diff --git a/control/statesp.py b/control/statesp.py
index 2419b4e62..288b0831d 100644
--- a/control/statesp.py
+++ b/control/statesp.py
@@ -10,7 +10,7 @@
# Python 3 compatibility (needs to go here)
from __future__ import print_function
-from __future__ import division # for _convertToStateSpace
+from __future__ import division # for _convertToStateSpace
"""Copyright (c) 2010 by California Institute of Technology
All rights reserved.
@@ -161,8 +161,8 @@ class StateSpace(LTI):
A class for representing state-space models
- The StateSpace class is used to represent state-space realizations of linear
- time-invariant (LTI) systems:
+ The StateSpace class is used to represent state-space realizations of
+ linear time-invariant (LTI) systems:
dx/dt = A x + B u
y = C x + D u
@@ -216,7 +216,6 @@ class StateSpace(LTI):
# Allow ndarray * StateSpace to give StateSpace._rmul_() priority
__array_priority__ = 11 # override ndarray and matrix types
-
def __init__(self, *args, **kwargs):
"""
StateSpace(A, B, C, D[, dt])
@@ -240,18 +239,21 @@ def __init__(self, *args, **kwargs):
elif len(args) == 1:
# Use the copy constructor.
if not isinstance(args[0], StateSpace):
- raise TypeError("The one-argument constructor can only take in a StateSpace "
- "object. Received %s." % type(args[0]))
+ raise TypeError(
+ "The one-argument constructor can only take in a "
+ "StateSpace object. Received %s." % type(args[0]))
A = args[0].A
B = args[0].B
C = args[0].C
D = args[0].D
else:
- raise ValueError("Expected 1, 4, or 5 arguments; received %i." % len(args))
+ raise ValueError(
+ "Expected 1, 4, or 5 arguments; received %i." % len(args))
# Process keyword arguments
- remove_useless = kwargs.get('remove_useless',
- config.defaults['statesp.remove_useless_states'])
+ remove_useless = kwargs.get(
+ 'remove_useless',
+ config.defaults['statesp.remove_useless_states'])
# Convert all matrices to standard form
A = _ssmatrix(A)
@@ -263,7 +265,7 @@ def __init__(self, *args, **kwargs):
if np.asarray(C).ndim == 1 and len(C) == A.shape[0]:
C = _ssmatrix(C, axis=1)
else:
- C = _ssmatrix(C, axis=0) #if this doesn't work, error below
+ C = _ssmatrix(C, axis=0) # if this doesn't work, error below
if np.isscalar(D) and D == 0 and B.shape[1] > 0 and C.shape[0] > 0:
# If D is a scalar zero, broadcast it to the proper size
D = np.zeros((C.shape[0], B.shape[1]))
@@ -302,9 +304,9 @@ def __init__(self, *args, **kwargs):
if 0 == self.states:
# static gain
# matrix's default "empty" shape is 1x0
- A.shape = (0,0)
- B.shape = (0,self.inputs)
- C.shape = (self.outputs,0)
+ A.shape = (0, 0)
+ B.shape = (0, self.inputs)
+ C.shape = (self.outputs, 0)
# Check that the matrix sizes are consistent.
if self.states != A.shape[0]:
@@ -319,14 +321,15 @@ def __init__(self, *args, **kwargs):
raise ValueError("C and D must have the same number of rows.")
# Check for states that don't do anything, and remove them.
- if remove_useless: self._remove_useless_states()
+ if remove_useless:
+ self._remove_useless_states()
def _remove_useless_states(self):
"""Check for states that don't do anything, and remove them.
Scan the A, B, and C matrices for rows or columns of zeros. If the
- zeros are such that a particular state has no effect on the input-output
- dynamics, then remove that state from the A, B, and C matrices.
+ zeros are such that a particular state has no effect on the input-
+ output dynamics, then remove that state from the A, B, and C matrices.
