def testConvert(self):
"""Test state space to transfer function conversion."""
verbose = self.debug
from control.statesp import _mimo2siso
#print __doc__
# Machine precision for floats.
eps = np.finfo(float).eps
for states in range(1, self.maxStates):
for inputs in range(1, self.maxIO):
for outputs in range(1, self.maxIO):
# start with a random SS system and transform to TF then
# back to SS, check that the matrices are the same.
ssOriginal = matlab.rss(states, outputs, inputs)
if (verbose):
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = control.ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
if (verbose):
print(" skipping (not reachable)")
continue
Omat = control.obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
if (verbose):
print(" skipping (not observable)")
continue
tfOriginal = matlab.tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = matlab.ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = matlab.tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.states != ssTransformed.states):
print("WARNING: state space dimension mismatch: " + \
"%d versus %d" % \
(ssOriginal.states, ssTransformed.states))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d" \
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
control.bode(_mimo2siso(ssOriginal, \
inputNum, outputNum), \
deg=False, Plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = control.tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
control.bode(tforig, ssorig_omega, \
deg=False, Plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
control.bode(_mimo2siso(ssTransformed, \
inputNum, outputNum), \
ssorig_omega, \
deg=False, Plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, ssxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, ssxfrm_imag)
#
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = control.tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
control.bode(tfxfrm, ssorig_omega, \
deg=False, Plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tfxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tfxfrm_imag)
def test_convert_MIMO_to_SISO(self):
'''Convert mimo to siso systems'''
#Test with our usual systems --------------------------------------------
#SISO PT2 system
As, Bs, Cs, Ds = self.make_SISO_mats()
sys_siso = ss(As, Bs, Cs, Ds)
#MIMO system that contains two independent copies of the SISO system above
Am, Bm, Cm, Dm = self.make_MIMO_mats()
sys_mimo = ss(Am, Bm, Cm, Dm)
# t, y = step(sys_siso)
# plot(t, y, label='sys_siso d=0')
sys_siso_00 = _mimo2siso(sys_mimo,
input=0,
output=0,
warn_conversion=False)
sys_siso_11 = _mimo2siso(sys_mimo,
input=1,
output=1,
warn_conversion=False)
#print("sys_siso_00 ---------------------------------------------")
#print(sys_siso_00)
#print("sys_siso_11 ---------------------------------------------")
#print(sys_siso_11)
#gain of converted system and equivalent SISO system must be the same
self.assert_systems_behave_equal(sys_siso, sys_siso_00)
self.assert_systems_behave_equal(sys_siso, sys_siso_11)
#Test with additional systems --------------------------------------------
#They have crossed inputs and direct feedthrough
#SISO system
As = matrix([[-81.82, -45.45], [10., -1.]])
Bs = matrix([[9.09], [0.]])
Cs = matrix([[0, 0.159]])
Ds = matrix([[0.02]])
sys_siso = ss(As, Bs, Cs, Ds)
# t, y = step(sys_siso)
# plot(t, y, label='sys_siso d=0.02')
# legend(loc='best')
#MIMO system
#The upper left sub-system uses : input 0, output 1
#The lower right sub-system uses: input 1, output 0
Am = array([[-81.82, -45.45, 0, 0], [10, -1, 0, 0],
[0, 0, -81.82, -45.45], [
0,
0,
10,
-1,
]])
Bm = array([[9.09, 0], [0, 0], [0, 9.09], [0, 0]])
Cm = array([[0, 0, 0, 0.159], [0, 0.159, 0, 0]])
Dm = matrix([[0, 0.02], [0.02, 0]])
sys_mimo = ss(Am, Bm, Cm, Dm)
sys_siso_01 = _mimo2siso(sys_mimo,
input=0,
output=1,
warn_conversion=False)
sys_siso_10 = _mimo2siso(sys_mimo,
input=1,
output=0,
warn_conversion=False)
# print("sys_siso_01 ---------------------------------------------")
# print(sys_siso_01)
# print("sys_siso_10 ---------------------------------------------")
# print(sys_siso_10)
#gain of converted system and equivalent SISO system must be the same
self.assert_systems_behave_equal(sys_siso, sys_siso_01)
self.assert_systems_behave_equal(sys_siso, sys_siso_10)
def impulse_response(sys, T=None, X0=0., input=0, output=0,
transpose=False, **keywords):
#pylint: disable=W0622
"""Impulse response of a linear system
If the system has multiple inputs or outputs (MIMO), one input and one
output have to be selected for the simulation. The parameters `input`
and `output` do this. All other inputs are set to 0, all other outputs
are ignored.
