blob: ed0062a86dbb68b95fc4d08524d9ea3d75880996 [file] [log] [blame]
#!/usr/bin/python3
import numpy
from matplotlib import pylab
import scipy.integrate
from frc971.control_loops.python import controls
import time
import operator
K1 = 1.81e04
K2 = 0.0
# Make the amplitude of the fundamental 1 for ease of playing with.
K2 /= K1
K1 = 1
vcc = 14.0 # volts
R_motor = 0.1073926073926074 # ohms for the motor
R = R_motor + 0.080 + 0.02 # motor + fets + wires ohms for system
L = 80.0 * 1e-6 # Henries
M = L / 10.0
Kv = 37.6 # rad/s/volt, where the voltage is measured from the neutral to the phase.
J = 0.0000007
R_shunt = 0.0003
# RC circuit for current sense filtering.
R_sense1 = 768.0
R_sense2 = 1470.0
C_sense = 10.0 * 1e-9
# So, we measured the inductance by switching between ~5 and ~20 amps through
# the motor.
# We then looked at the change in voltage that should give us (assuming duty
# cycle * vin), and divided it by the corresponding change in current.
# We then looked at the amount of time it took to decay the current to 1/e
# That gave us the inductance.
# Overrides for experiments
J = J * 10.0
# Firing phase A -> 0.0
# Firing phase B -> - numpy.pi * 2.0 / 3.0
# Firing phase C -> + numpy.pi * 2.0 / 3.0
hz = 20000.0
#switching_pattern = 'front'
switching_pattern = 'centered'
#switching_pattern = 'rear'
#switching_pattern = 'centered front shifted'
#switching_pattern = 'anticentered'
Vconv = numpy.matrix([[2.0, -1.0, -1.0], [-1.0, 2.0, -1.0], [-1.0, -1.0, 2.0]
]) / 3.0
def f_single(theta):
return K1 * numpy.sin(theta) + K2 * numpy.sin(theta * 5)
def g_single(theta):
return K1 * numpy.sin(theta) - K2 * numpy.sin(theta * 5)
def gdot_single(theta):
"""Derivitive of the current.
Must be multiplied by omega externally.
"""
return K1 * numpy.cos(theta) - 5.0 * K2 * numpy.cos(theta * 5.0)
f = numpy.vectorize(f_single, otypes=(numpy.float, ))
g = numpy.vectorize(g_single, otypes=(numpy.float, ))
gdot = numpy.vectorize(gdot_single, otypes=(numpy.float, ))
def torque(theta):
return f(theta) * g(theta)
def phase_a(function, theta):
return function(theta)
def phase_b(function, theta):
return function(theta + 2 * numpy.pi / 3)
def phase_c(function, theta):
return function(theta + 4 * numpy.pi / 3)
def phases(function, theta):
return numpy.matrix([[phase_a(function,
theta)], [phase_b(function, theta)],
[phase_c(function, theta)]])
def all_phases(function, theta_range):
return (phase_a(function, theta_range) + phase_b(function, theta_range) +
phase_c(function, theta_range))
theta_range = numpy.linspace(start=0, stop=4 * numpy.pi, num=10000)
one_amp_driving_voltage = R * g(theta_range) + (
L * gdot(theta_range) + M * gdot(theta_range + 2.0 / 3.0 * numpy.pi) +
M * gdot(theta_range - 2.0 / 3.0 * numpy.pi)) * Kv * vcc / 2.0
max_one_amp_driving_voltage = max(one_amp_driving_voltage)
# The number to divide the product of the unit BEMF and the per phase current
# by to get motor current.
one_amp_scalar = (phases(f_single, 0.0).T * phases(g_single, 0.0))[0, 0]
print('Max BEMF', max(f(theta_range)))
print('Max current', max(g(theta_range)))
print('Max drive voltage (one_amp_driving_voltage)',
max(one_amp_driving_voltage))
print('one_amp_scalar', one_amp_scalar)
pylab.figure()
pylab.subplot(1, 1, 1)
pylab.plot(theta_range, f(theta_range), label='bemf')
pylab.plot(theta_range, g(theta_range), label='phase_current')
pylab.plot(theta_range, torque(theta_range), label='phase_torque')
pylab.plot(theta_range,
all_phases(torque, theta_range),
label='sum_torque/current')
pylab.legend()
def full_sample_times(Ton, Toff, dt, n, start_time):
"""Returns n + 4 samples for the provided switching times.
We need the timesteps and Us to integrate.
Args:
Ton: On times for each phase.
Toff: Off times for each phase.
dt: The cycle time.
n: Number of intermediate points to include in the result.
start_time: Starting value for the t values in the result.