"""
@@ -504,7 +507,8 @@ def _repr_latex_(self):
return self._latex_separate()
else:
cfg = config.defaults['statesp.latex_repr_type']
- raise ValueError("Unknown statesp.latex_repr_type '{cfg}'".format(cfg=cfg))
+ raise ValueError(
+ "Unknown statesp.latex_repr_type '{cfg}'".format(cfg=cfg))
# Negation of a system
def __neg__(self):
@@ -535,10 +539,9 @@ def __add__(self, other):
# Concatenate the various arrays
A = concatenate((
concatenate((self.A, zeros((self.A.shape[0],
- other.A.shape[-1]))),axis=1),
+ other.A.shape[-1]))), axis=1),
concatenate((zeros((other.A.shape[0], self.A.shape[-1])),
- other.A),axis=1)
- ),axis=0)
+ other.A), axis=1)), axis=0)
B = concatenate((self.B, other.B), axis=0)
C = concatenate((self.C, other.C), axis=1)
D = self.D + other.D
@@ -590,7 +593,7 @@ def __mul__(self, other):
concatenate((np.dot(self.B, other.C), self.A), axis=1)),
axis=0)
B = concatenate((other.B, np.dot(self.B, other.D)), axis=0)
- C = concatenate((np.dot(self.D, other.C), self.C),axis=1)
+ C = concatenate((np.dot(self.D, other.C), self.C), axis=1)
D = np.dot(self.D, other.D)
return StateSpace(A, B, C, D, dt)
@@ -634,7 +637,8 @@ def __div__(self, other):
def __rdiv__(self, other):
"""Right divide two LTI systems."""
- raise NotImplementedError("StateSpace.__rdiv__ is not implemented yet.")
+ raise NotImplementedError(
+ "StateSpace.__rdiv__ is not implemented yet.")
def evalfr(self, omega):
"""Evaluate a SS system's transfer function at a single frequency.
@@ -779,7 +783,8 @@ def zero(self):
if nu == 0:
return np.array([])
else:
- return sp.linalg.eigvals(out[8][0:nu, 0:nu], out[9][0:nu, 0:nu])
+ return sp.linalg.eigvals(out[8][0:nu, 0:nu],
+ out[9][0:nu, 0:nu])
except ImportError: # Slycot unavailable. Fall back to scipy.
if self.C.shape[0] != self.D.shape[1]:
@@ -801,7 +806,8 @@ def zero(self):
concatenate((self.C, self.D), axis=1)), axis=0)
M = pad(eye(self.A.shape[0]), ((0, self.C.shape[0]),
(0, self.B.shape[1])), "constant")
- return np.array([x for x in sp.linalg.eigvals(L, M, overwrite_a=True)
+ return np.array([x for x in sp.linalg.eigvals(L, M,
+ overwrite_a=True)
if not isinf(x)])
# Feedback around a state space system
@@ -812,8 +818,8 @@ def feedback(self, other=1, sign=-1):
# Check to make sure the dimensions are OK
if (self.inputs != other.outputs) or (self.outputs != other.inputs):
- raise ValueError("State space systems don't have compatible inputs/outputs for "
- "feedback.")
+ raise ValueError("State space systems don't have compatible "
+ "inputs/outputs for feedback.")
dt = common_timebase(self.dt, other.dt)
A1 = self.A
@@ -827,7 +833,8 @@ def feedback(self, other=1, sign=-1):
F = eye(self.inputs) - sign * np.dot(D2, D1)
if matrix_rank(F) != self.inputs:
- raise ValueError("I - sign * D2 * D1 is singular to working precision.")
+ raise ValueError(
+ "I - sign * D2 * D1 is singular to working precision.")
# Precompute F\D2 and F\C2 (E = inv(F))
# We can solve two linear systems in one pass, since the
@@ -916,16 +923,20 @@ def lft(self, other, nu=-1, ny=-1):
