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scripts: scripts to simulate input_shaper response and toolhead movement (#3063)

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Signed-off-by: Dmitry Butyugin <dmbutyugin@google.com>
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scripts/graph_shaper.py Executable file
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#!/usr/bin/env python2
# Script to plot input shapers
#
# Copyright (C) 2020 Kevin O'Connor <kevin@koconnor.net>
# Copyright (C) 2020 Dmitry Butyugin <dmbutyugin@google.com>
#
# This file may be distributed under the terms of the GNU GPLv3 license.
import optparse, math
import matplotlib
# A set of damping ratios to calculate shaper response for
DAMPING_RATIOS=[0.05, 0.1, 0.2]
# Parameters of the input shaper
SHAPER_FREQ=50.0
SHAPER_DAMPING_RATIO=0.1
# Simulate input shaping of step function for these true resonance frequency
# and damping ratio
STEP_SIMULATION_RESONANCE_FREQ=60.
STEP_SIMULATION_DAMPING_RATIO=0.15
# If set, defines which range of frequencies to plot shaper frequency responce
PLOT_FREQ_RANGE = [] # If empty, will be automatically determined
#PLOT_FREQ_RANGE = [10., 100.]
PLOT_FREQ_STEP = .01
######################################################################
# Input shapers
######################################################################
def get_zv_shaper():
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
A = [1., K]
T = [0., .5*t_d]
return (A, T, "ZV")
def get_zvd_shaper():
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
A = [1., 2.*K, K**2]
T = [0., .5*t_d, t_d]
return (A, T, "ZVD")
def get_mzv_shaper():
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-.75 * SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
a1 = 1. - 1. / math.sqrt(2.)
a2 = (math.sqrt(2.) - 1.) * K
a3 = a1 * K * K
A = [a1, a2, a3]
T = [0., .375*t_d, .75*t_d]
return (A, T, "MZV")
def get_ei_shaper():
v_tol = 0.05 # vibration tolerance
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
a1 = .25 * (1. + v_tol)
a2 = .5 * (1. - v_tol) * K
a3 = a1 * K * K
A = [a1, a2, a3]
T = [0., .5*t_d, t_d]
return (A, T, "EI")
def get_2hump_ei_shaper():
v_tol = 0.05 # vibration tolerance
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
V2 = v_tol**2
X = pow(V2 * (math.sqrt(1. - V2) + 1.), 1./3.)
a1 = (3.*X*X + 2.*X + 3.*V2) / (16.*X)
a2 = (.5 - a1) * K
a3 = a2 * K
a4 = a1 * K * K * K
A = [a1, a2, a3, a4]
T = [0., .5*t_d, t_d, 1.5*t_d]
return (A, T, "2-hump EI")
def get_3hump_ei_shaper():
v_tol = 0.05 # vibration tolerance
df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
t_d = 1. / (SHAPER_FREQ * df)
K2 = K*K
a1 = 0.0625 * (1. + 3. * v_tol + 2. * math.sqrt(2. * (v_tol + 1.) * v_tol))
a2 = 0.25 * (1. - v_tol) * K
a3 = (0.5 * (1. + v_tol) - 2. * a1) * K2
a4 = a2 * K2
a5 = a1 * K2 * K2
A = [a1, a2, a3, a4, a5]
T = [0., .5*t_d, t_d, 1.5*t_d, 2.*t_d]
return (A, T, "3-hump EI")
def estimate_shaper(shaper, freq, damping_ratio):
A, T, _ = shaper
n = len(T)
inv_D = 1. / sum(A)
omega = 2. * math.pi * freq
damping = damping_ratio * omega
omega_d = omega * math.sqrt(1. - damping_ratio**2)
S = C = 0
for i in range(n):
W = A[i] * math.exp(-damping * (T[-1] - T[i]))
S += W * math.sin(omega_d * T[i])
C += W * math.cos(omega_d * T[i])
return math.sqrt(S*S + C*C) * inv_D
def shift_pulses(shaper):
A, T, name = shaper
n = len(T)
ts = sum([A[i] * T[i] for i in range(n)]) / sum(A)
for i in range(n):
T[i] -= ts
# Shaper selection
get_shaper = get_ei_shaper
######################################################################
# Plotting and startup
######################################################################
def bisect(func, left, right):
lhs_sign = math.copysign(1., func(left))
while right-left > 1e-8:
mid = .5 * (left + right)
val = func(mid)
if math.copysign(1., val) == lhs_sign:
