def ConservativeLaw(self, flux_variables, output_variable):
if output_variable == self.variable:
v1 = Variable(hidden='True')
b1 = WeightedSum(flux_variables, v1, [1] * len(flux_variables),
-self.friction)
b2 = ODE(v1, self.variable, [1], [self.SCx, self.mass])
return [b1, b2]
else:
v1 = Variable(hidden='True')
b1 = ODE(self.variable, v1, [self.SCx, self.mass], [1])
b2 = WeightedSum([v1] + flux_variables, output_variable,
[1] + [-1] * len(flux_variables), self.friction)
return [b1, b2]
def PartialDynamicSystem(self, ieq, variable):
"""
returns dynamical system blocks associated to output variable
"""
if ieq == 0:
if variable == self.physical_nodes[0].variable:
print('1')
# U1 is output
# U1=i1/pC+U2
Uc = Variable(hidden=True)
block1 = ODE(self.variables[0], Uc, [1], [0, self.C])
sub1 = Sum([self.physical_nodes[1].variable, Uc], variable)
return [block1, sub1]
elif variable == self.physical_nodes[1].variable:
print('2')
# U2 is output
# U2=U1-i1/pC
Uc = Variable(hidden=True)
block1 = ODE(self.variables[0], Uc, [-1], [0, self.C])
sum1 = Sum([self.physical_nodes[0].variable, Uc], variable)
return [block1, sum1]
# elif variable==self.variables[0]:
# print('3')
# # i1 is output
# # i1=pC(U1-U2)
# ic=Variable(hidden=True)
# subs1=Subtraction(self.physical_nodes[0].variable,self.physical_nodes[1].variable,ic)
# block1=ODE(ic,variable,[0,self.C],[1])
# return [block1,subs1]
elif ieq == 1:
# i1=-i2
if variable == self.variables[0]:
# i1 as output
# print('Bat1#0')
return [Gain(self.variables[1], self.variables[0], -1)]
elif variable == self.variables[1]:
# i2 as output
# print('Bat1#1')
return [Gain(self.variables[0], self.variables[1], -1)]
def partial_dynamic_system(self, ieq, variable):
"""
returns dynamical system blocks associated to output variable
"""
if ieq == 0:
# Soc determination
# soc=1-UI/CP
v1 = Variable('UI', hidden=True) # UI
v2 = Variable('UI/CP', hidden=True) # UI/CP
v3 = Variable('soc0-UI/CP', hidden=True) # soc0-UI/CP
b1 = Product(self.u, self.variables[0], v1)
b2 = ODE(v1, v2, [1], [1, self.c])
b3 = WeightedSum([v2], v3, [-1], self.initial_soc)
b4 = Saturation(v3, self.soc, 0, 1)
b5 = WeightedSum([self.soc], self.u, [self.u_max - self.u_min],
self.u_min)
blocks = [b1, b2, b3, b4, b5]
# U2-U1=U+Ri1
# U=soc(Umax-Umin)+Umin
if variable == self.physical_nodes[0].variable:
print('Bat0#1')
# U1 is output
# U1=-U-Ri1+U2
blocks.append(
WeightedSum([
self.u, self.variables[0], self.physical_nodes[1].variable
], variable, [-1, -self.r, 1]))
elif variable == self.physical_nodes[1].variable:
print('Bat0#2')
# U2 is output
# U2=U1+Ri1+U
blocks.append(
WeightedSum([
self.physical_nodes[0].variable, self.variables[0], self.u
], variable, [1, self.r, 1]))
elif variable == self.variables[0]:
print('Bat0#3')
# i1 is output
# i1=(-U1+U2-U)/R
blocks.append(
WeightedSum([
self.physical_nodes[0].variable,
self.physical_nodes[1].variable, self.u
], variable, [-1 / self.r, 1 / self.r, -1 / self.r]))
return blocks
def partial_dynamic_system(self, ieq, variable):
"""
returns dynamical system blocks associated to output variable
"""
if ieq == 0:
# if variable==self.physical_nodes[0].variable:
# print('1')
# # U1 is output
# # U1=i1/pC+U2
# Uc=Variable(hidden=True)
# block1=ODE(self.variables[0],Uc,[1],[0,self.C])
# sub1=Sum([self.physical_nodes[1].variable,Uc],variable)
# return [block1,sub1]
# elif variable==self.physical_nodes[1].variable:
# print('2')
# # U2 is output
# # U2=U1-i1/pC
# Uc=Variable(hidden=True)
# block1=ODE(self.variables[0],Uc,[-1],[0,self.C])
# sum1=Sum([self.physical_nodes[0].variable,Uc],variable)
# return [block1,sum1]
if variable == self.variables[0]: # i1=(u1-u2)/Lp
print('3')
# i1 is output
# i1=pC(U1-U2)
uc = Variable(hidden=True)
subs1 = Subtraction(
self.physical_nodes[0].variable, self.physical_nodes[1].variable, uc)
block1 = ODE(uc, variable, [1], [0, self.L])
return [block1, subs1]
elif ieq == 1:
# i1=-i2
if variable == self.variables[0]:
# i1 as output
return [Gain(self.variables[1], self.variables[0], -1)]
elif variable == self.variables[1]:
# i2 as output
return [Gain(self.variables[0], self.variables[1], -1)]
# -*- coding: utf-8 -*-
"""
Created on Tue Dec 22 18:42:33 2015
@author: steven
"""
import bms
from bms.signals.functions import Sinus
from bms.blocks.continuous import ODE
K = 1
Q = 0.3
w0 = 3
#e=bms.Step('e',4.)