# solve for the resulting ss by solving for [y, u] using [x,
# xbar] and [w1, w2].
TH = np.linalg.solve(F, np.block(
- [[C2, np.zeros((ny, other.states)), D21, np.zeros((ny, other.inputs - ny))],
- [np.zeros((nu, self.states)), Cbar1, np.zeros((nu, self.inputs - nu)), Dbar12]]
+ [[C2, np.zeros((ny, other.states)),
+ D21, np.zeros((ny, other.inputs - ny))],
+ [np.zeros((nu, self.states)), Cbar1,
+ np.zeros((nu, self.inputs - nu)), Dbar12]]
))
T11 = TH[:ny, :self.states]
T12 = TH[:ny, self.states: self.states + other.states]
T21 = TH[ny:, :self.states]
T22 = TH[ny:, self.states: self.states + other.states]
- H11 = TH[:ny, self.states + other.states: self.states + other.states + self.inputs - nu]
+ H11 = TH[:ny, self.states + other.states:self.states +
+ other.states + self.inputs - nu]
H12 = TH[:ny, self.states + other.states + self.inputs - nu:]
- H21 = TH[ny:, self.states + other.states: self.states + other.states + self.inputs - nu]
+ H21 = TH[ny:, self.states + other.states:self.states +
+ other.states + self.inputs - nu]
H22 = TH[ny:, self.states + other.states + self.inputs - nu:]
Ares = np.block([
@@ -956,13 +967,13 @@ def minreal(self, tol=0.0):
try:
from slycot import tb01pd
B = empty((self.states, max(self.inputs, self.outputs)))
- B[:,:self.inputs] = self.B
+ B[:, :self.inputs] = self.B
C = empty((max(self.outputs, self.inputs), self.states))
- C[:self.outputs,:] = self.C
+ C[:self.outputs, :] = self.C
A, B, C, nr = tb01pd(self.states, self.inputs, self.outputs,
self.A, B, C, tol=tol)
- return StateSpace(A[:nr,:nr], B[:nr,:self.inputs],
- C[:self.outputs,:nr], self.D)
+ return StateSpace(A[:nr, :nr], B[:nr, :self.inputs],
+ C[:self.outputs, :nr], self.D)
except ImportError:
raise TypeError("minreal requires slycot tb01pd")
else:
@@ -1052,7 +1063,8 @@ def __getitem__(self, indices):
raise IOError('must provide indices of length 2 for state space')
i = indices[0]
j = indices[1]
- return StateSpace(self.A, self.B[:, j], self.C[i, :], self.D[i, j], self.dt)
+ return StateSpace(self.A, self.B[:, j], self.C[i, :],
+ self.D[i, j], self.dt)
def sample(self, Ts, method='zoh', alpha=None, prewarp_frequency=None):
"""Convert a continuous time system to discrete time
@@ -1104,9 +1116,9 @@ def sample(self, Ts, method='zoh', alpha=None, prewarp_frequency=None):
raise ValueError("System must be continuous time system")
sys = (self.A, self.B, self.C, self.D)
- if (method=='bilinear' or (method=='gbt' and alpha==0.5)) and \
+ if (method == 'bilinear' or (method == 'gbt' and alpha == 0.5)) and \
prewarp_frequency is not None:
- Twarp = 2*np.tan(prewarp_frequency*Ts/2)/prewarp_frequency
+ Twarp = 2 * np.tan(prewarp_frequency * Ts/2)/prewarp_frequency
else:
Twarp = Ts
Ad, Bd, C, D, _ = cont2discrete(sys, Twarp, method, alpha)
@@ -1133,7 +1145,8 @@ def dcgain(self):
"""
try:
if self.isctime():
- gain = np.asarray(self.D-self.C.dot(np.linalg.solve(self.A, self.B)))
+ gain = np.asarray(self.D -
+ self.C.dot(np.linalg.solve(self.A, self.B)))
else:
gain = self.horner(1)
except LinAlgError:
@@ -1151,28 +1164,34 @@ def is_static_gain(self):
def _convertToStateSpace(sys, **kw):
"""Convert a system to state space form (if needed).
- If sys is already a state space, then it is returned. If sys is a transfer
- function object, then it is converted to a state space and returned. If sys
- is a scalar, then the number of inputs and outputs can be specified
- manually, as in:
+ If sys is already a state space, then it is returned. If sys is a
+ transfer function object, then it is converted to a state space and
+ returned. If sys is a scalar, then the number of inputs and outputs can
+ be specified manually, as in:
>>> sys = _convertToStateSpace(3.) # Assumes inputs = outputs = 1
>>> sys = _convertToStateSpace(1., inputs=3, outputs=2)
In the latter example, A = B = C = 0 and D = [[1., 1., 1.]
[1., 1., 1.]].
