mirror of
https://github.com/Klipper3d/klipper.git
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d825d43108
The change removes the shapers defined there in favor of the standard ones and makes the script a lot more configurable via command-line arguments. Signed-off-by: Dmitry Butyugin <dmbutyugin@google.com>
245 lines
8.9 KiB
Python
Executable File
245 lines
8.9 KiB
Python
Executable File
#!/usr/bin/env python
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# Script to plot input shapers
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#
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# Copyright (C) 2020 Kevin O'Connor <kevin@koconnor.net>
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# Copyright (C) 2020 Dmitry Butyugin <dmbutyugin@google.com>
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#
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# This file may be distributed under the terms of the GNU GPLv3 license.
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import importlib, math, optparse, os, sys
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import matplotlib
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sys.path.append(os.path.join(os.path.dirname(os.path.realpath(__file__)),
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'..', 'klippy'))
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shaper_defs = importlib.import_module('.shaper_defs', 'extras')
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# A set of damping ratios to calculate shaper response for
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DEFAULT_DAMPING_RATIOS=[0.075, 0.1, 0.15]
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# If set, defines which range of frequencies to plot shaper frequency response
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PLOT_FREQ_RANGE = [] # If empty, will be automatically determined
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#PLOT_FREQ_RANGE = [10., 100.]
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PLOT_FREQ_STEP = .01
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######################################################################
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# Input shapers
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######################################################################
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def estimate_shaper(shaper, freq, damping_ratio):
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A, T = shaper
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n = len(T)
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inv_D = 1. / sum(A)
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omega = 2. * math.pi * freq
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damping = damping_ratio * omega
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omega_d = omega * math.sqrt(1. - damping_ratio**2)
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S = C = 0
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for i in range(n):
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W = A[i] * math.exp(-damping * (T[-1] - T[i]))
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S += W * math.sin(omega_d * T[i])
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C += W * math.cos(omega_d * T[i])
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return math.sqrt(S*S + C*C) * inv_D
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def shift_pulses(shaper):
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A, T = shaper
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n = len(T)
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ts = sum([A[i] * T[i] for i in range(n)]) / sum(A)
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for i in range(n):
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T[i] -= ts
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# Shaper selection
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def get_shaper(shaper_name, shaper_freq, damping_ratio):
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for s in shaper_defs.INPUT_SHAPERS:
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if shaper_name.lower() == s.name:
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return s.init_func(shaper_freq, damping_ratio)
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return shaper_defs.get_none_shaper()
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######################################################################
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# Plotting and startup
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######################################################################
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def bisect(func, left, right):
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lhs_sign = math.copysign(1., func(left))
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while right-left > 1e-8:
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mid = .5 * (left + right)
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val = func(mid)
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if math.copysign(1., val) == lhs_sign:
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left = mid
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else:
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right = mid
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return .5 * (left + right)
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def find_shaper_plot_range(shaper, shaper_freq, test_damping_ratios, vib_tol):
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def eval_shaper(freq):
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return estimate_shaper(shaper, freq, test_damping_ratios[0]) - vib_tol
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if not PLOT_FREQ_RANGE:
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left = bisect(eval_shaper, 0., shaper_freq)
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right = bisect(eval_shaper, shaper_freq, 2.4 * shaper_freq)
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else:
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left, right = PLOT_FREQ_RANGE
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return (left, right)
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def gen_shaper_response(shaper, shaper_freq, test_damping_ratios):
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# Calculate shaper vibration response on a range of frequencies
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response = []
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freqs = []
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freq, freq_end = find_shaper_plot_range(shaper, shaper_freq,
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test_damping_ratios, vib_tol=0.25)
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while freq <= freq_end:
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vals = []
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for damping_ratio in test_damping_ratios:
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vals.append(estimate_shaper(shaper, freq, damping_ratio))
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response.append(vals)
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freqs.append(freq)
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freq += PLOT_FREQ_STEP
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legend = ['damping ratio = %.3f' % d_r for d_r in test_damping_ratios]
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return freqs, response, legend
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def gen_shaped_step_function(shaper, shaper_freq,
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system_freq, system_damping_ratio):
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# Calculate shaping of a step function
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A, T = shaper
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inv_D = 1. / sum(A)
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n = len(T)
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omega = 2. * math.pi * system_freq
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damping = system_damping_ratio * omega
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omega_d = omega * math.sqrt(1. - system_damping_ratio**2)
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phase = math.acos(system_damping_ratio)
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t_start = T[0] - .5 / shaper_freq
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t_end = T[-1] + 1.5 / system_freq
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result = []
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time = []
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t = t_start
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def step_response(t):
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if t < 0.:
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return 0.
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return 1. - math.exp(-damping * t) * math.sin(omega_d * t
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+ phase) / math.sin(phase)
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while t <= t_end:
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val = []
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val.append(1. if t >= 0. else 0.)
