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Add support for discrete systems to lti/damp #175

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Merged
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Jan 3, 2018
Merged

Add support for discrete systems to lti/damp #175

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23 changes: 21 additions & 2 deletions control/lti.py
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Original file line number Diff line number Diff line change
Expand Up @@ -86,8 +86,13 @@ def issiso(self):

def damp(self):
poles = self.pole()
wn = absolute(poles)
Z = -real(poles)/wn

if isdtime(self, strict=True):
splane_poles = np.log(poles)/self.dt
else:
splane_poles = poles
wn = absolute(splane_poles)
Z = -real(splane_poles)/wn
return wn, Z, poles

def dcgain(self):
Expand Down Expand Up @@ -280,6 +285,20 @@ def damp(sys, doprint=True):
poles: array
Pole locations


Algorithm
--------
If the system is continuous,
wn = abs(poles)
Z = -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
and
wn = abs(s)
Z = -real(s)/wn.

See Also
--------
pole
Expand Down
11 changes: 11 additions & 0 deletions control/tests/lti_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,7 @@
import numpy as np
from control.lti import *
from control.xferfcn import tf
from control import c2d
import numpy as np

class TestUtils(unittest.TestCase):
Expand All @@ -18,6 +19,7 @@ def test_zero(self):
np.testing.assert_equal(zero(sys), 42)

def test_damp(self):
# Test the continuous time case.
zeta = 0.1
wn = 42
p = -wn * zeta + 1j * wn * np.sqrt(1 - zeta**2)
Expand All @@ -26,6 +28,15 @@ def test_damp(self):
np.testing.assert_equal(sys.damp(), expected)
np.testing.assert_equal(damp(sys), expected)

# Also test the discrete time case.
dt = 0.001
sys_dt = c2d(sys, dt, method='matched')
p_zplane = np.exp(p*dt)
expected_dt = ([wn, wn], [zeta, zeta],
[p_zplane, p_zplane.conjugate()])
np.testing.assert_almost_equal(sys_dt.damp(), expected_dt)
np.testing.assert_almost_equal(damp(sys_dt), expected_dt)

def test_dcgain(self):
sys = tf(84, [1, 2])
np.testing.assert_equal(sys.dcgain(), 42)
Expand Down