diff --git a/control/rlocus.py b/control/rlocus.py
index ee30fe489..4b1af57f7 100644
--- a/control/rlocus.py
+++ b/control/rlocus.py
@@ -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(
@@ -180,7 +180,7 @@ 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)))
@@ -188,7 +188,7 @@ def root_locus(sys, kvect=None, xlim=None, ylim=None,
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',
@@ -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')
@@ -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
diff --git a/control/sisotool.py b/control/sisotool.py
index 18c3b5d12..5accd1453 100644
--- a/control/sisotool.py
+++ b/control/sisotool.py
@@ -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
@@ -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, minster@uw.edu 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)
diff --git a/control/tests/lti_test.py b/control/tests/lti_test.py
index 7e4f0ddb4..e2f7f2e03 100644
--- a/control/tests/lti_test.py
+++ b/control/tests/lti_test.py
@@ -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)
@@ -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
diff --git a/control/tests/sisotool_test.py b/control/tests/sisotool_test.py
index ab5d546dd..fb2ac46e5 100644
--- a/control/tests/sisotool_test.py
+++ b/control/tests/sisotool_test.py
@@ -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:
@@ -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)
+
diff --git a/doc/control.rst b/doc/control.rst
index a3e28881b..4b18cfb53 100644
--- a/doc/control.rst
+++ b/doc/control.rst
@@ -124,6 +124,7 @@ Control system synthesis
lqe
mixsyn
place
+ rlocus_pid_designer
Model simplification tools
==========================
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