Returns:
array of [t, U matrix]
"""
assert ((Toff <= 1.0).all())
assert ((Ton <= 1.0).all())
assert ((Toff >= 0.0).all())
assert ((Ton >= 0.0).all())
if (Ton <= Toff).all():
on_before_off = True
else:
# Verify that they are all ordered correctly.
assert (not (Ton <= Toff).any())
on_before_off = False
Toff = Toff.copy() * dt
Toff[Toff < 100e-9] = -1.0
Toff[Toff > dt] = dt
Ton = Ton.copy() * dt
Ton[Ton < 100e-9] = -1.0
Ton[Ton > dt - 100e-9] = dt + 1.0
result = []
t = 0
result_times = numpy.concatenate(
(numpy.linspace(0, dt, num=n),
numpy.reshape(
numpy.asarray(Ton[numpy.logical_and(Ton < dt, Ton > 0.0)]),
(-1, )),
numpy.reshape(
numpy.asarray(Toff[numpy.logical_and(Toff < dt, Toff > 0.0)]),
(-1, ))))
result_times.sort()
assert ((result_times >= 0).all())
assert ((result_times <= dt).all())
for t in result_times:
if on_before_off:
U = numpy.matrix([[vcc], [vcc], [vcc]])
U[t <= Ton] = 0.0
U[Toff < t] = 0.0
else:
U = numpy.matrix([[0.0], [0.0], [0.0]])
U[t > Ton] = vcc
U[t <= Toff] = vcc
result.append((float(t + start_time), U.copy()))
return result
def sample_times(T, dt, n, start_time):
if switching_pattern == 'rear':
T = 1.0 - T
ans = full_sample_times(T,
numpy.matrix(numpy.ones((3, 1))) * 1.0, dt, n,
start_time)
elif switching_pattern == 'centered front shifted':
# Centered, but shifted to the beginning of the cycle.
Ton = 0.5 - T / 2.0
Toff = 0.5 + T / 2.0
tn = min(Ton)[0, 0]
Ton -= tn
Toff -= tn
ans = full_sample_times(Ton, Toff, dt, n, start_time)
elif switching_pattern == 'centered':
# Centered, looks waaay better.
Ton = 0.5 - T / 2.0
Toff = 0.5 + T / 2.0
ans = full_sample_times(Ton, Toff, dt, n, start_time)
elif switching_pattern == 'anticentered':
# Centered, looks waaay better.
Toff = T / 2.0
Ton = 1.0 - T / 2.0
ans = full_sample_times(Ton, Toff, dt, n, start_time)
elif switching_pattern == 'front':
ans = full_sample_times(numpy.matrix(numpy.zeros((3, 1))), T, dt, n,
start_time)
else:
assert (False)
return ans
class DataLogger(object):
def __init__(self, title=None):
self.title = title
self.ia = []
self.ib = []
self.ic = []
self.ia_goal = []
self.ib_goal = []
self.ic_goal = []
self.ia_controls = []
self.ib_controls = []
self.ic_controls = []
self.isensea = []
self.isenseb = []
self.isensec = []
self.va = []
self.vb = []
self.vc = []
self.van = []
self.vbn = []
self.vcn = []
self.ea = []
self.eb = []
self.ec = []
self.theta = []
self.omega = []
self.i_goal = []
self.time = []
self.controls_time = []
self.predicted_time = []
self.ia_pred = []
self.ib_pred = []
self.ic_pred = []
self.voltage_time = []
self.estimated_velocity = []
self.U_last = numpy.matrix(numpy.zeros((3, 1)))
def log_predicted(self, current_time, p):
self.predicted_time.append(current_time)
self.ia_pred.append(p[0, 0])
self.ib_pred.append(p[1, 0])
self.ic_pred.append(p[2, 0])
def log_controls(self, current_time, measured_current, In, E,
estimated_velocity):
self.controls_time.append(current_time)
self.ia_controls.append(measured_current[0, 0])
self.ib_controls.append(measured_current[1, 0])
self.ic_controls.append(measured_current[2, 0])
self.ea.append(E[0, 0])
self.eb.append(E[1, 0])
self.ec.append(E[2, 0])
self.ia_goal.append(In[0, 0])
self.ib_goal.append(In[1, 0])
self.ic_goal.append(In[2, 0])
self.estimated_velocity.append(estimated_velocity)
def log_data(self, X, U, current_time, Vn, i_goal):
self.ia.append(X[0, 0])
self.ib.append(X[1, 0])
self.ic.append(X[2, 0])
self.i_goal.append(i_goal)
self.isensea.append(X[5, 0])
self.isenseb.append(X[6, 0])
