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"""interconnect_test.py - test input/output interconnect function
RMM, 22 Jan 2021
This set of unit tests covers the various operatons of the interconnect()
function, as well as some of the support functions associated with
interconnect().
Note: additional tests are available in iosys_test.py, which focuses on the
raw InterconnectedSystem constructor. This set of unit tests focuses on
functionality implemented in the interconnect() function itself.
"""
import pytest
import numpy as np
import scipy as sp
import control as ct
@pytest.mark.parametrize("inputs, output, dimension, D", [
[1, 1, None, [[1]] ],
['u', 'y', None, [[1]] ],
[['u'], ['y'], None, [[1]] ],
[2, 1, None, [[1, 1]] ],
[['r', '-y'], ['e'], None, [[1, -1]] ],
[5, 1, None, np.ones((1, 5)) ],
['u', 'y', 1, [[1]] ],
['u', 'y', 2, [[1, 0], [0, 1]] ],
[['r', '-y'], ['e'], 2, [[1, 0, -1, 0], [0, 1, 0, -1]] ],
])
def test_summing_junction(inputs, output, dimension, D):
ninputs = 1 if isinstance(inputs, str) else \
inputs if isinstance(inputs, int) else len(inputs)
sum = ct.summing_junction(
inputs=inputs, output=output, dimension=dimension)
dim = 1 if dimension is None else dimension
np.testing.assert_allclose(sum.A, np.ndarray((0, 0)))
np.testing.assert_allclose(sum.B, np.ndarray((0, ninputs*dim)))
np.testing.assert_allclose(sum.C, np.ndarray((dim, 0)))
np.testing.assert_allclose(sum.D, D)
def test_summation_exceptions():
# Bad input description
with pytest.raises(ValueError, match="could not parse input"):
sumblk = ct.summing_junction(np.pi, 'y')
# Bad output description
with pytest.raises(ValueError, match="could not parse output"):
sumblk = ct.summing_junction('u', np.pi)
# Bad input dimension
with pytest.raises(ValueError, match="unrecognized dimension"):
sumblk = ct.summing_junction('u', 'y', dimension=False)
def test_interconnect_implicit():
"""Test the use of implicit connections in interconnect()"""
import random
# System definition
P = ct.ss2io(
ct.rss(2, 1, 1, strictly_proper=True),
inputs='u', outputs='y', name='P')
kp = ct.tf(random.uniform(1, 10), [1])
ki = ct.tf(random.uniform(1, 10), [1, 0])
C = ct.tf2io(kp + ki, inputs='e', outputs='u', name='C')
# same but static C2
C2 = ct.tf(random.uniform(1, 10), 1,
inputs='e', outputs='u', name='C2')
# Block diagram computation
Tss = ct.feedback(P * C, 1)
Tss2 = ct.feedback(P * C2, 1)
# Construct the interconnection explicitly
Tio_exp = ct.interconnect(
(C, P),
connections = [['P.u', 'C.u'], ['C.e', '-P.y']],
inplist='C.e', outlist='P.y')
# Compare to bdalg computation
np.testing.assert_almost_equal(Tio_exp.A, Tss.A)
np.testing.assert_almost_equal(Tio_exp.B, Tss.B)
np.testing.assert_almost_equal(Tio_exp.C, Tss.C)
np.testing.assert_almost_equal(Tio_exp.D, Tss.D)
# Construct the interconnection via a summing junction
sumblk = ct.summing_junction(inputs=['r', '-y'], output='e', name="sum")
Tio_sum = ct.interconnect(
(C, P, sumblk), inplist=['r'], outlist=['y'])
np.testing.assert_almost_equal(Tio_sum.A, Tss.A)
np.testing.assert_almost_equal(Tio_sum.B, Tss.B)
np.testing.assert_almost_equal(Tio_sum.C, Tss.C)
np.testing.assert_almost_equal(Tio_sum.D, Tss.D)
# test whether signal names work for static system C2
Tio_sum2 = ct.interconnect(
[C2, P, sumblk], inputs='r', outputs='y')
np.testing.assert_almost_equal(Tio_sum2.A, Tss2.A)
np.testing.assert_almost_equal(Tio_sum2.B, Tss2.B)
np.testing.assert_almost_equal(Tio_sum2.C, Tss2.C)
np.testing.assert_almost_equal(Tio_sum2.D, Tss2.D)