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#val.append(step_response(t))
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commanded = 0.
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response = 0.
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S = C = 0
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for i in range(n):
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if t < T[i]:
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continue
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commanded += A[i]
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response += A[i] * step_response(t - T[i])
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val.append(commanded * inv_D)
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val.append(response * inv_D)
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result.append(val)
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time.append(t)
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t += .01 / shaper_freq
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legend = ['step', 'shaper commanded', 'system response']
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return time, result, legend
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def plot_shaper(shaper_name, shaper_freq, damping_ratio, test_damping_ratios,
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system_freq, system_damping_ratio):
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shaper = get_shaper(shaper_name, shaper_freq, damping_ratio)
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shift_pulses(shaper)
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freqs, response, response_legend = gen_shaper_response(
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shaper, shaper_freq, test_damping_ratios)
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time, step_vals, step_legend = gen_shaped_step_function(
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shaper, shaper_freq, system_freq, system_damping_ratio)
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fig, (ax1, ax2) = matplotlib.pyplot.subplots(nrows=2, figsize=(10,9))
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ax1.set_title("Vibration response simulation for shaper '%s',\n"
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"shaper_freq=%.1f Hz, damping_ratio=%.3f"
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% (shaper_name, shaper_freq, damping_ratio))
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ax1.plot(freqs, response)
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ax1.set_ylim(bottom=0.)
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fontP = matplotlib.font_manager.FontProperties()
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fontP.set_size('x-small')
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ax1.legend(response_legend, loc='best', prop=fontP)
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ax1.set_xlabel('Resonance frequency, Hz')
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ax1.set_ylabel('Remaining vibrations, ratio')
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ax1.xaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
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ax1.yaxis.set_minor_locator(matplotlib.ticker.AutoMinorLocator())
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ax1.grid(which='major', color='grey')
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ax1.grid(which='minor', color='lightgrey')
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ax2.set_title("Unit step input, resonance frequency=%.1f Hz, "
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"damping ratio=%.3f" % (system_freq, system_damping_ratio))
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ax2.plot(time, step_vals)
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ax2.legend(step_legend, loc='best', prop=fontP)
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ax2.set_xlabel('Time, sec')
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ax2.set_ylabel('Amplitude')
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ax2.grid()
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fig.tight_layout()
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return fig
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def setup_matplotlib(output_to_file):
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global matplotlib
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if output_to_file:
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matplotlib.use('Agg')
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import matplotlib.pyplot, matplotlib.dates, matplotlib.font_manager
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import matplotlib.ticker
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def main():
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# Parse command-line arguments
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usage = "%prog [options]"
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opts = optparse.OptionParser(usage)
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opts.add_option("-o", "--output", type="string", dest="output",
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default=None, help="filename of output graph")
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opts.add_option("--shaper", type="string", dest="shaper", default="mzv",
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help="a shaper to plot")
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opts.add_option("--shaper_freq", type="float", dest="shaper_freq",
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default=50.0, help="shaper frequency")
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opts.add_option("--damping_ratio", type="float", dest="damping_ratio",
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default=shaper_defs.DEFAULT_DAMPING_RATIO,
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help="shaper damping_ratio parameter")
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opts.add_option("--test_damping_ratios", type="string",
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dest="test_damping_ratios",
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default=",".join(["%.3f" % dr
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for dr in DEFAULT_DAMPING_RATIOS]),
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help="a comma-separated list of damping ratios to test " +
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"input shaper for")
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opts.add_option("--system_freq", type="float", dest="system_freq",
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default=60.0,
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help="natural frequency of a system for step simulation")
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opts.add_option("--system_damping_ratio", type="float",
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dest="system_damping_ratio", default=0.15,
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help="damping_ratio of a system for step simulation")
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options, args = opts.parse_args()
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if len(args) != 0:
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opts.error("Incorrect number of arguments")
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if options.shaper.lower() not in [
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s.name for s in shaper_defs.INPUT_SHAPERS]:
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opts.error("Invalid --shaper=%s specified" % options.shaper)
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if options.test_damping_ratios:
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try:
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test_damping_ratios = [float(s) for s in
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options.test_damping_ratios.split(',')]
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except ValueError:
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opts.error("invalid floating point value in " +
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"--test_damping_ratios param")
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else:
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test_damping_ratios = None
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# Draw graph
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setup_matplotlib(options.output is not None)
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fig = plot_shaper(options.shaper, options.shaper_freq,
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options.damping_ratio, test_damping_ratios,
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options.system_freq, options.system_damping_ratio)
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# Show graph
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if options.output is None:
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matplotlib.pyplot.show()
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else:
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fig.set_size_inches(8, 6)
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fig.savefig(options.output)
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if __name__ == '__main__':
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main()
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