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ctrlutil.py
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ctrlutil.py
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# ctrlutil.py - control system utility functions
#
# Author: Richard M. Murray
# Date: 24 May 09
#
# These are some basic utility functions that are used in the control
# systems library and that didn't naturally fit anyplace else.
#
# Copyright (c) 2009 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.
#
# $Id$
# Packages that we need access to
from . import lti
import numpy as np
import math
import warnings
__all__ = ['unwrap', 'issys', 'db2mag', 'mag2db']
# Utility function to unwrap an angle measurement
def unwrap(angle, period=2*math.pi):
"""Unwrap a phase angle to give a continuous curve
Parameters
----------
angle : array_like
Array of angles to be unwrapped
period : float, optional
Period (defaults to `2*pi`)
Returns
-------
angle_out : array_like
Output array, with jumps of period/2 eliminated
Examples
--------
>>> # Already continuous
>>> theta1 = np.array([1.0, 1.5, 2.0, 2.5, 3.0]) * np.pi
>>> theta2 = ct.unwrap(theta1)
>>> theta2/np.pi # doctest: +SKIP
array([1. , 1.5, 2. , 2.5, 3. ])
>>> # Wrapped, discontinuous
>>> theta1 = np.array([1.0, 1.5, 0.0, 0.5, 1.0]) * np.pi
>>> theta2 = ct.unwrap(theta1)
>>> theta2/np.pi # doctest: +SKIP
array([1. , 1.5, 2. , 2.5, 3. ])
"""
dangle = np.diff(angle)
dangle_desired = (dangle + period/2.) % period - period/2.
correction = np.cumsum(dangle_desired - dangle)
angle[1:] += correction
return angle
def issys(obj):
"""Return True if an object is a Linear Time Invariant (LTI) system,
otherwise False
Examples
--------
>>> G = ct.tf([1], [1, 1])
>>> ct.issys(G)
True
>>> K = np.array([[1, 1]])
>>> ct.issys(K)
False
"""
warnings.warn("issys() is deprecated; use isinstance(obj, ct.LTI)",
FutureWarning, stacklevel=2)
return isinstance(obj, lti.LTI)
def db2mag(db):
"""Convert a gain in decibels (dB) to a magnitude
If A is magnitude,
db = 20 * log10(A)
Parameters
----------
db : float or ndarray
input value or array of values, given in decibels
Returns
-------
mag : float or ndarray
corresponding magnitudes
Examples
--------
>>> ct.db2mag(-40.0) # doctest: +SKIP
0.01
>>> ct.db2mag(np.array([0, -20])) # doctest: +SKIP
array([1. , 0.1])
"""
return 10. ** (db / 20.)
def mag2db(mag):
"""Convert a magnitude to decibels (dB)
If A is magnitude,
db = 20 * log10(A)
Parameters
----------
mag : float or ndarray
input magnitude or array of magnitudes
Returns
-------
db : float or ndarray
corresponding values in decibels
Examples
--------
>>> ct.mag2db(10.0) # doctest: +SKIP
20.0
>>> ct.mag2db(np.array([1, 0.01])) # doctest: +SKIP
array([ 0., -40.])
"""
return 20. * np.log10(mag)