-
"""
from .xferfcn import TransferFunction
import itertools
+
if isinstance(sys, StateSpace):
if len(kw):
- raise TypeError("If sys is a StateSpace, _convertToStateSpace \
-cannot take keywords.")
+ raise TypeError("If sys is a StateSpace, _convertToStateSpace "
+ "cannot take keywords.")
# Already a state space system; just return it
return sys
+
elif isinstance(sys, TransferFunction):
+ # Make sure the transfer function is proper
+ if any([[len(num) for num in col] for col in sys.num] >
+ [[len(num) for num in col] for col in sys.den]):
+ raise ValueError("Transfer function is non-proper; can't "
+ "convert to StateSpace system.")
try:
from slycot import td04ad
if len(kw):
@@ -1189,8 +1208,10 @@ def _convertToStateSpace(sys, **kw):
denorder, den, num, tol=0)
states = ssout[0]
- return StateSpace(ssout[1][:states, :states], ssout[2][:states, :sys.inputs],
- ssout[3][:sys.outputs, :states], ssout[4], sys.dt)
+ return StateSpace(ssout[1][:states, :states],
+ ssout[2][:states, :sys.inputs],
+ ssout[3][:sys.outputs, :states], ssout[4],
+ sys.dt)
except ImportError:
# No Slycot. Scipy tf->ss can't handle MIMO, but static
# MIMO is an easy special case we can check for here
@@ -1200,7 +1221,8 @@ def _convertToStateSpace(sys, **kw):
for drow in sys.den)
if 1 == maxn and 1 == maxd:
D = empty((sys.outputs, sys.inputs), dtype=float)
- for i, j in itertools.product(range(sys.outputs), range(sys.inputs)):
+ for i, j in itertools.product(range(sys.outputs),
+ range(sys.inputs)):
D[i, j] = sys.num[i][j][0] / sys.den[i][j][0]
return StateSpace([], [], [], D, sys.dt)
else:
@@ -1210,7 +1232,8 @@ def _convertToStateSpace(sys, **kw):
# TODO: do we want to squeeze first and check dimenations?
# I think this will fail if num and den aren't 1-D after
# the squeeze
- A, B, C, D = sp.signal.tf2ss(squeeze(sys.num), squeeze(sys.den))
+ A, B, C, D = \
+ sp.signal.tf2ss(squeeze(sys.num), squeeze(sys.den))
return StateSpace(A, B, C, D, sys.dt)
elif isinstance(sys, (int, float, complex, np.number)):
@@ -1227,18 +1250,19 @@ def _convertToStateSpace(sys, **kw):
# The following Doesn't work due to inconsistencies in ltisys:
# return StateSpace([[]], [[]], [[]], eye(outputs, inputs))
return StateSpace(0., zeros((1, inputs)), zeros((outputs, 1)),
- sys * ones((outputs, inputs)))
+ sys * ones((outputs, inputs)))
# If this is a matrix, try to create a constant feedthrough
try:
D = _ssmatrix(sys)
return StateSpace([], [], [], D)
except Exception as e:
- print("Failure to assume argument is matrix-like in" \
- " _convertToStateSpace, result %s" % e)
+ print("Failure to assume argument is matrix-like in"
+ " _convertToStateSpace, result %s" % e)
raise TypeError("Can't convert given type to StateSpace system.")
+
# TODO: add discrete time option
def _rss_generate(states, inputs, outputs, type):
"""Generate a random state space.
@@ -1264,13 +1288,13 @@ def _rss_generate(states, inputs, outputs, type):
# Check for valid input arguments.
if states < 1 or states % 1:
raise ValueError("states must be a positive integer. states = %g." %
- states)
+ states)
if inputs < 1 or inputs % 1:
raise ValueError("inputs must be a positive integer. inputs = %g." %
- inputs)
+ inputs)
if outputs < 1 or outputs % 1:
raise ValueError("outputs must be a positive integer. outputs = %g." %
- outputs)
+ outputs)
# Make some poles for A. Preallocate a complex array.
poles = zeros(states) + zeros(states) * 0.j
@@ -1358,7 +1382,7 @@ def _rss_generate(states, inputs, outputs, type):
# Convert a MIMO system to a SISO system
# TODO: add discrete time check
def _mimo2siso(sys, input, output, warn_conversion=False):
- #pylint: disable=W0622
+ # pylint: disable=W0622
"""
Convert a MIMO system to a SISO system. (Convert a system with multiple
inputs and/or outputs, to a system with a single input and output.)
