456 lines
16 KiB
Python
456 lines
16 KiB
Python
|
from __future__ import division, print_function, absolute_import
|
||
|
|
|
||
|
|
import numpy as np
|
||
|
|
from numpy.testing import \
|
||
|
|
assert_array_almost_equal, assert_almost_equal, \
|
||
|
|
assert_allclose, assert_equal
|
||
|
|
|
||
|
|
import pytest
|
||
|
|
from scipy.signal import cont2discrete as c2d
|
||
|
|
from scipy.signal import dlsim, ss2tf, ss2zpk, lsim2, lti
|
||
|
|
from scipy.signal import tf2ss, impulse2, dimpulse, step2, dstep
|
||
|
|
|
||
|
|
# Author: Jeffrey Armstrong <jeff@approximatrix.com>
|
||
|
|
# March 29, 2011
|
||
|
|
|
||
|
|
|
||
|
|
class TestC2D(object):
|
||
|
|
def test_zoh(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
ad_truth = 1.648721270700128 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.324360635350064)
|
||
|
|
# c and d in discrete should be equal to their continuous counterparts
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='zoh')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cc, cd)
|
||
|
|
assert_array_almost_equal(dc, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_foh(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
# True values are verified with Matlab
|
||
|
|
ad_truth = 1.648721270700128 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.420839287058789)
|
||
|
|
cd_truth = cc
|
||
|
|
dd_truth = np.array([[0.260262223725224],
|
||
|
|
[0.297442541400256],
|
||
|
|
[-0.144098411624840]])
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested, method='foh')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_impulse(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [0.0]])
|
||
|
|
|
||
|
|
# True values are verified with Matlab
|
||
|
|
ad_truth = 1.648721270700128 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.412180317675032)
|
||
|
|
cd_truth = cc
|
||
|
|
dd_truth = np.array([[0.4375], [0.5], [0.3125]])
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='impulse')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_gbt(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
alpha = 1.0 / 3.0
|
||
|
|
|
||
|
|
ad_truth = 1.6 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.3)
|
||
|
|
cd_truth = np.array([[0.9, 1.2],
|
||
|
|
[1.2, 1.2],
|
||
|
|
[1.2, 0.3]])
|
||
|
|
dd_truth = np.array([[0.175],
|
||
|
|
[0.2],
|
||
|
|
[-0.205]])
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='gbt', alpha=alpha)
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
|
||
|
|
def test_euler(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad_truth = 1.5 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.25)
|
||
|
|
cd_truth = np.array([[0.75, 1.0],
|
||
|
|
[1.0, 1.0],
|
||
|
|
[1.0, 0.25]])
|
||
|
|
dd_truth = dc
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='euler')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_backward_diff(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad_truth = 2.0 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.5)
|
||
|
|
cd_truth = np.array([[1.5, 2.0],
|
||
|
|
[2.0, 2.0],
|
||
|
|
[2.0, 0.5]])
|
||
|
|
dd_truth = np.array([[0.875],
|
||
|
|
[1.0],
|
||
|
|
[0.295]])
