pytest.mark.parametrize("k", [1, 2, 3])
def test_c2d_matched_integrator(k, dt):
# matched discretization of 1/s**k is the textbook Ts**k / (z - 1)**k
sys_dt = ct.tf([1.], [1.] + [0.] * k).sample(dt, method='matched')
np.testing.assert_allclose(sys_dt.num[0][0], [dt**k])
np.testing.assert_allclose(sys_dt.den[0][0], np.poly([1.] * k))