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autotune: add structural mode #47

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f03d677
autotune: show stability margins on bode plot
bresch Nov 10, 2025
3025eb0
autotune: add option to set a structural mode
bresch Nov 11, 2025
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188 changes: 168 additions & 20 deletions autotune/autotune.py
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Original file line number Diff line number Diff line change
Expand Up @@ -77,6 +77,28 @@
from system_identification import SystemIdentification


def create2ndOrderLpf(fc, zeta, fs):
T = 1.0 / fs
wn = 2.0 * np.pi * fc
K = wn / np.tan(wn * T / 2.0)
K2 = K**2
b2a = wn**2
a0a = 1.0
a1a = 2.0 * zeta * wn
a2a = wn**2
D = a0a * K2 + a1a * K + a2a
b0_prime = b2a
b1_prime = 2.0 * b2a
b2_prime = b2a
a0_prime = D
a1_prime = 2.0 * a2a - 2.0 * K2
a2_prime = a0a * K2 - a1a * K + a2a

b = [b0_prime / D, b1_prime / D, b2_prime / D]
a = [a0_prime / D, a1_prime / D, a2_prime / D]
return b, a


def isNumber(value):
try:
float(value)
Expand All @@ -93,7 +115,7 @@ def __init__(self, parent=None):
self.input_ref = None
self.closed_loop_ref = None
self.closed_loop_ax = None
self.bode_plot_ref = None
self.bode_plot_ref = []
self.pz_plot_refs = []
self.file_name = None
self.is_system_identified = False
Expand All @@ -110,6 +132,8 @@ def __init__(self, parent=None):
self.sys_id_delays = 1
self.sys_id_n_zeros = 2
self.sys_id_n_poles = 2
self.cutoff_freq = 0.0
self.damping_ratio = 0.0

# this is the Canvas Widget that displays the `figure`
# it takes the `figure` instance as a parameter to __init__
Expand Down Expand Up @@ -198,6 +222,10 @@ def __init__(self, parent=None):
self.tab_gmvc.setLayout(self.createGmvcLayout())
self.tuning_tabs.addTab(self.tab_gmvc, "GMVC")

self.tab_mode = QWidget()
self.tab_mode.setLayout(self.createModeLayout())
self.tuning_tabs.addTab(self.tab_mode, "Mode")

layout_plot = QVBoxLayout()
layout_h.addLayout(left_menu)
layout_h.addLayout(layout_plot)
Expand All @@ -213,7 +241,7 @@ def reset(self):
self.model_ref = None
self.input_ref = None
self.closed_loop_ref = None
self.bode_plot_ref = None
self.bode_plot_ref = []
self.pz_plot_refs = []
self.is_system_identified = False

Expand Down Expand Up @@ -480,6 +508,47 @@ def updateLabelDetune(self):
if self.slider_detune.isSliderDown():
self.computeController()

def createModeLayout(self):
layout_mode = QFormLayout()

layout_cutoff_freq = QHBoxLayout()
self.slider_cutoff_freq = DoubleSlider(Qt.Horizontal)
self.slider_cutoff_freq.setMinimum(0.0)
self.slider_cutoff_freq.setMaximum(100.0)
self.slider_cutoff_freq.setInterval(0.1)
self.slider_cutoff_freq.setValue(0.0)
self.lbl_cutoff_freq = QLabel("{:.1f}".format(self.cutoff_freq))
layout_cutoff_freq.addWidget(self.slider_cutoff_freq)
layout_cutoff_freq.addWidget(self.lbl_cutoff_freq)
self.slider_cutoff_freq.valueChanged.connect(self.updateLabelCutoffFreq)
layout_mode.addRow(QLabel("Cutoff frequency"), layout_cutoff_freq)

layout_damping_ratio = QHBoxLayout()
self.slider_damping_ratio = DoubleSlider(Qt.Horizontal)
self.slider_damping_ratio.setMinimum(0.0)
self.slider_damping_ratio.setMaximum(0.1)
self.slider_damping_ratio.setInterval(0.001)
self.slider_damping_ratio.setValue(0.0)
self.lbl_damping_ratio = QLabel("{:.3f}".format(self.damping_ratio))
layout_damping_ratio.addWidget(self.slider_damping_ratio)
layout_damping_ratio.addWidget(self.lbl_damping_ratio)
self.slider_damping_ratio.valueChanged.connect(self.updateLabelDampingRatio)
layout_mode.addRow(QLabel("Damping ratio"), layout_damping_ratio)

return layout_mode

def updateLabelCutoffFreq(self):
self.cutoff_freq = self.slider_cutoff_freq.value()
self.lbl_cutoff_freq.setText("{:.1f}".format(self.cutoff_freq))
if self.slider_cutoff_freq.isSliderDown():
self.updateClosedLoop()

def updateLabelDampingRatio(self):
self.damping_ratio = self.slider_damping_ratio.value()
self.lbl_damping_ratio.setText("{:.3f}".format(self.damping_ratio))
if self.slider_damping_ratio.isSliderDown():
self.updateClosedLoop()

def runIdentification(self):
n_steps = len(self.t)