e = Sinus('e', 4., 5)
s = bms.Variable('s', [0])
block = ODE(e, s, [1], [1, 2 * Q / w0, 1 / w0**2])
ds = bms.DynamicSystem(5, 200, [block])
#ds.DrawModel()
ds.Simulate()
ds.PlotVariables()
@author: Steven Masfaraud
"""
import bms
from bms.signals.functions import Ramp
from bms.blocks.continuous import ODE
K = 1.
tau = 1.254
#e=bms.Step('e',1.)
e = Ramp('e', 1.)
s = bms.Variable('s', [0])
block = ODE(e, s, [K], [1, tau])
ds = bms.DynamicSystem(10, 100, [block])
#res=ds.ResolutionOrder()
#print(res)
ds.Simulate()
#ds.PlotVariables()
#ds.DrawModel()
## External plot for verification
import matplotlib.pyplot as plt
plt.figure()
plt.plot(ds.t, e.values)
plt.plot(ds.t, s.values)
s_inf = K * (ds.t.copy() - tau)
plt.plot(ds.t, e.values)
#I2=Sinus(('input','i'),100.)
#O2=bms.Variable(('Output','O'))#
#b=ODE(I2,O2,[0,1],[1])
#ds2=bms.DynamicSystem(15,3000,[b])
#ds2.Simulate()
#ds2.PlotVariables()
#print(b.Mi,b.Mo)
#print()
#==============================================================================
# Feedback with derivative for stability test
#==============================================================================
I = Step(('input', 'i'), 100.)
AI = bms.Variable(('adapted input', 'ai'), [100.])
dI = bms.Variable(('error', 'dI'))
O = bms.Variable(('Output', 'O')) #
F = bms.Variable(('Feedback', 'F')) #
b1 = Gain(I, AI, Ka)
b2 = WeightedSum([AI, dI], F, [1, -1])
b3 = ODE(O, dI, [1, tau], [Kb])
b4 = Gain(F, O, 1 / Kc)
#
#ds.
ds = bms.DynamicSystem(0.1, 20, [b1, b2, b3, b4])
ds.Simulate()
ds.PlotVariables([[I, O, dI, F]])
cc = Sinus(('Brake command', 'cc'), 0.5, 0.1, 0, 0.5)
it = Step(('Input torque', 'it'), 100)
rt = Step(('Resistant torque', 'rt'), -80)
tc = bms.Variable(('brake Torque capacity', 'Tc'))
bt = bms.Variable(('brake torque', 'bt'))
w1 = bms.Variable(('Rotational speed shaft 1', 'w1'))
#dw12=bms.Variable(('Clutch differential speed','dw12'))
st1 = bms.Variable(('Sum torques on 1', 'st1'))
et1 = bms.Variable(('Sum of ext torques on 1', 'et1'))
b1 = Gain(cc, tc, Cmax)
b2 = WeightedSum([it, rt], et1, [1, 1])
b3 = CoulombVariableValue(et1, w1, tc, bt, 0.1)
#b3=Coulomb(it,dw12,ct,150)
b4 = ODE(st1, w1, [1], [fv1, I1])
#b5=ODE(st2,w2,[1],[fv2,I2])
b6 = WeightedSum([it, rt, bt], st1, [1, 1, 1])
#b7=WeightedSum([it,rt],et1,[1,1])
ds = bms.DynamicSystem(100, 400, [b1, b2, b3, b4, b6])
#ds.DrawModel()
r = ds.Simulate()
ds.PlotVariables([[w1], [tc, bt, rt, it, st1, et1]])
import matplotlib.pyplot as plt
plt.figure()
plt.plot(r)
plt.show()
#ds.PlotVariables([[cc]])
Up = bms.Variable(('Voltage corrector proportionnal', 'Ucp'))
Ui = bms.Variable(('Voltage corrector integrator', 'Uci'))
Uc = bms.Variable(('Voltage command', 'Uc'))
Um = bms.Variable(('Voltage Input motor', 'Uim'))
