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284 lines
8.6 KiB
Python
Executable File
284 lines
8.6 KiB
Python
Executable File
#!/usr/bin/env python2
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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 optparse, math
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import matplotlib
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# A set of damping ratios to calculate shaper response for
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DAMPING_RATIOS=[0.05, 0.1, 0.2]
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# Parameters of the input shaper
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SHAPER_FREQ=50.0
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SHAPER_DAMPING_RATIO=0.1
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# Simulate input shaping of step function for these true resonance frequency
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# and damping ratio
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STEP_SIMULATION_RESONANCE_FREQ=60.
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STEP_SIMULATION_DAMPING_RATIO=0.15
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# If set, defines which range of frequencies to plot shaper frequency responce
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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 get_zv_shaper():
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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A = [1., K]
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T = [0., .5*t_d]
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return (A, T, "ZV")
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def get_zvd_shaper():
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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A = [1., 2.*K, K**2]
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T = [0., .5*t_d, t_d]
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return (A, T, "ZVD")
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def get_mzv_shaper():
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-.75 * SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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a1 = 1. - 1. / math.sqrt(2.)
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a2 = (math.sqrt(2.) - 1.) * K
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a3 = a1 * K * K
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A = [a1, a2, a3]
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T = [0., .375*t_d, .75*t_d]
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return (A, T, "MZV")
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def get_ei_shaper():
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v_tol = 0.05 # vibration tolerance
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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a1 = .25 * (1. + v_tol)
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a2 = .5 * (1. - v_tol) * K
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a3 = a1 * K * K
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A = [a1, a2, a3]
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T = [0., .5*t_d, t_d]
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return (A, T, "EI")
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def get_2hump_ei_shaper():
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v_tol = 0.05 # vibration tolerance
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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V2 = v_tol**2
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X = pow(V2 * (math.sqrt(1. - V2) + 1.), 1./3.)
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a1 = (3.*X*X + 2.*X + 3.*V2) / (16.*X)
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a2 = (.5 - a1) * K
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a3 = a2 * K
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a4 = a1 * K * K * K
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A = [a1, a2, a3, a4]
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T = [0., .5*t_d, t_d, 1.5*t_d]
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return (A, T, "2-hump EI")
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def get_3hump_ei_shaper():
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v_tol = 0.05 # vibration tolerance
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df = math.sqrt(1. - SHAPER_DAMPING_RATIO**2)
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K = math.exp(-SHAPER_DAMPING_RATIO * math.pi / df)
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t_d = 1. / (SHAPER_FREQ * df)
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K2 = K*K
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a1 = 0.0625 * (1. + 3. * v_tol + 2. * math.sqrt(2. * (v_tol + 1.) * v_tol))
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a2 = 0.25 * (1. - v_tol) * K
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a3 = (0.5 * (1. + v_tol) - 2. * a1) * K2
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a4 = a2 * K2
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a5 = a1 * K2 * K2
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A = [a1, a2, a3, a4, a5]
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T = [0., .5*t_d, t_d, 1.5*t_d, 2.*t_d]
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return (A, T, "3-hump EI")
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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, name = 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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get_shaper = get_ei_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, vib_tol):
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def eval_shaper(freq):
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return estimate_shaper(shaper, freq, 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):
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# Calculate shaper vibration responce on a range of requencies
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response = []
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freqs = []
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freq, freq_end = find_shaper_plot_range(shaper, 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 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 DAMPING_RATIOS]
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return freqs, response, legend
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def gen_shaped_step_function(shaper):
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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 * STEP_SIMULATION_RESONANCE_FREQ
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damping = STEP_SIMULATION_DAMPING_RATIO * omega
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omega_d = omega * math.sqrt(1. - STEP_SIMULATION_DAMPING_RATIO**2)
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phase = math.acos(STEP_SIMULATION_DAMPING_RATIO)
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t_start = T[0] - .5 / SHAPER_FREQ
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t_end = T[-1] + 1.5 / STEP_SIMULATION_RESONANCE_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):
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shift_pulses(shaper)
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freqs, response, response_legend = gen_shaper_response(shaper)
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time, step_vals, step_legend = gen_shaped_step_function(shaper)
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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[-1], SHAPER_FREQ, SHAPER_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" % (STEP_SIMULATION_RESONANCE_FREQ,
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STEP_SIMULATION_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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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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# Draw graph
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setup_matplotlib(options.output is not None)
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fig = plot_shaper(get_shaper())
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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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