self.isensec.append(X[7, 0])
self.theta.append(X[3, 0])
self.omega.append(X[4, 0])
self.time.append(current_time)
self.van.append(Vn[0, 0])
self.vbn.append(Vn[1, 0])
self.vcn.append(Vn[2, 0])
if (self.U_last != U).any():
self.va.append(self.U_last[0, 0])
self.vb.append(self.U_last[1, 0])
self.vc.append(self.U_last[2, 0])
self.voltage_time.append(current_time)
self.va.append(U[0, 0])
self.vb.append(U[1, 0])
self.vc.append(U[2, 0])
self.voltage_time.append(current_time)
self.U_last = U.copy()
def plot(self):
fig = pylab.figure()
pylab.subplot(3, 1, 1)
pylab.plot(self.controls_time,
self.ia_controls,
'ro',
label='ia_controls')
pylab.plot(self.controls_time,
self.ib_controls,
'go',
label='ib_controls')
pylab.plot(self.controls_time,
self.ic_controls,
'bo',
label='ic_controls')
pylab.plot(self.controls_time, self.ia_goal, 'r--', label='ia_goal')
pylab.plot(self.controls_time, self.ib_goal, 'g--', label='ib_goal')
pylab.plot(self.controls_time, self.ic_goal, 'b--', label='ic_goal')
#pylab.plot(self.controls_time, self.ia_pred, 'r*', label='ia_pred')
#pylab.plot(self.controls_time, self.ib_pred, 'g*', label='ib_pred')
#pylab.plot(self.controls_time, self.ic_pred, 'b*', label='ic_pred')
pylab.plot(self.time, self.isensea, 'r:', label='ia_sense')
pylab.plot(self.time, self.isenseb, 'g:', label='ib_sense')
pylab.plot(self.time, self.isensec, 'b:', label='ic_sense')
pylab.plot(self.time, self.ia, 'r', label='ia')
pylab.plot(self.time, self.ib, 'g', label='ib')
pylab.plot(self.time, self.ic, 'b', label='ic')
pylab.plot(self.time, self.i_goal, label='i_goal')
if self.title is not None:
fig.canvas.set_window_title(self.title)
pylab.legend()
pylab.subplot(3, 1, 2)
pylab.plot(self.voltage_time, self.va, label='va')
pylab.plot(self.voltage_time, self.vb, label='vb')
pylab.plot(self.voltage_time, self.vc, label='vc')
pylab.plot(self.time, self.van, label='van')
pylab.plot(self.time, self.vbn, label='vbn')
pylab.plot(self.time, self.vcn, label='vcn')
pylab.plot(self.controls_time, self.ea, label='ea')
pylab.plot(self.controls_time, self.eb, label='eb')
pylab.plot(self.controls_time, self.ec, label='ec')
pylab.legend()
pylab.subplot(3, 1, 3)
pylab.plot(self.time, self.theta, label='theta')
pylab.plot(self.time, self.omega, label='omega')
#pylab.plot(self.controls_time, self.estimated_velocity, label='estimated omega')
pylab.legend()
fig = pylab.figure()
pylab.plot(self.controls_time,
map(operator.sub, self.ia_goal, self.ia_controls),
'r',
label='ia_error')
pylab.plot(self.controls_time,
map(operator.sub, self.ib_goal, self.ib_controls),
'g',
label='ib_error')
pylab.plot(self.controls_time,
map(operator.sub, self.ic_goal, self.ic_controls),
'b',
label='ic_error')
if self.title is not None:
fig.canvas.set_window_title(self.title)
pylab.legend()
pylab.show()
# So, from running a bunch of math, we know the following:
# Van + Vbn + Vcn = 0
# ia + ib + ic = 0
# ea + eb + ec = 0
# d ia/dt + d ib/dt + d ic/dt = 0
#
# We also have:
# [ Van ] [ 2/3 -1/3 -1/3] [Va]
# [ Vbn ] = [ -1/3 2/3 -1/3] [Vb]
# [ Vcn ] [ -1/3 -1/3 2/3] [Vc]
#
# or,
#
# Vabcn = Vconv * V
#
# The base equation is:
#
# [ Van ] [ R 0 0 ] [ ia ] [ L M M ] [ dia/dt ] [ ea ]
# [ Vbn ] = [ 0 R 0 ] [ ib ] + [ M L M ] [ dib/dt ] + [ eb ]
# [ Vbn ] [ 0 0 R ] [ ic ] [ M M L ] [ dic/dt ] [ ec ]
#
# or
#
# Vabcn = R_matrix * I + L_matrix * I_dot + E
#
# We can re-arrange this as:
#
# inv(L_matrix) * (Vconv * V - E - R_matrix * I) = I_dot
# B * V - inv(L_matrix) * E - A * I = I_dot
class Simulation(object):
