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

Signed-off-by: Dmitry Butyugin <dmbutyugin@google.com>
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scripts/graph_motion.py Executable file
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#!/usr/bin/env python2
# Script to graph motion results
#
# Copyright (C) 2019-2020 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, datetime, math
import matplotlib
SEG_TIME = .000100
INV_SEG_TIME = 1. / SEG_TIME
SPRING_FREQ=35.0
DAMPING_RATIO=0.05
CONFIG_FREQ=40.0
CONFIG_DAMPING_RATIO=0.1
######################################################################
# Basic trapezoid motion
######################################################################
# List of moves: [(start_v, end_v, move_t), ...]
Moves = [
(0., 0., .100),
(6.869, 89.443, None), (89.443, 89.443, .120), (89.443, 17.361, None),
(19.410, 120., None), (120., 120., .130), (120., 5., None),
(0., 0., 0.01),
(-5., -100., None), (-100., -100., .100), (-100., -.5, None),
(0., 0., .200)
]
ACCEL = 3000.
MAX_JERK = ACCEL * 0.6 * SPRING_FREQ
def get_accel(start_v, end_v):
return ACCEL
def get_accel_jerk_limit(start_v, end_v):
effective_accel = math.sqrt(MAX_JERK * abs(end_v - start_v) / 6.)
return min(effective_accel, ACCEL)
# Standard constant acceleration generator
def get_acc_pos_ao2(rel_t, start_v, accel, move_t):
return (start_v + 0.5 * accel * rel_t) * rel_t
# Bezier curve "accel_order=4" generator
def get_acc_pos_ao4(rel_t, start_v, accel, move_t):
inv_accel_t = 1. / move_t
accel_div_accel_t = accel * inv_accel_t
accel_div_accel_t2 = accel_div_accel_t * inv_accel_t
c4 = -.5 * accel_div_accel_t2;
c3 = accel_div_accel_t;
c1 = start_v
return ((c4 * rel_t + c3) * rel_t * rel_t + c1) * rel_t
# Bezier curve "accel_order=6" generator
def get_acc_pos_ao6(rel_t, start_v, accel, move_t):
inv_accel_t = 1. / move_t
accel_div_accel_t = accel * inv_accel_t
accel_div_accel_t2 = accel_div_accel_t * inv_accel_t
accel_div_accel_t3 = accel_div_accel_t2 * inv_accel_t
accel_div_accel_t4 = accel_div_accel_t3 * inv_accel_t
c6 = accel_div_accel_t4;
c5 = -3. * accel_div_accel_t3;
c4 = 2.5 * accel_div_accel_t2;
c1 = start_v;
return (((c6 * rel_t + c5) * rel_t + c4)
* rel_t * rel_t * rel_t + c1) * rel_t
get_acc_pos = get_acc_pos_ao2
get_acc = get_accel
# Calculate positions based on 'Moves' list
def gen_positions():
out = []
start_d = start_t = t = 0.
for start_v, end_v, move_t in Moves:
if move_t is None:
move_t = abs(end_v - start_v) / get_acc(start_v, end_v)
accel = (end_v - start_v) / move_t
end_t = start_t + move_t
while t <= end_t:
rel_t = t - start_t
out.append(start_d + get_acc_pos(rel_t, start_v, accel, move_t))
t += SEG_TIME
start_d += get_acc_pos(move_t, start_v, accel, move_t)
start_t = end_t
return out
######################################################################
# Estimated motion with belt as spring
######################################################################
def estimate_spring(positions):
ang_freq2 = (SPRING_FREQ * 2. * math.pi)**2
damping_factor = 4. * math.pi * DAMPING_RATIO * SPRING_FREQ
head_pos = head_v = 0.
