GeezerVison is showing github.com — new Pid design function built on sisotool by sawyerbfuller · Pull Request #662 · python-control/python-control
new Pid design function built on sisotool
#662
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3263646
new pid-designer, built on sisotool, for manual tuning of a PID contr…
sawyerbfuller Nov 2, 2021
c4bd384
attribution
sawyerbfuller Nov 2, 2021
ffd7b5f
changed color of root locus pole markers to black instead of randomly…
sawyerbfuller Nov 2, 2021
cd7faaa
fixed unit test code
sawyerbfuller Nov 2, 2021
ec0f0a8
renamed function to highlight that it is based on root locus, set ini…
sawyerbfuller Nov 4, 2021
3dca645
fix for github #623
sawyerbfuller Nov 4, 2021
5c3e823
added pointer to new function to docs
sawyerbfuller Nov 5, 2021
2af1171
more comprehensive system construction tests
sawyerbfuller Nov 5, 2021
746e089
return loop transfer function as statespace
sawyerbfuller Nov 5, 2021
4ee9fd1
small docstring fix
sawyerbfuller Nov 5, 2021
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Original file line number
Diff line number
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Expand Up
@@ -168,8 +168,8 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
else:
if ax is None:
ax = plt.gca()
fig = ax.figure
ax.set_title('Root Locus')
fig = ax.figure
ax.set_title('Root Locus')
if print_gain and not sisotool:
fig.canvas.mpl_connect(
Expand All
@@ -180,15 +180,15 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
fig.axes[1].plot(
[root.real for root in start_mat],
[root.imag for root in start_mat],
marker='s', markersize=8 , zorder=20, label='gain_point')
marker='s', markersize=6 , zorder=20, color='k' , label='gain_point')
s = start_mat[0][0]
if isdtime(sys, strict=True):
zeta = -np.cos(np.angle(np.log(s)))
else:
zeta = -1 * s.real / abs(s)
fig.suptitle(
"Clicked at: %10.4g%+10.4gj gain: %10.4g damp: %10.4g" %
(s.real, s.imag, 1 , zeta),
(s.real, s.imag, kvect[0] , zeta),
fontsize=12 if int(mpl.__version__[0]) == 1 else 10)
fig.canvas.mpl_connect(
'button_release_event',
Expand Down
Expand Up
@@ -623,7 +623,7 @@ def _RLFeedbackClicksPoint(event, sys, fig, ax_rlocus, sisotool=False):
ax_rlocus.plot(
[root.real for root in mymat],
[root.imag for root in mymat],
marker='s', markersize=8 , zorder=20, label='gain_point')
marker='s', markersize=6 , zorder=20, label='gain_point', color='k ')
else:
ax_rlocus.plot(s.real, s.imag, 'k.', marker='s', markersize=8,
zorder=20, label='gain_point')
Expand Down
Expand Up
@@ -769,7 +769,7 @@ def _default_wn(xloc, yloc, max_lines=7):
"""
sep = xloc[1]-xloc[0] # separation between x-ticks
# Decide whether to use the x or y axis for determining wn
if yloc[-1] / sep > max_lines*10:
# y-axis scale >> x-axis scale
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Original file line number
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@@ -1,11 +1,15 @@
__all__ = ['sisotool']
__all__ = ['sisotool', 'rootlocus_pid_designer' ]
from control.exception import ControlMIMONotImplemented
from .freqplot import bode_plot
from .timeresp import step_response
from .lti import issiso, isdtime
from .xferfcn import TransferFunction
from .xferfcn import tf
from .statesp import ss
from .bdalg import append, connect
from .iosys import tf2io, ss2io, summing_junction, interconnect
from control.statesp import _convert_to_statespace, StateSpace
from control.lti import common_timebase, isctime
import matplotlib
import matplotlib.pyplot as plt
import warnings
Expand Down
Expand Up
@@ -176,3 +180,156 @@ def _SisotoolUpdate(sys, fig, K, bode_plot_params, tvect=None):
fig.subplots_adjust(top=0.9,wspace = 0.3,hspace=0.35)
fig.canvas.draw()
# contributed by Sawyer Fuller, [email protected] 2021.11.02, based on
# an implementation in Matlab by Martin Berg.
def rootlocus_pid_designer(plant, gain='P', sign=+1, input_signal='r',
Kp0=0, Ki0=0, Kd0=0, tau=0.01,
C_ff=0, derivative_in_feedback_path=False,
plot=True):
"""Manual PID controller design based on root locus using Sisotool
Uses `Sisotool` to investigate the effect of adding or subtracting an
amount `deltaK` to the proportional, integral, or derivative (PID) gains of
a controller. One of the PID gains, `Kp`, `Ki`, or `Kd`, respectively, can
be modified at a time. `Sisotool` plots the step response, frequency
response, and root locus.
