diff --git a/control/lti.py b/control/lti.py
index 216332e91..c904c1509 100644
--- a/control/lti.py
+++ b/control/lti.py
@@ -2,22 +2,14 @@
The lti module contains the LTI parent class to the child classes StateSpace
and TransferFunction. It is designed for use in the python-control library.
-
-Routines in this module:
-
-LTI.__init__
-isdtime()
-isctime()
-timebase()
-common_timebase()
"""
import numpy as np
-from numpy import absolute, real, angle, abs
+from numpy import real, angle, abs
from warnings import warn
from . import config
-from .namedio import NamedIOSystem, isdtime
+from .namedio import NamedIOSystem
__all__ = ['poles', 'zeros', 'damp', 'evalfr', 'frequency_response',
'freqresp', 'dcgain', 'bandwidth', 'pole', 'zero']
@@ -110,11 +102,11 @@ def damp(self):
Returns
-------
wn : array
- Natural frequencies for each system pole
+ Natural frequency for each system pole
zeta : array
Damping ratio for each system pole
poles : array
- Array of system poles
+ System pole locations
'''
poles = self.poles()
@@ -122,9 +114,9 @@ def damp(self):
splane_poles = np.log(poles.astype(complex))/self.dt
else:
splane_poles = poles
- wn = absolute(splane_poles)
- Z = -real(splane_poles)/wn
- return wn, Z, poles
+ wn = abs(splane_poles)
+ zeta = -real(splane_poles)/wn
+ return wn, zeta, poles
def frequency_response(self, omega, squeeze=None):
"""Evaluate the linear time-invariant system at an array of angular
@@ -346,25 +338,23 @@ def zero(sys):
def damp(sys, doprint=True):
"""
- Compute natural frequency, damping ratio, and poles of a system
-
- The function takes 1 or 2 parameters
+ Compute natural frequencies, damping ratios, and poles of a system
Parameters
----------
- sys: LTI (StateSpace or TransferFunction)
+ sys : LTI (StateSpace or TransferFunction)
A linear system object
- doprint:
- if true, print table with values
+ doprint : bool (optional)
+ if True, print table with values
Returns
-------
- wn: array
- Natural frequencies of the poles
- damping: array
- Damping values
- poles: array
- Pole locations
+ wn : array
+ Natural frequency for each system pole
+ zeta : array
+ Damping ratio for each system pole
+ poles : array
+ System pole locations
See Also
--------
@@ -374,37 +364,37 @@ def damp(sys, doprint=True):
-----
If the system is continuous,
wn = abs(poles)
- Z = -real(poles)/poles.
+ zeta = -real(poles)/poles
If the system is discrete, the discrete poles are mapped to their
equivalent location in the s-plane via
- s = log10(poles)/dt
+ s = log(poles)/dt
and
wn = abs(s)
- Z = -real(s)/wn.
+ zeta = -real(s)/wn.
Examples
--------
>>> G = ct.tf([1], [1, 4])
- >>> wn, damping, poles = ct.damp(G)
- _____Eigenvalue______ Damping___ Frequency_
- -4 1 4
+ >>> wn, zeta, poles = ct.damp(G)
+ Eigenvalue (pole) Damping Frequency
+ -4 1 4
"""
- wn, damping, poles = sys.damp()
+ wn, zeta, poles = sys.damp()
if doprint:
- print('_____Eigenvalue______ Damping___ Frequency_')
- for p, d, w in zip(poles, damping, wn):
+ print(' Eigenvalue (pole) Damping Frequency')
+ for p, z, w in zip(poles, zeta, wn):
if abs(p.imag) < 1e-12:
- print("%10.4g %10.4g %10.4g" %
- (p.real, 1.0, -p.real))
+ print(" %10.4g %10.4g %10.4g" %
+ (p.real, 1.0, w))
else:
- print("%10.4g%+10.4gj %10.4g %10.4g" %
- (p.real, p.imag, d, w))
- return wn, damping, poles
+ print("%10.4g%+10.4gj %10.4g %10.4g" %
+ (p.real, p.imag, z, w))
+ return wn, zeta, poles
def evalfr(sys, x, squeeze=None):
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