out = []
for stepper_pos in positions:
head_pos += head_v * SEG_TIME
head_a = (stepper_pos - head_pos) * ang_freq2
head_v += head_a * SEG_TIME
head_v -= head_v * damping_factor * SEG_TIME
out.append(head_pos)
return out
######################################################################
# List helper functions
######################################################################
MARGIN_TIME = 0.050
def time_to_index(t):
return int(t * INV_SEG_TIME + .5)
def indexes(positions):
drop = time_to_index(MARGIN_TIME)
return range(drop, len(positions)-drop)
def trim_lists(*lists):
keep = len(lists[0]) - time_to_index(2. * MARGIN_TIME)
for l in lists:
del l[keep:]
######################################################################
# Common data filters
######################################################################
# Generate estimated first order derivative
def gen_deriv(data):
return [0.] + [(data[i+1] - data[i]) * INV_SEG_TIME
for i in range(len(data)-1)]
# Simple average between two points smooth_time away
def calc_average(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
out = [0.] * len(positions)
for i in indexes(positions):
out[i] = .5 * (positions[i-offset] + positions[i+offset])
return out
# Average (via integration) of smooth_time range
def calc_smooth(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
weight = 1. / (2*offset - 1)
out = [0.] * len(positions)
for i in indexes(positions):
out[i] = sum(positions[i-offset+1:i+offset]) * weight
return out
# Time weighted average (via integration) of smooth_time range
def calc_weighted(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
weight = 1. / offset**2
out = [0.] * len(positions)
for i in indexes(positions):
weighted_data = [positions[j] * (offset - abs(j-i))
for j in range(i-offset, i+offset)]
out[i] = sum(weighted_data) * weight
return out
# Weighted average (`h**2 - (t-T)**2`) of smooth_time range
def calc_weighted2(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
weight = .75 / offset**3
out = [0.] * len(positions)
for i in indexes(positions):
weighted_data = [positions[j] * (offset**2 - (j-i)**2)
for j in range(i-offset, i+offset)]
out[i] = sum(weighted_data) * weight
return out
# Weighted average (`(h**2 - (t-T)**2)**2`) of smooth_time range
def calc_weighted4(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
weight = 15 / (16. * offset**5)
out = [0.] * len(positions)
for i in indexes(positions):
weighted_data = [positions[j] * ((offset**2 - (j-i)**2))**2
for j in range(i-offset, i+offset)]
out[i] = sum(weighted_data) * weight
return out
# Weighted average (`(h - abs(t-T))**2 * (2 * abs(t-T) + h)`) of range
def calc_weighted3(positions, smooth_time):
offset = time_to_index(smooth_time * .5)
weight = 1. / offset**4
out = [0.] * len(positions)
for i in indexes(positions):
weighted_data = [positions[j] * (offset - abs(j-i))**2
* (2. * abs(j-i) + offset)
for j in range(i-offset, i+offset)]
out[i] = sum(weighted_data) * weight
return out
######################################################################
# Spring motion estimation
######################################################################
def calc_spring_raw(positions):
sa = (INV_SEG_TIME / (CONFIG_FREQ * 2. * math.pi))**2
ra = 2. * CONFIG_DAMPING_RATIO * math.sqrt(sa)
out = [0.] * len(positions)
for i in indexes(positions):
out[i] = (positions[i]
+ sa * (positions[i-1] - 2.*positions[i] + positions[i+1])
+ ra * (positions[i+1] - positions[i]))
return out
def calc_spring_double_weighted(positions, smooth_time):
offset = time_to_index(smooth_time * .25)
sa = (INV_SEG_TIME / (offset * CONFIG_FREQ * 2. * math.pi))**2
ra = 2. * CONFIG_DAMPING_RATIO * math.sqrt(sa)
out = [0.] * len(positions)
for i in indexes(positions):
out[i] = (positions[i]
+ sa * (positions[i-offset] - 2.*positions[i]
+ positions[i+offset])
+ ra * (positions[i+1] - positions[i]))
return calc_weighted(out, smooth_time=.5 * smooth_time)
######################################################################
# Input shapers
######################################################################
def get_zv_shaper():