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='backward_diff')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
|
||
|
|
def test_bilinear(self):
|
||
|
|
ac = np.eye(2)
|
||
|
|
bc = np.full((2, 1), 0.5)
|
||
|
|
cc = np.array([[0.75, 1.0], [1.0, 1.0], [1.0, 0.25]])
|
||
|
|
dc = np.array([[0.0], [0.0], [-0.33]])
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
ad_truth = (5.0 / 3.0) * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 1.0 / 3.0)
|
||
|
|
cd_truth = np.array([[1.0, 4.0 / 3.0],
|
||
|
|
[4.0 / 3.0, 4.0 / 3.0],
|
||
|
|
[4.0 / 3.0, 1.0 / 3.0]])
|
||
|
|
dd_truth = np.array([[0.291666666666667],
|
||
|
|
[1.0 / 3.0],
|
||
|
|
[-0.121666666666667]])
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='bilinear')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
# Same continuous system again, but change sampling rate
|
||
|
|
|
||
|
|
ad_truth = 1.4 * np.eye(2)
|
||
|
|
bd_truth = np.full((2, 1), 0.2)
|
||
|
|
cd_truth = np.array([[0.9, 1.2], [1.2, 1.2], [1.2, 0.3]])
|
||
|
|
dd_truth = np.array([[0.175], [0.2], [-0.205]])
|
||
|
|
|
||
|
|
dt_requested = 1.0 / 3.0
|
||
|
|
|
||
|
|
ad, bd, cd, dd, dt = c2d((ac, bc, cc, dc), dt_requested,
|
||
|
|
method='bilinear')
|
||
|
|
|
||
|
|
assert_array_almost_equal(ad_truth, ad)
|
||
|
|
assert_array_almost_equal(bd_truth, bd)
|
||
|
|
assert_array_almost_equal(cd_truth, cd)
|
||
|
|
assert_array_almost_equal(dd_truth, dd)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_transferfunction(self):
|
||
|
|
numc = np.array([0.25, 0.25, 0.5])
|
||
|
|
denc = np.array([0.75, 0.75, 1.0])
|
||
|
|
|
||
|
|
numd = np.array([[1.0 / 3.0, -0.427419169438754, 0.221654141101125]])
|
||
|
|
dend = np.array([1.0, -1.351394049721225, 0.606530659712634])
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
num, den, dt = c2d((numc, denc), dt_requested, method='zoh')
|
||
|
|
|
||
|
|
assert_array_almost_equal(numd, num)
|
||
|
|
assert_array_almost_equal(dend, den)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_zerospolesgain(self):
|
||
|
|
zeros_c = np.array([0.5, -0.5])
|
||
|
|
poles_c = np.array([1.j / np.sqrt(2), -1.j / np.sqrt(2)])
|
||
|
|
k_c = 1.0
|
||
|
|
|
||
|
|
zeros_d = [1.23371727305860, 0.735356894461267]
|
||
|
|
polls_d = [0.938148335039729 + 0.346233593780536j,
|
||
|
|
0.938148335039729 - 0.346233593780536j]
|
||
|
|
k_d = 1.0
|
||
|
|
|
||
|
|
dt_requested = 0.5
|
||
|
|
|
||
|
|
zeros, poles, k, dt = c2d((zeros_c, poles_c, k_c), dt_requested,
|
||
|
|
method='zoh')
|
||
|
|
|
||
|
|
assert_array_almost_equal(zeros_d, zeros)
|
||
|
|
assert_array_almost_equal(polls_d, poles)
|
||
|
|
assert_almost_equal(k_d, k)
|
||
|
|
assert_almost_equal(dt_requested, dt)
|
||
|
|
|
||
|
|
def test_gbt_with_sio_tf_and_zpk(self):
|
||
|
|
"""Test method='gbt' with alpha=0.25 for tf and zpk cases."""
|
||
|
|
# State space coefficients for the continuous SIO system.
|
||
|
|
A = -1.0
|
||
|
|
B = 1.0
|
||
|
|
C = 1.0
|
||
|
|
D = 0.5
|
||
|
|
|
||
|
|
# The continuous transfer function coefficients.
|
||
|
|
cnum, cden = ss2tf(A, B, C, D)
|
||
|
|
|
||
|
|
# Continuous zpk representation
|
||
|
|
cz, cp, ck = ss2zpk(A, B, C, D)