For information on the **shape** of parameters `T`, `X0` and
return values `T`, `yout` see: :ref:`time-series-convention`
Parameters
----------
sys: StateSpace, TransferFunction
LTI system to simulate
T: array-like object, optional
Time vector (argument is autocomputed if not given)
X0: array-like object or number, optional
Initial condition (default = 0)
Numbers are converted to constant arrays with the correct shape.
input: int
Index of the input that will be used in this simulation.
output: int
Index of the output that will be used in this simulation.
transpose: bool
If True, transpose all input and output arrays (for backward
compatibility with MATLAB and scipy.signal.lsim)
**keywords:
Additional keyword arguments control the solution algorithm for the
differential equations. These arguments are passed on to the function
:func:`lsim`, which in turn passes them on to
:func:`scipy.integrate.odeint`. See the documentation for
:func:`scipy.integrate.odeint` for information about these
arguments.
Returns
-------
T: array
Time values of the output
yout: array
Response of the system
See Also
--------
ForcedReponse, initial_response, step_response
Examples
--------
>>> T, yout = impulse_response(sys, T, X0)
"""
sys = _convertToStateSpace(sys)
sys = _mimo2siso(sys, input, output, warn_conversion=True)
# System has direct feedthrough, can't simulate impulse response numerically
if np.any(sys.D != 0) and isctime(sys):
warnings.warn('System has direct feedthrough: ``D != 0``. The infinite '
'impulse at ``t=0`` does not appear in the output. \n'
'Results may be meaningless!')
# create X0 if not given, test if X0 has correct shape.
# Must be done here because it is used for computations here.
n_states = sys.A.shape[0]
X0 = _check_convert_array(X0, [(n_states,), (n_states,1)],
'Parameter ``X0``: \n', squeeze=True)
# Compute new X0 that contains the impulse
# We can't put the impulse into U because there is no numerical
# representation for it (infinitesimally short, infinitely high).
# See also: http://www.mathworks.com/support/tech-notes/1900/1901.html
B = np.asarray(sys.B).squeeze()
new_X0 = B + X0
# Compute T and U, no checks necessary, they will be checked in lsim
if T is None:
T = _default_response_times(sys.A, 100)
U = np.zeros_like(T)
T, yout, _xout = forced_response(sys, T, U, new_X0, \
transpose=transpose, **keywords)
return T, yout
def testConvert(self):
"""Test state space to transfer function conversion."""
verbose = self.debug
# print __doc__
# Machine precision for floats.
# eps = np.finfo(float).eps
for states in range(1, self.maxStates):
for inputs in range(1, self.maxIO):
for outputs in range(1, self.maxIO):
# start with a random SS system and transform to TF then
# back to SS, check that the matrices are the same.
ssOriginal = matlab.rss(states, outputs, inputs)
if (verbose):
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
if (verbose):
print(" skipping (not reachable)")
continue
Omat = obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
if (verbose):
print(" skipping (not observable)")
continue
tfOriginal = matlab.tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = matlab.ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = matlab.tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.states != ssTransformed.states):
print("WARNING: state space dimension mismatch: " + \
"%d versus %d" % \
(ssOriginal.states, ssTransformed.states))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d" \
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
bode(_mimo2siso(ssOriginal, \
inputNum, outputNum), \
deg=False, plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
bode(tforig, ssorig_omega, \
deg=False, plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
bode(_mimo2siso(ssTransformed, \
inputNum, outputNum), \
ssorig_omega, \
deg=False, plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, ssxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, ssxfrm_imag)
#
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
bode(tfxfrm, ssorig_omega, \
deg=False, plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal( \
ssorig_real, tfxfrm_real)
np.testing.assert_array_almost_equal( \
ssorig_imag, tfxfrm_imag)
def initial_response(sys, T=None, X0=0., input=0, output=0, transpose=False,
**keywords):
#pylint: disable=W0622
"""Initial condition response of a linear system
If the system has multiple inputs or outputs (MIMO), one input and one
output have to be selected for the simulation. The parameters `input`
and `output` do this. All other inputs are set to 0, all other outputs
are ignored.