Expand Down Expand Up @@ -538,7 +607,7 @@ def plotPolesZeros(self):
poles = self.Gz.poles()
zeros = self.Gz.zeros()
if not self.pz_plot_refs:
ax = self.figure.add_subplot(3, 3, 6)
ax = self.figure.add_subplot(3, 3, 4)
plot_ref = ax.plot(poles.real, poles.imag, "rx", markersize=10)
self.pz_plot_refs.append(plot_ref[0])
plot_ref = ax.plot(zeros.real, zeros.imag, "ro", markersize=10)
Expand Down Expand Up @@ -635,9 +704,18 @@ def updateClosedLoop(self):
outputs="rd",
)
plant = ctrl.TransferFunction(num, den, dt, inputs="u", outputs="plant_out")
sampler = ctrl.TransferFunction(
[1], [1, 0], dt, inputs="plant_out", outputs="y"
)

if self.cutoff_freq > 0.0:
b, a = create2ndOrderLpf(
fc=self.cutoff_freq, zeta=self.damping_ratio, fs=1 / dt
)
else:
b = 1.0
a = 1.0

mode = ctrl.TransferFunction(b, a, dt, inputs="plant_out", outputs="mode_out")

sampler = ctrl.TransferFunction([1], [1, 0], dt, inputs="mode_out", outputs="y")
sum_feedback = ctrl.summing_junction(inputs=["rd", "-y"], output="e")

# Default is standard PID
Expand Down Expand Up @@ -704,6 +782,7 @@ def updateClosedLoop(self):
id_control,
out_sign,
plant,
mode,
],
inputs="r",
outputs="y",
Expand All @@ -727,6 +806,7 @@ def updateClosedLoop(self):
id_control,
out_sign,
plant,
mode,
],
inputs="disturbance",
outputs="y",
Expand All @@ -737,11 +817,28 @@ def updateClosedLoop(self):
y_out += y_d

self.plotClosedLoop(t_out, y_out)
w = np.logspace(-1, 3, 40).tolist()
(mag_cl, phase_cl, omega_cl) = ctrl.frequency_response(
closed_loop, omega=np.asarray(w)

sum_feedback = ctrl.summing_junction(inputs=["rd"], output="e")
open_loop = ctrl.interconnect(
[
delays,
sampler,
sum_feedback,
feedforward,
sum_control,
p_control,
i_control,
d_control,
id_control,
out_sign,
plant,
mode,
],
inputs="r",
outputs="y",
)
self.plotBode(omega_cl, mag_cl)

self.plotBode(open_loop, closed_loop)

def plotClosedLoop(self, t, y):
if self.closed_loop_ref is None:
Expand All @@ -760,21 +857,72 @@ def plotClosedLoop(self, t, y):

self.canvas.draw()

def plotBode(self, w_cl, mag_cl):
if self.bode_plot_ref is None:
ax = self.figure.add_subplot(3, 3, (8, 9))
f = w_cl / (2 * np.pi)
plot_ref = ax.semilogx(f, 20 * np.log10(mag_cl))
def plotBode(self, open_loop, closed_loop):

(
gain_margin,
phase_margin,
stab_margin,
phase_crossover,
gain_crossover,
stab_margin_w,
) = ctrl.stability_margins(open_loop)
stability_margins_text = f"Gain margin: {20 * np.log10(gain_margin):.2f}dB (@{phase_crossover / (2 * np.pi):.1f}Hz)\nPhase margin: {phase_margin:.1f}deg (@{gain_crossover / (2 * np.pi):.1f}Hz)"

w = np.logspace(-1, 3, 500).tolist()
(mag_ol, phase_ol, omega_ol) = ctrl.frequency_response(
open_loop, omega=np.asarray(w)
)

(mag_cl, phase_cl, omega_cl) = ctrl.frequency_response(
closed_loop, omega=np.asarray(w)
)
f = omega_cl / (2 * np.pi)

if not self.bode_plot_ref:
ax = self.figure.add_subplot(3, 3, (5, 6))
plot_ref = ax.semilogx(f, 20 * np.log10(mag_ol), label="Open-loop")
self.bode_plot_ref.append(plot_ref[0])
plot_ref = ax.semilogx(f, 20 * np.log10(mag_cl), label="Closed-loop")
self.bode_plot_ref.append(plot_ref[0])
ax.set_ylim(-20, 20)
ax.plot([f[0], f[-1]], [0, 0], "k--")
ax.plot([f[0], f[-1]], [-3, -3], "g--")
self.bode_plot_ref = plot_ref[0]

ax.set_title("Bode")
ax.set_xlabel("Frequency (Hz)")
ax.set_ylabel("Magnitude (dB)")
ax.legend()

ax = self.figure.add_subplot(3, 3, (8, 9))
plot_ref = ax.semilogx(f, phase_ol * 180 / np.pi, label="Open-loop")
self.bode_plot_ref.append(plot_ref[0])
plot_ref = ax.semilogx(f, phase_cl * 180 / np.pi, label="Closed-loop")
self.bode_plot_ref.append(plot_ref[0])
ax.set_ylim(-180, 180)

ax.set_xlabel("Frequency (Hz)")
ax.set_ylabel("Phase (deg)")
self.gain_margin_text_ref = ax.text(
0.01,
0.9,
stability_margins_text,
verticalalignment="top",
transform=ax.transAxes,
)

else:
f = w_cl / (2 * np.pi)
self.bode_plot_ref.set_xdata(f)
self.bode_plot_ref.set_ydata(20 * np.log10(mag_cl))
self.bode_plot_ref[0].set_xdata(f)
mag_ol_db = 20 * np.log10(mag_ol)
self.bode_plot_ref[0].set_ydata(mag_ol_db)
self.bode_plot_ref[1].set_xdata(f)
mag_cl_db = 20 * np.log10(mag_cl)
self.bode_plot_ref[1].set_ydata(mag_cl_db)
self.gain_margin_text_ref.set_text(stability_margins_text)

self.bode_plot_ref[2].set_xdata(f)
self.bode_plot_ref[2].set_ydata(phase_ol * 180 / np.pi)
self.bode_plot_ref[3].set_xdata(f)
self.bode_plot_ref[3].set_ydata(phase_cl * 180 / np.pi)

self.canvas.draw()

Expand Down
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