df = math.sqrt(1. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_FREQ * df)
A = [1., K]
T = [0., .5*t_d]
return (A, T, "ZV")
def get_zvd_shaper():
df = math.sqrt(1. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_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. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-.75 * CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_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. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_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. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_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. - CONFIG_DAMPING_RATIO**2)
K = math.exp(-CONFIG_DAMPING_RATIO * math.pi / df)
t_d = 1. / (CONFIG_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 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
def calc_shaper(shaper, positions):
shift_pulses(shaper)
A = shaper[0]
inv_D = 1. / sum(A)
n = len(A)
T = [time_to_index(-shaper[1][j]) for j in range(n)]
out = [0.] * len(positions)
for i in indexes(positions):
out[i] = sum([positions[i + T[j]] * A[j] for j in range(n)]) * inv_D
return out
# Ideal values
SMOOTH_TIME = (2./3.) / CONFIG_FREQ
def gen_updated_position(positions):
#return calc_weighted(positions, 0.040)
#return calc_spring_double_weighted(positions, SMOOTH_TIME)
#return calc_weighted4(calc_spring_raw(positions), SMOOTH_TIME)
return calc_shaper(get_ei_shaper(), positions)
######################################################################
# Plotting and startup
######################################################################
def plot_motion():
# Nominal motion
positions = gen_positions()
velocities = gen_deriv(positions)
accels = gen_deriv(velocities)
# Updated motion
upd_positions = gen_updated_position(positions)
upd_velocities = gen_deriv(upd_positions)
upd_accels = gen_deriv(upd_velocities)
# Estimated position with model of belt as spring
spring_orig = estimate_spring(positions)
spring_upd = estimate_spring(upd_positions)
spring_diff_orig = [n-o for n, o in zip(spring_orig, positions)]
spring_diff_upd = [n-o for n, o in zip(spring_upd, positions)]
head_velocities = gen_deriv(spring_orig)
head_accels = gen_deriv(head_velocities)
head_upd_velocities = gen_deriv(spring_upd)
head_upd_accels = gen_deriv(head_upd_velocities)
# Build plot
times = [SEG_TIME * i for i in range(len(positions))]
trim_lists(times, velocities, accels,
upd_velocities, upd_velocities, upd_accels,
spring_diff_orig, spring_diff_upd,
head_velocities, head_upd_velocities,
head_accels, head_upd_accels)
fig, (ax1, ax2, ax3) = matplotlib.pyplot.subplots(nrows=3, sharex=True)
ax1.set_title("Simulation: resonance freq=%.1f Hz, damping_ratio=%.3f,\n"
"configured freq=%.1f Hz, damping_ratio = %.3f"
% (SPRING_FREQ, DAMPING_RATIO, CONFIG_FREQ
, CONFIG_DAMPING_RATIO))
ax1.set_ylabel('Velocity (mm/s)')
ax1.plot(times, upd_velocities, 'r', label='New Velocity', alpha=0.8)
ax1.plot(times, velocities, 'g', label='Nominal Velocity', alpha=0.8)
ax1.plot(times, head_velocities, label='Head Velocity', alpha=0.4)
ax1.plot(times, head_upd_velocities, label='New Head Velocity', alpha=0.4)
fontP = matplotlib.font_manager.FontProperties()
fontP.set_size('x-small')
ax1.legend(loc='best', prop=fontP)
ax1.grid(True)
ax2.set_ylabel('Acceleration (mm/s^2)')
ax2.plot(times, upd_accels, 'r', label='New Accel', alpha=0.8)
ax2.plot(times, accels, 'g', label='Nominal Accel', alpha=0.8)
ax2.plot(times, head_accels, alpha=0.4)
ax2.plot(times, head_upd_accels, alpha=0.4)
ax2.set_ylim([-5. * ACCEL, 5. * ACCEL])
ax2.legend(loc='best', prop=fontP)
ax2.grid(True)
ax3.set_ylabel('Deviation (mm)')
ax3.plot(times, spring_diff_upd, 'r', label='New', alpha=0.8)
ax3.plot(times, spring_diff_orig, 'g', label='Nominal', alpha=0.8)
ax3.grid(True)
ax3.legend(loc='best', prop=fontP)
ax3.set_xlabel('Time (s)')
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_motion()
# 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()

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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()