For information on the **shape** of parameters `T`, `X0` and
return values `T`, `yout` see: :ref:`time-series-convention`
Parameters
----------
sys: StateSpace, or TransferFunction
LTI system to simulate
T: array-like object, optional
Time vector (argument is autocomputed if not given)
X0: array-like object or number, optional
Initial condition (default = 0)
Numbers are converted to constant arrays with the correct shape.
input: int
Index of the input that will be used in this simulation.
output: int
Index of the output that will be used in this simulation.
transpose: bool
If True, transpose all input and output arrays (for backward
compatibility with MATLAB and scipy.signal.lsim)
**keywords:
Additional keyword arguments control the solution algorithm for the
differential equations. These arguments are passed on to the function
:func:`lsim`, which in turn passes them on to
:func:`scipy.integrate.odeint`. See the documentation for
:func:`scipy.integrate.odeint` for information about these
arguments.
Returns
-------
T: array
Time values of the output
yout: array
Response of the system
See Also
--------
forced_response, impulse_response, step_response
Examples
--------
>>> T, yout = initial_response(sys, T, X0)
"""
sys = _convertToStateSpace(sys)
sys = _mimo2siso(sys, input, output, warn_conversion=True)
# Create time and input vectors; checking is done in forced_response(...)
# The initial vector X0 is created in forced_response(...) if necessary
if T is None:
T = _default_response_times(sys.A, 100)
U = np.zeros_like(T)
T, yout, _xout = forced_response(sys, T, U, X0, transpose=transpose,
**keywords)
return T, yout
def test_convert_MIMO_to_SISO(self):
'''Convert mimo to siso systems'''
#Test with our usual systems --------------------------------------------
#SISO PT2 system
As, Bs, Cs, Ds = self.make_SISO_mats()
sys_siso = ss(As, Bs, Cs, Ds)
#MIMO system that contains two independent copies of the SISO system above
Am, Bm, Cm, Dm = self.make_MIMO_mats()
sys_mimo = ss(Am, Bm, Cm, Dm)
# t, y = step(sys_siso)
# plot(t, y, label='sys_siso d=0')
sys_siso_00 = _mimo2siso(sys_mimo, input=0, output=0,
warn_conversion=False)
sys_siso_11 = _mimo2siso(sys_mimo, input=1, output=1,
warn_conversion=False)
#print("sys_siso_00 ---------------------------------------------")
#print(sys_siso_00)
#print("sys_siso_11 ---------------------------------------------")
#print(sys_siso_11)
#gain of converted system and equivalent SISO system must be the same
self.assert_systems_behave_equal(sys_siso, sys_siso_00)
self.assert_systems_behave_equal(sys_siso, sys_siso_11)
#Test with additional systems --------------------------------------------
#They have crossed inputs and direct feedthrough
#SISO system
As = matrix([[-81.82, -45.45],
[ 10., -1. ]])
Bs = matrix([[9.09],
[0. ]])
Cs = matrix([[0, 0.159]])
Ds = matrix([[0.02]])
sys_siso = ss(As, Bs, Cs, Ds)
# t, y = step(sys_siso)
# plot(t, y, label='sys_siso d=0.02')
# legend(loc='best')
#MIMO system
#The upper left sub-system uses : input 0, output 1
#The lower right sub-system uses: input 1, output 0
Am = array([[-81.82, -45.45, 0, 0 ],
[ 10, -1, 0, 0 ],
[ 0, 0, -81.82, -45.45],
[ 0, 0, 10, -1, ]])
Bm = array([[9.09, 0 ],
[0 , 0 ],
[0 , 9.09],
[0 , 0 ]])
Cm = array([[0, 0, 0, 0.159],
[0, 0.159, 0, 0 ]])
Dm = matrix([[0, 0.02],
[0.02, 0 ]])
sys_mimo = ss(Am, Bm, Cm, Dm)
sys_siso_01 = _mimo2siso(sys_mimo, input=0, output=1,
warn_conversion=False)
sys_siso_10 = _mimo2siso(sys_mimo, input=1, output=0,
warn_conversion=False)
print("sys_siso_01 ---------------------------------------------")
print(sys_siso_01)
print("sys_siso_10 ---------------------------------------------")
print(sys_siso_10)
#gain of converted system and equivalent SISO system must be the same
self.assert_systems_behave_equal(sys_siso, sys_siso_01)
self.assert_systems_behave_equal(sys_siso, sys_siso_10)
def testConvert(self, fixedseed, states, inputs, outputs):
"""Test state space to transfer function conversion.
start with a random SS system and transform to TF then
back to SS, check that the matrices are the same.