When first run, `deltaK` is set to 0; click on a branch of the root locus
plot to try a different value. Each click updates plots and prints
the corresponding `deltaK`. To tune all three PID gains, repeatedly call
`rootlocus_pid_designer`, and select a different `gain` each time (`'P'`,
`'I'`, or `'D'`). Make sure to add the resulting `deltaK` to your chosen
initial gain on the next iteration.
Example: to examine the effect of varying `Kp` starting from an intial
value of 10, use the arguments `gain='P', Kp0=10`. Suppose a `deltaK`
value of 5 gives satisfactory performance. Then on the next iteration,
to tune the derivative gain, use the arguments `gain='D', Kp0=15`.
By default, all three PID terms are in the forward path C_f in the diagram
shown below, that is,
C_f = Kp + Ki/s + Kd*s/(tau*s + 1).
If `plant` is a discrete-time system, then the proportional, integral, and
derivative terms are given instead by Kp, Ki*dt/2*(z+1)/(z-1), and
Kd/dt*(z-1)/z, respectively.
------> C_ff ------ d
| | |
r | e V V u y
------->O---> C_f --->O--->O---> plant --->
^- ^- |
| | |
| ----- C_b <-------|
---------------------------------
It is also possible to move the derivative term into the feedback path
`C_b` using `derivative_in_feedback_path=True`. This may be desired to
avoid that the plant is subject to an impulse function when the reference
`r` is a step input. `C_b` is otherwise set to zero.
If `plant` is a 2-input system, the disturbance `d` is fed directly into
its second input rather than being added to `u`.
Remark: It may be helpful to zoom in using the magnifying glass on the
plot. Just ake sure to deactivate magnification mode when you are done by
clicking the magnifying glass. Otherwise you will not be able to be able to choose
a gain on the root locus plot.
Parameters
----------
plant : :class:`LTI` (:class:`TransferFunction` or :class:`StateSpace` system)
The dynamical system to be controlled
gain : string (optional)
Which gain to vary by `deltaK`. Must be one of `'P'`, `'I'`, or `'D'`
(proportional, integral, or derative)
sign : int (optional)
The sign of deltaK gain perturbation
input : string (optional)
The input used for the step response; must be `'r'` (reference) or
`'d'` (disturbance) (see figure above)
Kp0, Ki0, Kd0 : float (optional)
Initial values for proportional, integral, and derivative gains,
respectively
tau : float (optional)
The time constant associated with the pole in the continuous-time
derivative term. This is required to make the derivative transfer
function proper.
C_ff : float or :class:`LTI` system (optional)
Feedforward controller. If :class:`LTI`, must have timebase that is
compatible with plant.
derivative_in_feedback_path : bool (optional)
Whether to place the derivative term in feedback transfer function
`C_b` instead of the forward transfer function `C_f`.
plot : bool (optional)
Whether to create Sisotool interactive plot.
Returns
----------
closedloop : class:`StateSpace` system
The closed-loop system using initial gains.
"""
plant = _convert_to_statespace(plant)
if plant.ninputs == 1:
plant = ss2io(plant, inputs='u', outputs='y')
elif plant.ninputs == 2:
plant = ss2io(plant, inputs=['u', 'd'], outputs='y')
else:
raise ValueError("plant must have one or two inputs")
C_ff = ss2io(_convert_to_statespace(C_ff), inputs='r', outputs='uff')
dt = common_timebase(plant, C_ff)
# create systems used for interconnections
e_summer = summing_junction(['r', '-y'], 'e')
if plant.ninputs == 2:
u_summer = summing_junction(['ufb', 'uff'], 'u')
else:
u_summer = summing_junction(['ufb', 'uff', 'd'], 'u')
if isctime(plant):
prop = tf(1, 1)
integ = tf(1, [1, 0])
deriv = tf([1, 0], [tau, 1])
else: # discrete-time
prop = tf(1, 1, dt)
integ = tf([dt/2, dt/2], [1, -1], dt)
deriv = tf([1, -1], [dt, 0], dt)
# add signal names by turning into iosystems
prop = tf2io(prop, inputs='e', outputs='prop_e')
integ = tf2io(integ, inputs='e', outputs='int_e')
if derivative_in_feedback_path:
deriv = tf2io(-deriv, inputs='y', outputs='deriv')
else:
deriv = tf2io(deriv, inputs='e', outputs='deriv')
# create gain blocks
Kpgain = tf2io(tf(Kp0, 1), inputs='prop_e', outputs='ufb')
Kigain = tf2io(tf(Ki0, 1), inputs='int_e', outputs='ufb')
Kdgain = tf2io(tf(Kd0, 1), inputs='deriv', outputs='ufb')
# for the gain that is varied, replace gain block with a special block
# that has an 'input' and an 'output' that creates loop transfer function
if gain in ('P', 'p'):
Kpgain = ss2io(ss([],[],[],[[0, 1], [-sign, Kp0]]),
inputs=['input', 'prop_e'], outputs=['output', 'ufb'])
elif gain in ('I', 'i'):
Kigain = ss2io(ss([],[],[],[[0, 1], [-sign, Ki0]]),
inputs=['input', 'int_e'], outputs=['output', 'ufb'])
elif gain in ('D', 'd'):
Kdgain = ss2io(ss([],[],[],[[0, 1], [-sign, Kd0]]),
inputs=['input', 'deriv'], outputs=['output', 'ufb'])
else:
raise ValueError(gain + ' gain not recognized.')