# Setting connections to False should lead to an empty connection map
empty = ct.interconnect(
(C, P, sumblk), connections=False, inplist=['r'], outlist=['y'])
np.testing.assert_allclose(empty.connect_map, np.zeros((4, 3)))
# Implicit summation across repeated signals
kp_io = ct.tf2io(kp, inputs='e', outputs='u', name='kp')
ki_io = ct.tf2io(ki, inputs='e', outputs='u', name='ki')
Tio_sum = ct.interconnect(
(kp_io, ki_io, P, sumblk), inplist=['r'], outlist=['y'])
np.testing.assert_almost_equal(Tio_sum.A, Tss.A)
np.testing.assert_almost_equal(Tio_sum.B, Tss.B)
np.testing.assert_almost_equal(Tio_sum.C, Tss.C)
np.testing.assert_almost_equal(Tio_sum.D, Tss.D)
# TODO: interconnect a MIMO system using implicit connections
# P = control.ss2io(
# control.rss(2, 2, 2, strictly_proper=True),
# input_prefix='u', output_prefix='y', name='P')
# C = control.ss2io(
# control.rss(2, 2, 2),
# input_prefix='e', output_prefix='u', name='C')
# sumblk = control.summing_junction(
# inputs=['r', '-y'], output='e', dimension=2)
# S = control.interconnect([P, C, sumblk], inplist='r', outlist='y')
# Make sure that repeated inplist/outlist names work
pi_io = ct.interconnect(
(kp_io, ki_io), inplist=['e'], outlist=['u'])
pi_ss = ct.tf2ss(kp + ki)
np.testing.assert_almost_equal(pi_io.A, pi_ss.A)
np.testing.assert_almost_equal(pi_io.B, pi_ss.B)
np.testing.assert_almost_equal(pi_io.C, pi_ss.C)
np.testing.assert_almost_equal(pi_io.D, pi_ss.D)
# Default input and output lists, along with singular versions
Tio_sum = ct.interconnect(
(kp_io, ki_io, P, sumblk), input='r', output='y')
np.testing.assert_almost_equal(Tio_sum.A, Tss.A)
np.testing.assert_almost_equal(Tio_sum.B, Tss.B)
np.testing.assert_almost_equal(Tio_sum.C, Tss.C)
np.testing.assert_almost_equal(Tio_sum.D, Tss.D)
# Signal not found
with pytest.raises(ValueError, match="could not find"):
Tio_sum = ct.interconnect(
(C, P, sumblk), inplist=['x'], outlist=['y'])
with pytest.raises(ValueError, match="could not find"):
Tio_sum = ct.interconnect(
(C, P, sumblk), inplist=['r'], outlist=['x'])
def test_interconnect_docstring():
"""Test the examples from the interconnect() docstring"""
# MIMO interconnection (note: use [C, P] instead of [P, C] for state order)
P = ct.LinearIOSystem(
ct.rss(2, 2, 2, strictly_proper=True), name='P')
C = ct.LinearIOSystem(ct.rss(2, 2, 2), name='C')
T = ct.interconnect(
[C, P],
connections = [
['P.u[0]', 'C.y[0]'], ['P.u[1]', 'C.y[1]'],
['C.u[0]', '-P.y[0]'], ['C.u[1]', '-P.y[1]']],
inplist = ['C.u[0]', 'C.u[1]'],
outlist = ['P.y[0]', 'P.y[1]'],
)
T_ss = ct.feedback(P * C, ct.ss([], [], [], np.eye(2)))
np.testing.assert_almost_equal(T.A, T_ss.A)
np.testing.assert_almost_equal(T.B, T_ss.B)
np.testing.assert_almost_equal(T.C, T_ss.C)
np.testing.assert_almost_equal(T.D, T_ss.D)
# Implicit interconnection (note: use [C, P, sumblk] for proper state order)
P = ct.tf2io(ct.tf(1, [1, 0]), inputs='u', outputs='y')
C = ct.tf2io(ct.tf(10, [1, 1]), inputs='e', outputs='u')
sumblk = ct.summing_junction(inputs=['r', '-y'], output='e')
T = ct.interconnect([C, P, sumblk], inplist='r', outlist='y')
T_ss = ct.feedback(P * C, 1)
np.testing.assert_almost_equal(T.A, T_ss.A)
np.testing.assert_almost_equal(T.B, T_ss.B)
np.testing.assert_almost_equal(T.C, T_ss.C)
np.testing.assert_almost_equal(T.D, T_ss.D)
def test_interconnect_exceptions():
# First make sure the docstring example works
P = ct.tf2io(ct.tf(1, [1, 0]), input='u', output='y')
C = ct.tf2io(ct.tf(10, [1, 1]), input='e', output='u')
sumblk = ct.summing_junction(inputs=['r', '-y'], output='e')