"""
ssOriginal = rss(states, outputs, inputs)
if verbose:
self.printSys(ssOriginal, 1)
# Make sure the system is not degenerate
Cmat = ctrb(ssOriginal.A, ssOriginal.B)
if (np.linalg.matrix_rank(Cmat) != states):
pytest.skip("not reachable")
Omat = obsv(ssOriginal.A, ssOriginal.C)
if (np.linalg.matrix_rank(Omat) != states):
pytest.skip("not observable")
tfOriginal = tf(ssOriginal)
if (verbose):
self.printSys(tfOriginal, 2)
ssTransformed = ss(tfOriginal)
if (verbose):
self.printSys(ssTransformed, 3)
tfTransformed = tf(ssTransformed)
if (verbose):
self.printSys(tfTransformed, 4)
# Check to see if the state space systems have same dim
if (ssOriginal.nstates != ssTransformed.nstates) and verbose:
print("WARNING: state space dimension mismatch: %d versus %d" %
(ssOriginal.nstates, ssTransformed.nstates))
# Now make sure the frequency responses match
# Since bode() only handles SISO, go through each I/O pair
# For phase, take sine and cosine to avoid +/- 360 offset
for inputNum in range(inputs):
for outputNum in range(outputs):
if (verbose):
print("Checking input %d, output %d"
% (inputNum, outputNum))
ssorig_mag, ssorig_phase, ssorig_omega = \
bode(_mimo2siso(ssOriginal, inputNum, outputNum),
deg=False, plot=False)
ssorig_real = ssorig_mag * np.cos(ssorig_phase)
ssorig_imag = ssorig_mag * np.sin(ssorig_phase)
#
# Make sure TF has same frequency response
#
num = tfOriginal.num[outputNum][inputNum]
den = tfOriginal.den[outputNum][inputNum]
tforig = tf(num, den)
tforig_mag, tforig_phase, tforig_omega = \
bode(tforig, ssorig_omega,
deg=False, plot=False)
tforig_real = tforig_mag * np.cos(tforig_phase)
tforig_imag = tforig_mag * np.sin(tforig_phase)
np.testing.assert_array_almost_equal(
ssorig_real, tforig_real)
np.testing.assert_array_almost_equal(
ssorig_imag, tforig_imag)
#
# Make sure xform'd SS has same frequency response
#
ssxfrm_mag, ssxfrm_phase, ssxfrm_omega = \
bode(_mimo2siso(ssTransformed,
inputNum, outputNum),
ssorig_omega,
deg=False, plot=False)
ssxfrm_real = ssxfrm_mag * np.cos(ssxfrm_phase)
ssxfrm_imag = ssxfrm_mag * np.sin(ssxfrm_phase)
np.testing.assert_array_almost_equal(
ssorig_real, ssxfrm_real, decimal=5)
np.testing.assert_array_almost_equal(
ssorig_imag, ssxfrm_imag, decimal=5)
# Make sure xform'd TF has same frequency response
#
num = tfTransformed.num[outputNum][inputNum]
den = tfTransformed.den[outputNum][inputNum]
tfxfrm = tf(num, den)
tfxfrm_mag, tfxfrm_phase, tfxfrm_omega = \
bode(tfxfrm, ssorig_omega,
deg=False, plot=False)
tfxfrm_real = tfxfrm_mag * np.cos(tfxfrm_phase)
tfxfrm_imag = tfxfrm_mag * np.sin(tfxfrm_phase)
np.testing.assert_array_almost_equal(
ssorig_real, tfxfrm_real, decimal=5)
np.testing.assert_array_almost_equal(
ssorig_imag, tfxfrm_imag, decimal=5)
def impulse_response(sys,
T=None,
X0=0.,
input=0,
output=None,
transpose=False,
**keywords):
#pylint: disable=W0622
"""Impulse response of a linear system
If the system has multiple inputs or outputs (MIMO), one input and one
output have to be selected for the simulation. The parameters `input`
and `output` do this. All other inputs are set to 0, all other outputs
are ignored.