# the second input and output are used by sisotool to plot step response
loop = interconnect((plant, Kpgain, Kigain, Kdgain, prop, integ, deriv,
C_ff, e_summer, u_summer),
inplist=['input', input_signal],
outlist=['output', 'y'])
if plot:
sisotool(loop, kvect=(0.,))
cl = loop[1, 1] # closed loop transfer function with initial gains
return StateSpace(cl.A, cl.B, cl.C, cl.D, cl.dt)
Original file line number
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Expand Up
@@ -77,7 +77,7 @@ def test_damp(self):
p2_splane = -wn2 * zeta2 + 1j * wn2 * np.sqrt(1 - zeta2**2)
p2_zplane = np.exp(p2_splane * dt)
np.testing.assert_almost_equal(p2, p2_zplane)
def test_dcgain(self):
sys = tf(84, [1, 2])
np.testing.assert_allclose(sys.dcgain(), 42)
Expand Down
Expand Up
@@ -136,7 +136,7 @@ def test_common_timebase(self, dt1, dt2, expected, sys1, sys2):
(0, 1),
(1, 2)])
def test_common_timebase_errors(self, i1, i2):
"""Test that common_timbase throws errors on invalid combinations"""
"""Test that common_timbase raises errors on invalid combinations"""
with pytest.raises(ValueError):
common_timebase(i1, i2)
# Make sure behaviour is symmetric
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Expand Up
@@ -6,11 +6,11 @@
from numpy.testing import assert_array_almost_equal
import pytest
from control.sisotool import sisotool
from control.sisotool import sisotool, rootlocus_pid_designer
from control.rlocus import _RLClickDispatcher
from control.xferfcn import TransferFunction
from control.statesp import StateSpace
from control import c2d
@pytest.mark.usefixtures("mplcleanup")
class TestSisotool:
Expand Down
Expand Up
@@ -140,3 +140,40 @@ def test_sisotool_mimo(self, sys222, sys221):
# but 2 input, 1 output should
with pytest.raises(ControlMIMONotImplemented):
sisotool(sys221)
@pytest.mark.usefixtures("mplcleanup")
class TestPidDesigner:
@pytest.fixture
def plant(self, request):
plants = {
'syscont':TransferFunction(1,[1, 3, 0]),
'sysdisc1':c2d(TransferFunction(1,[1, 3, 0]), .1),
'syscont221':StateSpace([[-.3, 0],[1,0]],[[-1,],[.1,]], [0, -.3], 0)}
return plants[request.param]
# test permutations of system construction without plotting
@pytest.mark.parametrize('plant', ('syscont', 'sysdisc1', 'syscont221'), indirect=True)
@pytest.mark.parametrize('gain', ('P', 'I', 'D'))
@pytest.mark.parametrize('sign', (1,))
@pytest.mark.parametrize('input_signal', ('r', 'd'))
@pytest.mark.parametrize('Kp0', (0,))
@pytest.mark.parametrize('Ki0', (1.,))
@pytest.mark.parametrize('Kd0', (0.1,))
@pytest.mark.parametrize('tau', (0.01,))
@pytest.mark.parametrize('C_ff', (0, 1,))
@pytest.mark.parametrize('derivative_in_feedback_path', (True, False,))
@pytest.mark.parametrize("kwargs", [{'plot':False},])
def test_pid_designer_1(self, plant, gain, sign, input_signal, Kp0, Ki0, Kd0, tau, C_ff,
derivative_in_feedback_path, kwargs):
rootlocus_pid_designer(plant, gain, sign, input_signal, Kp0, Ki0, Kd0, tau, C_ff,
derivative_in_feedback_path, **kwargs)
# test creation of sisotool plot
# input from reference or disturbance
@pytest.mark.parametrize('plant', ('syscont', 'syscont221'), indirect=True)
@pytest.mark.parametrize("kwargs", [
{'input_signal':'r', 'Kp0':0.01, 'derivative_in_feedback_path':True},
{'input_signal':'d', 'Kp0':0.01, 'derivative_in_feedback_path':True},])
def test_pid_designer_2(self, plant, kwargs):
rootlocus_pid_designer(plant, **kwargs)
Original file line number
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Expand Up
@@ -124,6 +124,7 @@ Control system synthesis
lqe
mixsyn
place
rlocus_pid_designer
Model simplification tools
==========================
Expand Down
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