@@ -1398,7 +1422,7 @@ def _mimo2siso(sys, input, output, warn_conversion=False):
"Selected output: {sel}, "
"number of system outputs: {ext}."
.format(sel=output, ext=sys.outputs))
- #Convert sys to SISO if necessary
+ # Convert sys to SISO if necessary
if sys.inputs > 1 or sys.outputs > 1:
if warn_conversion:
warn("Converting MIMO system to SISO system. "
@@ -1547,8 +1571,8 @@ def ss(*args, **kwargs):
elif isinstance(sys, TransferFunction):
return tf2ss(sys)
else:
- raise TypeError("ss(sys): sys must be a StateSpace or \
-TransferFunction object. It is %s." % type(sys))
+ raise TypeError("ss(sys): sys must be a StateSpace or "
+ "TransferFunction object. It is %s." % type(sys))
else:
raise ValueError("Needs 1, 4, or 5 arguments; received %i." % len(args))
@@ -1572,16 +1596,16 @@ def tf2ss(*args):
Parameters
----------
- sys: LTI (StateSpace or TransferFunction)
+ sys : LTI (StateSpace or TransferFunction)
A linear system
- num: array_like, or list of list of array_like
+ num : array_like, or list of list of array_like
Polynomial coefficients of the numerator
- den: array_like, or list of list of array_like
+ den : array_like, or list of list of array_like
Polynomial coefficients of the denominator
Returns
-------
- out: StateSpace
+ out : StateSpace
New linear system in state space form
Raises
@@ -1618,8 +1642,8 @@ def tf2ss(*args):
elif len(args) == 1:
sys = args[0]
if not isinstance(sys, TransferFunction):
- raise TypeError("tf2ss(sys): sys must be a TransferFunction \
-object.")
+ raise TypeError("tf2ss(sys): sys must be a TransferFunction "
+ "object.")
return _convertToStateSpace(sys)
else:
raise ValueError("Needs 1 or 2 arguments; received %i." % len(args))
diff --git a/control/tests/convert_test.py b/control/tests/convert_test.py
index de1cf01d1..f92029fe3 100644
--- a/control/tests/convert_test.py
+++ b/control/tests/convert_test.py
@@ -250,3 +250,16 @@ def test_tf2ss_robustness(self):
np.testing.assert_array_almost_equal(np.sort(sys2tf.pole()),
np.sort(sys2ss.pole()))
+ def test_tf2ss_nonproper(self):
+ """Unit tests for non-proper transfer functions"""
+ # Easy case: input 2 to output 1 is 's'
+ num = [ [[0], [1, 0]], [[1], [0]] ]
+ den1 = [ [[1], [1]], [[1,4], [1]] ]
+ with pytest.raises(ValueError):
+ tf2ss(tf(num, den1))
+
+ # Trickier case (make sure that leading zeros in den are handled)
+ num = [ [[0], [1, 0]], [[1], [0]] ]
+ den1 = [ [[1], [0, 1]], [[1,4], [1]] ]
+ with pytest.raises(ValueError):
+ tf2ss(tf(num, den1))
diff --git a/control/tests/iosys_test.py b/control/tests/iosys_test.py
index faed39e07..d96eefd39 100644
--- a/control/tests/iosys_test.py
+++ b/control/tests/iosys_test.py
@@ -18,7 +18,6 @@
from control import iosys as ios
from control.tests.conftest import noscipy0
-
class TestIOSys:
@pytest.fixture
@@ -81,6 +80,11 @@ def test_tf2io(self, tsys):
np.testing.assert_array_almost_equal(lti_t, ios_t)
np.testing.assert_allclose(lti_y, ios_y, atol=0.002, rtol=0.)
+ # Make sure that non-proper transfer functions generate an error
+ tfsys = ct.tf('s')
+ with pytest.raises(ValueError):
+ iosys=ct.tf2io(tfsys)
+
def test_ss2io(self, tsys):
# Create an input/output system from the linear system
linsys = tsys.siso_linsys
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