def __init__(self):
self.R_matrix = numpy.matrix(numpy.eye(3)) * R
self.L_matrix = numpy.matrix([[L, M, M], [M, L, M], [M, M, L]])
self.L_matrix_inv = numpy.linalg.inv(self.L_matrix)
self.A = self.L_matrix_inv * self.R_matrix
self.B = self.L_matrix_inv * Vconv
self.A_discrete, self.B_discrete = controls.c2d(
-self.A, self.B, 1.0 / hz)
self.B_discrete_inverse = numpy.matrix(
numpy.eye(3)) / (self.B_discrete[0, 0] - self.B_discrete[1, 0])
self.R_model = R * 1.0
self.L_model = L * 1.0
self.M_model = M * 1.0
self.R_matrix_model = numpy.matrix(numpy.eye(3)) * self.R_model
self.L_matrix_model = numpy.matrix(
[[self.L_model, self.M_model, self.M_model],
[self.M_model, self.L_model, self.M_model],
[self.M_model, self.M_model, self.L_model]])
self.L_matrix_inv_model = numpy.linalg.inv(self.L_matrix_model)
self.A_model = self.L_matrix_inv_model * self.R_matrix_model
self.B_model = self.L_matrix_inv_model * Vconv
self.A_discrete_model, self.B_discrete_model = \
controls.c2d(-self.A_model, self.B_model, 1.0 / hz)
self.B_discrete_inverse_model = numpy.matrix(numpy.eye(3)) / (
self.B_discrete_model[0, 0] - self.B_discrete_model[1, 0])
print('constexpr double kL = %g;' % self.L_model)
print('constexpr double kM = %g;' % self.M_model)
print('constexpr double kR = %g;' % self.R_model)
print('constexpr float kAdiscrete_diagonal = %gf;' %
self.A_discrete_model[0, 0])
print('constexpr float kAdiscrete_offdiagonal = %gf;' %
self.A_discrete_model[1, 0])
print('constexpr float kBdiscrete_inv_diagonal = %gf;' %
self.B_discrete_inverse_model[0, 0])
print('constexpr float kBdiscrete_inv_offdiagonal = %gf;' %
self.B_discrete_inverse_model[1, 0])
print('constexpr double kOneAmpScalar = %g;' % one_amp_scalar)
print('constexpr double kMaxOneAmpDrivingVoltage = %g;' %
max_one_amp_driving_voltage)
print('A_discrete', self.A_discrete)
print('B_discrete', self.B_discrete)
print('B_discrete_sub', numpy.linalg.inv(self.B_discrete[0:2, 0:2]))
print('B_discrete_inv', self.B_discrete_inverse)
# Xdot[5:, :] = (R_sense2 + R_sense1) / R_sense2 * (
# (1.0 / (R_sense1 * C_sense)) * (-Isense * R_sense2 / (R_sense1 + R_sense2) * (R_sense1 / R_sense2 + 1.0) + I))
self.mk1 = (R_sense2 + R_sense1) / R_sense2 * (1.0 /
(R_sense1 * C_sense))
self.mk2 = -self.mk1 * R_sense2 / (R_sense1 + R_sense2) * (
R_sense1 / R_sense2 + 1.0)
# ia, ib, ic, theta, omega, isensea, isenseb, isensec
self.X = numpy.matrix([[0.0], [0.0], [0.0], [-2.0 * numpy.pi / 3.0],
[0.0], [0.0], [0.0], [0.0]])
self.K = 0.05 * Vconv
print('A %s' % repr(self.A))
print('B %s' % repr(self.B))
print('K %s' % repr(self.K))
print('System poles are %s' % repr(numpy.linalg.eig(self.A)[0]))
print('Poles are %s' %
repr(numpy.linalg.eig(self.A - self.B * self.K)[0]))
controllability = controls.ctrb(self.A, self.B)
print('Rank of augmented controlability matrix. %d' %
numpy.linalg.matrix_rank(controllability))
self.data_logger = DataLogger(switching_pattern)
self.current_time = 0.0
self.estimated_velocity = self.X[4, 0]
def motor_diffeq(self, x, t, U):
I = numpy.matrix(x[0:3]).T
theta = x[3]
omega = x[4]
Isense = numpy.matrix(x[5:]).T
dflux = phases(f_single, theta) / Kv
Xdot = numpy.matrix(numpy.zeros((8, 1)))
di_dt = -self.A_model * I + self.B_model * U - self.L_matrix_inv_model * dflux * omega
torque = I.T * dflux
Xdot[0:3, :] = di_dt
Xdot[3, :] = omega
Xdot[4, :] = torque / J
Xdot[5:, :] = self.mk1 * I + self.mk2 * Isense
return numpy.squeeze(numpy.asarray(Xdot))
def DoControls(self, goal_current):
theta = self.X[3, 0]