T = ct.interconnect((P, C, sumblk), input='r', output='y')
assert (T.ninputs, T.noutputs, T.nstates) == (1, 1, 2)
# Unrecognized arguments
# LinearIOSystem
with pytest.raises(TypeError, match="unrecognized keyword"):
P = ct.LinearIOSystem(ct.rss(2, 1, 1), output_name='y')
# Interconnect
with pytest.raises(TypeError, match="unrecognized keyword"):
T = ct.interconnect((P, C, sumblk), input_name='r', output='y')
# Interconnected system
with pytest.raises(TypeError, match="unrecognized keyword"):
T = ct.InterconnectedSystem((P, C, sumblk), input_name='r', output='y')
# NonlinearIOSytem
with pytest.raises(TypeError, match="unrecognized keyword"):
nlios = ct.NonlinearIOSystem(
None, lambda t, x, u, params: u*u, input_count=1, output_count=1)
# Summing junction
with pytest.raises(TypeError, match="input specification is required"):
sumblk = ct.summing_junction()
with pytest.raises(TypeError, match="unrecognized keyword"):
sumblk = ct.summing_junction(input_count=2, output_count=2)
def test_string_inputoutput():
# regression test for gh-692
P1 = ct.rss(2, 1, 1)
P1_iosys = ct.LinearIOSystem(P1, inputs='u1', outputs='y1')
P2 = ct.rss(2, 1, 1)
P2_iosys = ct.LinearIOSystem(P2, inputs='y1', outputs='y2')
P_s1 = ct.interconnect([P1_iosys, P2_iosys], inputs='u1', outputs=['y2'])
assert P_s1.input_index == {'u1' : 0}
P_s2 = ct.interconnect([P1_iosys, P2_iosys], input='u1', outputs=['y2'])
assert P_s2.input_index == {'u1' : 0}
P_s1 = ct.interconnect([P1_iosys, P2_iosys], inputs=['u1'], outputs='y2')
assert P_s1.output_index == {'y2' : 0}
P_s2 = ct.interconnect([P1_iosys, P2_iosys], inputs=['u1'], output='y2')
assert P_s2.output_index == {'y2' : 0}
def test_linear_interconnect():
tf_ctrl = ct.tf(1, (10.1, 1), inputs='e', outputs='u', name='ctrl')
tf_plant = ct.tf(1, (10.1, 1), inputs='u', outputs='y', name='plant')
ss_ctrl = ct.ss(1, 2, 1, 0, inputs='e', outputs='u', name='ctrl')
ss_plant = ct.ss(1, 2, 1, 0, inputs='u', outputs='y', name='plant')
nl_ctrl = ct.NonlinearIOSystem(
lambda t, x, u, params: x*x, lambda t, x, u, params: u*x,
states=1, inputs='e', outputs='u', name='ctrl')
nl_plant = ct.NonlinearIOSystem(
lambda t, x, u, params: x*x, lambda t, x, u, params: u*x,
states=1, inputs='u', outputs='y', name='plant')
sumblk = ct.summing_junction(inputs=['r', '-y'], outputs=['e'], name='sum')
# Interconnections of linear I/O systems should be linear I/O system
assert isinstance(
ct.interconnect([tf_ctrl, tf_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert isinstance(
ct.interconnect([ss_ctrl, ss_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert isinstance(
ct.interconnect([tf_ctrl, ss_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert isinstance(
ct.interconnect([ss_ctrl, tf_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
# Interconnections with nonliner I/O systems should not be linear
assert ~isinstance(
ct.interconnect([nl_ctrl, ss_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert ~isinstance(
ct.interconnect([nl_ctrl, tf_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert ~isinstance(
ct.interconnect([ss_ctrl, nl_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
assert ~isinstance(
ct.interconnect([tf_ctrl, nl_plant, sumblk], inputs='r', outputs='y'),
ct.LinearIOSystem)
# Implicit converstion of transfer function should retain name
clsys = ct.interconnect(
[tf_ctrl, ss_plant, sumblk],
connections=[
['plant.u', 'ctrl.u'],
['ctrl.e', 'sum.e'],
['sum.y', 'plant.y']
],
inplist=['sum.r'], inputs='r',
outlist=['plant.y'], outputs='y')
assert clsys.syslist[0].name == 'ctrl'