left = mid
else:
right = mid
return .5 * (left + right)
def find_shaper_plot_range(shaper, vib_tol):
def eval_shaper(freq):
return estimate_shaper(shaper, freq, DAMPING_RATIOS[0]) - vib_tol
if not PLOT_FREQ_RANGE:
left = bisect(eval_shaper, 0., SHAPER_FREQ)
right = bisect(eval_shaper, SHAPER_FREQ, 2.4 * SHAPER_FREQ)
else:
left, right = PLOT_FREQ_RANGE
return (left, right)
def gen_shaper_response(shaper):
# Calculate shaper vibration responce on a range of requencies
response = []
freqs = []
freq, freq_end = find_shaper_plot_range(shaper, vib_tol=0.25)
while freq <= freq_end:
vals = []
for damping_ratio in DAMPING_RATIOS:
vals.append(estimate_shaper(shaper, freq, damping_ratio))
response.append(vals)
freqs.append(freq)
freq += PLOT_FREQ_STEP
legend = ['damping ratio = %.3f' % d_r for d_r in DAMPING_RATIOS]
return freqs, response, legend
def gen_shaped_step_function(shaper):
# Calculate shaping of a step function
A, T, _ = shaper
inv_D = 1. / sum(A)
n = len(T)
omega = 2. * math.pi * STEP_SIMULATION_RESONANCE_FREQ
damping = STEP_SIMULATION_DAMPING_RATIO * omega
omega_d = omega * math.sqrt(1. - STEP_SIMULATION_DAMPING_RATIO**2)
phase = math.acos(STEP_SIMULATION_DAMPING_RATIO)
t_start = T[0] - .5 / SHAPER_FREQ
t_end = T[-1] + 1.5 / STEP_SIMULATION_RESONANCE_FREQ
result = []
time = []
t = t_start
def step_response(t):
if t < 0.:
return 0.
return 1. - math.exp(-damping * t) * math.sin(omega_d * t
+ phase) / math.sin(phase)
while t <= t_end:
val = []
val.append(1. if t >= 0. else 0.)
#val.append(step_response(t))
commanded = 0.
response = 0.
S = C = 0
for i in range(n):
if t < T[i]:
continue
commanded += A[i]
response += A[i] * step_response(t - T[i])
val.append(commanded * inv_D)
val.append(response * inv_D)
result.append(val)
time.append(t)
t += .01 / SHAPER_FREQ
legend = ['step', 'shaper commanded', 'system response']
return time, result, legend
def plot_shaper(shaper):
shift_pulses(shaper)
freqs, response, response_legend = gen_shaper_response(shaper)
time, step_vals, step_legend = gen_shaped_step_function(shaper)
fig, (ax1, ax2) = matplotlib.pyplot.subplots(nrows=2, figsize=(10,9))
ax1.set_title("Vibration response simulation for shaper '%s',\n"
"shaper_freq=%.1f Hz, damping_ratio=%.3f"
% (shaper[-1], SHAPER_FREQ, SHAPER_DAMPING_RATIO))
ax1.plot(freqs, response)
ax1.set_ylim(bottom=0.)
fontP = matplotlib.font_manager.FontProperties()
fontP.set_size('x-small')
ax1.legend(response_legend, loc='best', prop=fontP)
ax1.set_xlabel('Resonance frequency, Hz')
ax1.set_ylabel('Remaining vibrations, ratio')
ax1.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
ax1.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
ax1.grid(which='major', color='grey')
ax1.grid(which='minor', color='lightgrey')
ax2.set_title("Unit step input, resonance frequency=%.1f Hz, "
"damping ratio=%.3f" % (STEP_SIMULATION_RESONANCE_FREQ,
STEP_SIMULATION_DAMPING_RATIO))
ax2.plot(time, step_vals)
ax2.legend(step_legend, loc='best', prop=fontP)
ax2.set_xlabel('Time, sec')
ax2.set_ylabel('Amplitude')
ax2.grid()
fig.tight_layout()
return fig
def setup_matplotlib(output_to_file):
global matplotlib
if output_to_file:
matplotlib.use('Agg')
import matplotlib.pyplot, matplotlib.dates, matplotlib.font_manager
import matplotlib.ticker
def main():
# Parse command-line arguments
usage = "%prog [options]"
opts = optparse.OptionParser(usage)
opts.add_option("-o", "--output", type="string", dest="output",
default=None, help="filename of output graph")
options, args = opts.parse_args()
if len(args) != 0:
opts.error("Incorrect number of arguments")
# Draw graph
setup_matplotlib(options.output is not None)
fig = plot_shaper(get_shaper())
# Show graph
if options.output is None:
matplotlib.pyplot.show()
else:
fig.set_size_inches(8, 6)
fig.savefig(options.output)
if __name__ == '__main__':
main()