# Use the actual angular velocity.
omega = self.X[4, 0]
measured_current = self.X[5:, :].copy()
# Ok, lets now fake it.
E_imag1 = numpy.exp(1j * theta) * K1 * numpy.matrix(
[[-1j], [-1j * numpy.exp(1j * numpy.pi * 2.0 / 3.0)],
[-1j * numpy.exp(-1j * numpy.pi * 2.0 / 3.0)]])
E_imag2 = numpy.exp(1j * 5.0 * theta) * K2 * numpy.matrix(
[[-1j], [-1j * numpy.exp(-1j * numpy.pi * 2.0 / 3.0)],
[-1j * numpy.exp(1j * numpy.pi * 2.0 / 3.0)]])
overall_measured_current = ((E_imag1 + E_imag2).real.T *
measured_current / one_amp_scalar)[0, 0]
current_error = goal_current - overall_measured_current
#print(current_error)
self.estimated_velocity += current_error * 1.0
omega = self.estimated_velocity
# Now, apply the transfer function of the inductor.
# Use that to difference the current across the cycle.
Icurrent = self.Ilast
# No history:
#Icurrent = phases(g_single, theta) * goal_current
Inext = phases(g_single, theta + omega * 1.0 / hz) * goal_current
deltaI = Inext - Icurrent
H1 = -numpy.linalg.inv(1j * omega * self.L_matrix +
self.R_matrix) * omega / Kv
H2 = -numpy.linalg.inv(1j * omega * 5.0 * self.L_matrix +
self.R_matrix) * omega / Kv
p_imag = H1 * E_imag1 + H2 * E_imag2
p_next_imag = numpy.exp(1j * omega * 1.0 / hz) * H1 * E_imag1 + \
numpy.exp(1j * omega * 5.0 * 1.0 / hz) * H2 * E_imag2
p = p_imag.real
# So, we now know how much the change in current is due to changes in BEMF.
# Subtract that, and then run the stock statespace equation.
Vn_ff = self.B_discrete_inverse * (Inext - self.A_discrete *
(Icurrent - p) - p_next_imag.real)
print('Vn_ff', Vn_ff)
print('Inext', Inext)
Vn = Vn_ff + self.K * (Icurrent - measured_current)
E = phases(f_single, self.X[3, 0]) / Kv * self.X[4, 0]
self.data_logger.log_controls(self.current_time, measured_current,
Icurrent, E, self.estimated_velocity)
self.Ilast = Inext
return Vn
def Simulate(self):
start_wall_time = time.time()
self.Ilast = numpy.matrix(numpy.zeros((3, 1)))
for n in range(200):
goal_current = 1.0
max_current = (
vcc - (self.X[4, 0] / Kv * 2.0)) / max_one_amp_driving_voltage
min_current = (
-vcc - (self.X[4, 0] / Kv * 2.0)) / max_one_amp_driving_voltage
goal_current = max(min_current, min(max_current, goal_current))
Vn = self.DoControls(goal_current)
#Vn = numpy.matrix([[1.00], [0.0], [0.0]])
Vn = numpy.matrix([[0.00], [1.00], [0.0]])
#Vn = numpy.matrix([[0.00], [0.0], [1.00]])
# T is the fractional rate.
T = Vn / vcc
tn = -numpy.min(T)
T += tn
if (T > 1.0).any():
T = T / numpy.max(T)
for t, U in sample_times(T=T,
dt=1.0 / hz,
n=10,
start_time=self.current_time):
# Analog amplifier mode!
#U = Vn
self.data_logger.log_data(self.X, (U - min(U)),
self.current_time, Vn, goal_current)
t_array = numpy.array([self.current_time, t])
self.X = numpy.matrix(
scipy.integrate.odeint(self.motor_diffeq,
numpy.squeeze(numpy.asarray(
self.X)),
t_array,
args=(U, )))[1, :].T
self.current_time = t
print('Took %f to simulate' % (time.time() - start_wall_time))
self.data_logger.plot()
simulation = Simulation()
simulation.Simulate()