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dtime.py
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"""dtime.py
Functions for manipulating discrete time systems.
Routines in this module:
sample_system()
c2d()
"""
"""Copyright (c) 2012 by California Institute of Technology
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. Neither the name of the California Institute of Technology nor
the names of its contributors may be used to endorse or promote
products derived from this software without specific prior
written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL CALTECH
OR THE CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
SUCH DAMAGE.
Author: Richard M. Murray
Date: 6 October 2012
$Id: dtime.py 185 2012-08-30 05:44:32Z murrayrm $
"""
from .namedio import isctime
from .statesp import StateSpace
__all__ = ['sample_system', 'c2d']
# Sample a continuous time system
def sample_system(sysc, Ts, method='zoh', alpha=None, prewarp_frequency=None,
name=None, copy_names=True, **kwargs):
"""
Convert a continuous time system to discrete time by sampling
Parameters
----------
sysc : LTI (:class:`StateSpace` or :class:`TransferFunction`)
Continuous time system to be converted
Ts : float > 0
Sampling period
method : string
Method to use for conversion, e.g. 'bilinear', 'zoh' (default)
alpha : float within [0, 1]
The generalized bilinear transformation weighting parameter, which
should only be specified with method="gbt", and is ignored
otherwise. See :func:`scipy.signal.cont2discrete`.
prewarp_frequency : float within [0, infinity)
The frequency [rad/s] at which to match with the input continuous-
time system's magnitude and phase (only valid for method='bilinear')
name : string, optional
Set the name of the sampled system. If not specified and
if `copy_names` is `False`, a generic name <sys[id]> is generated
with a unique integer id. If `copy_names` is `True`, the new system
name is determined by adding the prefix and suffix strings in
config.defaults['namedio.sampled_system_name_prefix'] and
config.defaults['namedio.sampled_system_name_suffix'], with the
default being to add the suffix '$sampled'.
copy_names : bool, Optional
If True, copy the names of the input signals, output
signals, and states to the sampled system.
Returns
-------
sysd : linsys
Discrete time system, with sampling rate Ts
Other Parameters
----------------
inputs : int, list of str or None, optional
Description of the system inputs. If not specified, the origional
system inputs are used. See :class:`InputOutputSystem` for more
information.
outputs : int, list of str or None, optional
Description of the system outputs. Same format as `inputs`.
states : int, list of str, or None, optional
Description of the system states. Same format as `inputs`. Only
available if the system is :class:`StateSpace`.
Notes
-----
See :meth:`StateSpace.sample` or :meth:`TransferFunction.sample` for
further details.
Examples
--------
>>> sysc = TransferFunction([1], [1, 2, 1])
>>> sysd = sample_system(sysc, 1, method='bilinear')
"""
# Make sure we have a continuous time system
if not isctime(sysc):
raise ValueError("First argument must be continuous time system")
return sysc.sample(Ts,
method=method, alpha=alpha, prewarp_frequency=prewarp_frequency,
name=name, copy_names=copy_names, **kwargs)
def c2d(sysc, Ts, method='zoh', prewarp_frequency=None):
"""
Convert a continuous time system to discrete time by sampling
Parameters
----------
sysc : LTI (:class:`StateSpace` or :class:`TransferFunction`)
Continuous time system to be converted
Ts : float > 0
Sampling period
method : string
Method to use for conversion, e.g. 'bilinear', 'zoh' (default)
prewarp_frequency : real within [0, infinity)
The frequency [rad/s] at which to match with the input continuous-
time system's magnitude and phase (only valid for method='bilinear')
Returns
-------
sysd : LTI of the same class
Discrete time system, with sampling rate Ts
Notes
-----
See :meth:`StateSpace.sample` or :meth:`TransferFunction.sample`` for
further details.
Examples
--------
>>> sysc = TransferFunction([1], [1, 2, 1])
>>> sysd = sample_system(sysc, 1, method='bilinear')
"""
# Call the sample_system() function to do the work
sysd = sample_system(sysc, Ts,
method=method, prewarp_frequency=prewarp_frequency)
return sysd