For information on the **shape** of parameters `T`, `X0` and
return values `T`, `yout` see: :ref:`time-series-convention`
Parameters
----------
sys: StateSpace, TransferFunction
LTI system to simulate
T: array-like object, optional
Time vector (argument is autocomputed if not given)
X0: array-like object or number, optional
Initial condition (default = 0)
Numbers are converted to constant arrays with the correct shape.
input: int
Index of the input that will be used in this simulation.
output: int
Index of the output that will be used in this simulation. Set to None
to not trim outputs
transpose: bool
If True, transpose all input and output arrays (for backward
compatibility with MATLAB and scipy.signal.lsim)
**keywords:
Additional keyword arguments control the solution algorithm for the
differential equations. These arguments are passed on to the function
:func:`lsim`, which in turn passes them on to
:func:`scipy.integrate.odeint`. See the documentation for
:func:`scipy.integrate.odeint` for information about these
arguments.
Returns
-------
T: array
Time values of the output
yout: array
Response of the system
See Also
--------
ForcedReponse, initial_response, step_response
Examples
--------
>>> T, yout = impulse_response(sys, T, X0)
"""
sys = _convertToStateSpace(sys)
if output == None:
sys = _mimo2simo(sys, input, warn_conversion=True)
else:
sys = _mimo2siso(sys, input, output, warn_conversion=True)
# System has direct feedthrough, can't simulate impulse response numerically
if np.any(sys.D != 0) and isctime(sys):
warnings.warn(
'System has direct feedthrough: ``D != 0``. The infinite '
'impulse at ``t=0`` does not appear in the output. \n'
'Results may be meaningless!')
# create X0 if not given, test if X0 has correct shape.
# Must be done here because it is used for computations here.
n_states = sys.A.shape[0]
X0 = _check_convert_array(X0, [(n_states, ), (n_states, 1)],
'Parameter ``X0``: \n',
squeeze=True)
# Compute new X0 that contains the impulse
# We can't put the impulse into U because there is no numerical
# representation for it (infinitesimally short, infinitely high).
# See also: http://www.mathworks.com/support/tech-notes/1900/1901.html
B = np.asarray(sys.B).squeeze()
new_X0 = B + X0
# Compute T and U, no checks necessary, they will be checked in lsim
if T is None:
T = _default_response_times(sys.A, 100)
U = np.zeros_like(T)
T, yout, _xout = forced_response(sys, T, U, new_X0, \
transpose=transpose, **keywords)
return T, yout
def initial_response(sys,
T=None,
X0=0.,
input=0,
output=None,
transpose=False,
**keywords):
#pylint: disable=W0622
"""Initial condition response of a linear system
If the system has multiple inputs or outputs (MIMO), one input and one
output have to be selected for the simulation. The parameters `input`
and `output` do this. All other inputs are set to 0, all other outputs
are ignored.
For information on the **shape** of parameters `T`, `X0` and
return values `T`, `yout` see: :ref:`time-series-convention`
Parameters
----------
sys: StateSpace, or TransferFunction
LTI system to simulate
T: array-like object, optional
Time vector (argument is autocomputed if not given)
X0: array-like object or number, optional
Initial condition (default = 0)
Numbers are converted to constant arrays with the correct shape.
input: int
Index of the input that will be used in this simulation.
output: int
Index of the output that will be used in this simulation. Set to None
to not trim outputs
transpose: bool
If True, transpose all input and output arrays (for backward
compatibility with MATLAB and scipy.signal.lsim)
**keywords:
Additional keyword arguments control the solution algorithm for the
differential equations. These arguments are passed on to the function
:func:`lsim`, which in turn passes them on to
:func:`scipy.integrate.odeint`. See the documentation for
:func:`scipy.integrate.odeint` for information about these
arguments.
Returns
-------
T: array
Time values of the output
yout: array
Response of the system
See Also
--------
forced_response, impulse_response, step_response
Examples
--------
>>> T, yout = initial_response(sys, T, X0)
"""
sys = _convertToStateSpace(sys)
if output == None:
sys = _mimo2simo(sys, input, warn_conversion=False)
else:
sys = _mimo2siso(sys, input, output, warn_conversion=False)
# Create time and input vectors; checking is done in forced_response(...)
# The initial vector X0 is created in forced_response(...) if necessary
if T is None:
T = _default_response_times(sys.A, 100)
U = np.zeros_like(T)
T, yout, _xout = forced_response(sys,
T,
U,
X0,
transpose=transpose,
**keywords)
return T, yout
