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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.

# 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

__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

--------

>>> import numpy as np

>>> theta = [5.74, 5.97, 6.19, 0.13, 0.35, 0.57]

>>> unwrap(theta, period=2 * np.pi)

[5.74, 5.97, 6.19, 6.413185307179586, 6.633185307179586, 6.8531853071795865]

"""

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 system, otherwise False"""

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

"""

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

"""

return 20. * np.log10(mag)