|
||
|
|
|
||
|
|
h = 1.0
|
||
|
|
alpha = 0.25
|
||
|
|
|
||
|
|
# Explicit formulas, in the scalar case.
|
||
|
|
Ad = (1 + (1 - alpha) * h * A) / (1 - alpha * h * A)
|
||
|
|
Bd = h * B / (1 - alpha * h * A)
|
||
|
|
Cd = C / (1 - alpha * h * A)
|
||
|
|
Dd = D + alpha * C * Bd
|
||
|
|
|
||
|
|
# Convert the explicit solution to tf
|
||
|
|
dnum, dden = ss2tf(Ad, Bd, Cd, Dd)
|
||
|
|
|
||
|
|
# Compute the discrete tf using cont2discrete.
|
||
|
|
c2dnum, c2dden, dt = c2d((cnum, cden), h, method='gbt', alpha=alpha)
|
||
|
|
|
||
|
|
assert_allclose(dnum, c2dnum)
|
||
|
|
assert_allclose(dden, c2dden)
|
||
|
|
|
||
|
|
# Convert explicit solution to zpk.
|
||
|
|
dz, dp, dk = ss2zpk(Ad, Bd, Cd, Dd)
|
||
|
|
|
||
|
|
# Compute the discrete zpk using cont2discrete.
|
||
|
|
c2dz, c2dp, c2dk, dt = c2d((cz, cp, ck), h, method='gbt', alpha=alpha)
|
||
|
|
|
||
|
|
assert_allclose(dz, c2dz)
|
||
|
|
assert_allclose(dp, c2dp)
|
||
|
|
assert_allclose(dk, c2dk)
|
||
|
|
|
||
|
|
def test_discrete_approx(self):
|
||
|
|
"""
|
||
|
|
Test that the solution to the discrete approximation of a continuous
|
||
|
|
system actually approximates the solution to the continuous system.
|
||
|
|
This is an indirect test of the correctness of the implementation
|
||
|
|
of cont2discrete.
|
||
|
|
"""
|
||
|
|
|
||
|
|
def u(t):
|
||
|
|
return np.sin(2.5 * t)
|
||
|
|
|
||
|
|
a = np.array([[-0.01]])
|
||
|
|
b = np.array([[1.0]])
|
||
|
|
c = np.array([[1.0]])
|
||
|
|
d = np.array([[0.2]])
|
||
|
|
x0 = 1.0
|
||
|
|
|
||
|
|
t = np.linspace(0, 10.0, 101)
|
||
|
|
dt = t[1] - t[0]
|
||
|
|
u1 = u(t)
|
||
|
|
|
||
|
|
# Use lsim2 to compute the solution to the continuous system.
|
||
|
|
t, yout, xout = lsim2((a, b, c, d), T=t, U=u1, X0=x0,
|
||
|
|
rtol=1e-9, atol=1e-11)
|
||
|
|
|
||
|
|
# Convert the continuous system to a discrete approximation.
|
||
|
|
dsys = c2d((a, b, c, d), dt, method='bilinear')
|
||
|
|
|
||
|
|
# Use dlsim with the pairwise averaged input to compute the output
|
||
|
|
# of the discrete system.
|
||
|
|
u2 = 0.5 * (u1[:-1] + u1[1:])
|
||
|
|
t2 = t[:-1]
|
||
|
|
td2, yd2, xd2 = dlsim(dsys, u=u2.reshape(-1, 1), t=t2, x0=x0)