e = bms.Variable(('Counter electromotive force', 'Cef'))
Uind = bms.Variable(('Voltage Inductor', 'Vi'))
Iind = bms.Variable(('Intensity Inductor', 'Ii'))
Tm = bms.Variable(('Motor torque', 'Tm'))
Text = bms.Variable(('Resistant torque', 'Tr'))
T = bms.Variable(('Torque', 'T'))
W = bms.Variable(('Rotationnal speed', 'w'))
Pe = bms.Variable(('Electrical power', 'Pe'))
Pm = bms.Variable(('Mechanical power', 'Pm'))
block1 = Subtraction(Wc, W, dW)
block2 = ODE(dW, Ui, [1], [0, tau_i])
block3 = Gain(dW, Up, Gc)
block4 = Sum([Up, Ui], Uc)
block4a = Saturation(Uc, Um, -Umax, Umax)
block5 = Subtraction(Um, e, Uind)
block6 = ODE(Uind, Iind, [1], [R, L])
block7 = Gain(Iind, Tm, k)
block8 = Sum([Tm, Text], T)
block8a = Coulomb(Tm, W, Text, Tr, 2)
block9 = ODE(T, W, [1], [0, J])
block10 = Gain(W, e, k)
block11 = Product(Um, Iind, Pe)
block11a = Product(Tm, W, Pm)
ds = bms.DynamicSystem(10, 1000, [
block1, block2, block3, block4, block4a, block5, block6, block7, block8,
block8a, block9, block10, block11, block11a
import bms
from bms.signals.functions import Step
from bms.blocks.continuous import Gain, ODE, Sum, Subtraction, Product
Ka = 3
Kb = 4
Kc = 3
tau = 1
I = Step(('input', 'i'), 100.)
AI = bms.Variable(('adapted input', 'ai'), [100.])
dI = bms.Variable(('error', 'dI'))
O = bms.Variable(('Output', 'O'))
F = bms.Variable(('Feedback', 'F'))
b1 = Gain(I, AI, Ka)
b2 = Subtraction(AI, F, dI)
b3 = ODE(dI, O, [Kb], [1, tau])
b4 = Gain(O, F, Kc)
ds = bms.DynamicSystem(3, 1000, [b1, b2, b3, b4])
r = ds.Simulate()
ds.PlotVariables([[I, O, dI, F]])
# I2=Step(('input','i'),100.)
#O2=bms.Variable(('Output','O'))#
# ds2=bms.DynamicSystem(3,600,[ODE(I2,O2,[Ka*Kb],[1+Kc*Kb,tau])])
# ds2.Simulate()
# ds2.PlotVariables()
# e=bmsp.Step(1.,'e')
cc = Sinus(('Clutch command', 'cc'), 0.5, 0.1, 0, 0.5)
it = Step(('Input torque', 'it'), 200)
rt = Step(('Resistant torque', 'rt'), -180)
tc = bms.Variable(('Clutch Torque capacity', 'Tc'))
ct = bms.Variable(('clutch torque', 'ct'))
w1 = bms.Variable(('Rotational speed shaft 1', 'w1'))
w2 = bms.Variable(('Rotational speed shaft 2', 'w2'))
dw12 = bms.Variable(('Clutch differential speed', 'dw12'))
st1 = bms.Variable(('Sum torques on 1', 'st1'))
st2 = bms.Variable(('Sum torques on 2', 'st2'))
b1 = Gain(cc, tc, Cmax)
b2 = WeightedSum([w1, w2], dw12, [1, -1])
b3 = CoulombVariableValue(it, dw12, tc, ct, 1)
# b3=Coulomb(it,dw12,ct,150)
b4 = ODE(st1, w1, [1], [fv1, I1])
b5 = ODE(st2, w2, [1], [fv2, I2])
b6 = WeightedSum([it, ct], st1, [1, 1])
b7 = WeightedSum([rt, ct], st2, [1, -1])
ds = bms.DynamicSystem(50, 150, [b1, b2, b3, b4, b5, b6, b7])
# ds.DrawModel()
r = ds.Simulate()
ds.PlotVariables([[dw12, w1, w2], [tc, ct, rt, it]])
# ds.PlotVariables([[cc]])