|
||
|
|
|
||
|
|
# ymid is the average of consecutive terms of the "exact" output
|
||
|
|
# computed by lsim2. This is what the discrete approximation
|
||
|
|
# actually approximates.
|
||
|
|
ymid = 0.5 * (yout[:-1] + yout[1:])
|
||
|
|
|
||
|
|
assert_allclose(yd2.ravel(), ymid, rtol=1e-4)
|
||
|
|
|
||
|
|
def test_simo_tf(self):
|
||
|
|
# See gh-5753
|
||
|
|
tf = ([[1, 0], [1, 1]], [1, 1])
|
||
|
|
num, den, dt = c2d(tf, 0.01)
|
||
|
|
|
||
|
|
assert_equal(dt, 0.01) # sanity check
|
||
|
|
assert_allclose(den, [1, -0.990404983], rtol=1e-3)
|
||
|
|
assert_allclose(num, [[1, -1], [1, -0.99004983]], rtol=1e-3)
|
||
|
|
|
||
|
|
def test_multioutput(self):
|
||
|
|
ts = 0.01 # time step
|
||
|
|
|
||
|
|
tf = ([[1, -3], [1, 5]], [1, 1])
|
||
|
|
num, den, dt = c2d(tf, ts)
|
||
|
|
|
||
|
|
tf1 = (tf[0][0], tf[1])
|
||
|
|
num1, den1, dt1 = c2d(tf1, ts)
|
||
|
|
|
||
|
|
tf2 = (tf[0][1], tf[1])
|
||
|
|
num2, den2, dt2 = c2d(tf2, ts)
|
||
|
|
|
||
|
|
# Sanity checks
|
||
|
|
assert_equal(dt, dt1)
|
||
|
|
assert_equal(dt, dt2)
|
||
|
|
|
||
|
|
# Check that we get the same results
|
||
|
|
assert_allclose(num, np.vstack((num1, num2)), rtol=1e-13)
|
||
|
|
|
||
|
|
# Single input, so the denominator should
|
||
|
|
# not be multidimensional like the numerator
|
||
|
|
assert_allclose(den, den1, rtol=1e-13)
|
||
|
|
assert_allclose(den, den2, rtol=1e-13)
|
||
|
|
|
||
|
|
class TestC2dLti(object):
|
||
|
|
def test_c2d_ss(self):
|
||
|
|
# StateSpace
|
||
|
|
A = np.array([[-0.3, 0.1], [0.2, -0.7]])
|
||
|
|
B = np.array([[0], [1]])
|
||
|
|
C = np.array([[1, 0]])
|
||
|
|
D = 0
|
||
|
|
|
||
|
|
A_res = np.array([[0.985136404135682, 0.004876671474795],
|
||
|
|
[0.009753342949590, 0.965629718236502]])
|
||
|
|
B_res = np.array([[0.000122937599964], [0.049135527547844]])
|
||
|
|
|
||
|
|
sys_ssc = lti(A, B, C, D)
|
||
|
|
sys_ssd = sys_ssc.to_discrete(0.05)
|
||
|
|
|
||
|
|
assert_allclose(sys_ssd.A, A_res)
|
||
|
|
assert_allclose(sys_ssd.B, B_res)
|
||
|
|
assert_allclose(sys_ssd.C, C)
|
||
|
|
assert_allclose(sys_ssd.D, D)
|
||
|
|
|
||
|
|
def test_c2d_tf(self):
|
||
|
|
|
||
|
|
sys = lti([0.5, 0.3], [1.0, 0.4])
|
||
|
|
sys = sys.to_discrete(0.005)
|
||
|
|
|
||
|
|
# Matlab results
|
||
|
|
num_res = np.array([0.5, -0.485149004980066])
|
||
|
|
den_res = np.array([1.0, -0.980198673306755])
|
||
|
|
|
||
|
|
# Somehow a lot of numerical errors
|
||
|
|
assert_allclose(sys.den, den_res, atol=0.02)
|
||
|
|
assert_allclose(sys.num, num_res, atol=0.02)
|
||
|
|
|
||
|
|
class TestC2dLti(object):
|
||
|
|
def test_c2d_ss(self):
|
||
|
|
# StateSpace
|
||
|
|
A = np.array([[-0.3, 0.1], [0.2, -0.7]])
|
||
|
|
B = np.array([[0], [1]])
|
||
|
|
C = np.array([[1, 0]])
|
||
|
|
D = 0
|
||
|
|
|
||
|
|
A_res = np.array([[0.985136404135682, 0.004876671474795],
|
||
|
|
[0.009753342949590, 0.965629718236502]])
|
||
|
|
B_res = np.array([[0.000122937599964], [0.049135527547844]])
|
||
|
|
|
||
|
|
sys_ssc = lti(A, B, C, D)
|
||
|
|
sys_ssd = sys_ssc.to_discrete(0.05)
|
||
|
|
|
||
|
|
assert_allclose(sys_ssd.A, A_res)
|
||
|
|
assert_allclose(sys_ssd.B, B_res)
|
||
|
|
assert_allclose(sys_ssd.C, C)
|
||
|
|
assert_allclose(sys_ssd.D, D)
|
||
|
|
|
||
|
|
def test_c2d_tf(self):
|
||
|
|
|
||
|
|
sys = lti([0.5, 0.3], [1.0, 0.4])
|
||
|
|
sys = sys.to_discrete(0.005)
|
||
|
|
|
||
|
|
# Matlab results
|
||
|
|
num_res = np.array([0.5, -0.485149004980066])
|
||
|
|
den_res = np.array([1.0, -0.980198673306755])
|
||
|
|
|
||
|
|
# Somehow a lot of numerical errors
|
||
|
|
assert_allclose(sys.den, den_res, atol=0.02)
|
||
|
|
assert_allclose(sys.num, num_res, atol=0.02)
|
||
|
|
|
||
|
|
|
||
|
|
class TestC2dInvariants:
|
||
|
|
# Some test cases for checking the invariances.
|
||
|
|
# Array of triplets: (system, sample time, number of samples)
|
||
|
|
cases = [
|
||
|
|
(tf2ss([1, 1], [1, 1.5, 1]), 0.25, 10),
|
||
|
|
(tf2ss([1, 2], [1, 1.5, 3, 1]), 0.5, 10),
|
||
|
|
(tf2ss(0.1, [1, 1, 2, 1]), 0.5, 10),
|
||
|
|
]
|
||
|
|
|
||
|
|
# Some options for lsim2 and derived routines
|
||
|
|
tolerances = {'rtol': 1e-9, 'atol': 1e-11}
|
||
|
|
|
||
|
|
# Check that systems discretized with the impulse-invariant
|
||
|
|
# method really hold the invariant
|
||
|
|
@pytest.mark.parametrize("sys,sample_time,samples_number", cases)
|
||
|
|
def test_impulse_invariant(self, sys, sample_time, samples_number):
|
||
|
|
time = np.arange(samples_number) * sample_time
|
||
|
|
_, yout_cont = impulse2(sys, T=time, **self.tolerances)
|
||
|
|
_, yout_disc = dimpulse(c2d(sys, sample_time, method='impulse'),
|
||
|
|
n=len(time))
|
||
|
|
assert_allclose(sample_time * yout_cont.ravel(), yout_disc[0].ravel())
|
||
|
|
|
||
|
|
# Step invariant should hold for ZOH discretized systems
|
||
|
|
@pytest.mark.parametrize("sys,sample_time,samples_number", cases)
|
||
|
|
def test_step_invariant(self, sys, sample_time, samples_number):
|
||
|
|
time = np.arange(samples_number) * sample_time
|
||
|
|
_, yout_cont = step2(sys, T=time, **self.tolerances)
|
||
|
|
_, yout_disc = dstep(c2d(sys, sample_time, method='zoh'), n=len(time))
|
||
|
|
assert_allclose(yout_cont.ravel(), yout_disc[0].ravel())
|
||
|
|
|
||
|
|
# Linear invariant should hold for FOH discretized systems
|
||
|
|
@pytest.mark.parametrize("sys,sample_time,samples_number", cases)
|
||
|
|
def test_linear_invariant(self, sys, sample_time, samples_number):
|
||
|
|
time = np.arange(samples_number) * sample_time
|
||
|
|
_, yout_cont, _ = lsim2(sys, T=time, U=time, **self.tolerances)
|
||
|
|
_, yout_disc, _ = dlsim(c2d(sys, sample_time, method='foh'), u=time)
|
||
|
|
assert_allclose(yout_cont.ravel(), yout_disc.ravel())
|