def lsim(self, u, t, interp=0, returnall=False, X0=None):
"""Find the response of the TransferFunction to the input u
with time vector t. Uses signal.lsim.
return y the response of the system."""
if returnall:#most users will just want the system output y,
#but some will need the (t, y, x) tuple that
#signal.lsim returns
return signal.lsim(self, u, t, interp=interp, X0=X0)
else:
return signal.lsim(self, u, t, interp=interp, X0=X0)[1]
def time_response(self, F, t, ic=None):
r"""Time response for a mdof system.
This method returns the time response for a mdof system
given a force, time and initial conditions.
Parameters
----------
F : array
Force array (needs to have the same length as time array).
t : array
Time array.
ic : array, optional
The initial conditions on the state vector (zero by default).
Returns
----------
t : array
Time values for the output.
yout : array
System response.
xout : array
Time evolution of the state vector.
Examples
--------
>>> m1, m2 = 1, 1
>>> c1, c2, c3 = 1, 1, 1
>>> k1, k2, k3 = 1e3, 1e3, 1e3
>>> M = np.array([[m1, 0],
... [0, m2]])
>>> C = np.array([[c1+c2, -c2],
... [-c2, c2+c3]])
>>> K = np.array([[k1+k2, -k2],
... [-k2, k2+k3]])
>>> sys1 = VibSystem(M, C, K) # create the system
>>> t = np.linspace(0, 25, 1000) # time array
>>> F2 = np.zeros((len(t), 2))
>>> F2[:, 1] = 1000*np.sin(40*t) # force applied on m2
>>> t, yout, xout = sys1.time_response(F2, t)
>>> yout[:5, 0] # response on m1
array([ 0. , 0.00304585, 0.07034816, 0.32048951, 0.60748282])
>>> yout[:5, 1] # response on m2
array([ 0. , 0.08160348, 0.46442657, 0.7885541 , 0.47808092])
"""
if ic is not None:
return signal.lsim(self.H, F, t, ic)
else:
return signal.lsim(self.H, F, t)
def test_nonzero_initial_time(self):
system = self.lti_nowarn(-1.,1.,1.,0.)
t = np.linspace(1,2)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0])
expected_y = np.exp(-tout)
assert_almost_equal(y, expected_y)
def siggen_model(s, rad, phi, z, e, temp):
out = np.zeros(sample_length)
if temp < 40 or temp > 120:
return np.ones(sample_length)*-1.
detector.SetTemperature(temp)
siggen_wf= detector.GetSiggenWaveform(rad, phi, z, energy=2600)
if siggen_wf is None:
return np.ones(sample_length)*-1.
if np.amax(siggen_wf) == 0:
print "wtf is even happening here?"
return np.ones(sample_length)*-1.
siggen_wf = np.pad(siggen_wf, (detector.zeroPadding,0), 'constant', constant_values=(0, 0))
tout, siggen_wf, x = signal.lsim(system, siggen_wf, t)
siggen_wf /= np.amax(siggen_wf)
siggen_data = siggen_wf[detector.zeroPadding::]
siggen_data = siggen_data*e
siggen_start_idx = np.int(np.around(s, decimals=1) * data_to_siggen_size_ratio % data_to_siggen_size_ratio)
switchpoint_ceil = np.int( np.ceil(s) )
samples_to_fill = (sample_length - switchpoint_ceil)
sampled_idxs = np.arange(samples_to_fill, dtype=np.int)*data_to_siggen_size_ratio+siggen_start_idx
out[switchpoint_ceil:] = siggen_data[sampled_idxs]
return out
def siggen_model(s, rad, phi, z, e, temp, gradIdx, pcRadIdx):
out = np.zeros_like(data)
if (gradIdx > detectorList.shape[0]-1) or (pcRadIdx > detectorList.shape[1]-1) :
return np.ones_like(data)*-1.
detector = detectorList[gradIdx, pcRadIdx]
detector.SetTemperature(temp)
siggen_wf= detector.GetSiggenWaveform(rad, phi, z, energy=2600)
# print "len of siggen wf is %d" % len(siggen_wf)
if siggen_wf is None:
return np.ones_like(data)*-1.
if np.amax(siggen_wf) == 0:
print "wtf is even happening here?"
return np.ones_like(data)*-1.
siggen_wf = np.pad(siggen_wf, (detector.zeroPadding,0), 'constant', constant_values=(0, 0))
tout, siggen_wf, x = signal.lsim(system, siggen_wf, t)
siggen_wf /= np.amax(siggen_wf)
siggen_data = siggen_wf[detector.zeroPadding::]
siggen_data = siggen_data*e
out[s:] = siggen_data[0:(len(data) - s)]
return out
def rhSCCDisplacement(angVel, time):
radius = 3.2e-03
#define transfer function
T1 = 0.01 #value from wikibook
T2 = 5 #value from wikibook
#aligne with reid's line
rM_reid = thr.R2(-15)
#define orientation and size of right horizontal semicircular canal, and turn it into space-fixed coordinates
rhScc = np.array([0.32269,-0.03837,-0.94573])
rhSccSpace = rM_reid.dot(rhScc)
#sensed angular velocity in right horizontal semicircular canal
vel = angVel.dot(rhSccSpace)
numerator = [T1*T2, 0]
denominator = [T1*T2, T1+T2, 1]
scc = ss.lti(numerator,denominator)
#calculate system response of input using transfer function defined above
timeOut,sysResponse,timeEvol = ss.lsim(scc,vel,time)
#calculate the displacement of the cupula from the system response
displacementCupula = sysResponse*radius
return displacementCupula
def vestibularStimulation(self, sensor):
'''Stimulation of canals and otoliths.'''
# First for the angular velocity -----------------------
ReidangVel = rotmat.R2(15).dot(sensor.spaceAngVel.T)
# sensed angular velocity
omega = ReidangVel.T.dot(self.n_HorScc)
# Canal dynamics
tout, cupulaTheta, xout = ss.lsim(self.scc, omega, sensor.time)
# Displacement maxima
cupula = cupulaTheta * self.r_scc
sensedMaxima = {}
sensedMaxima['deflection_Max'] = max(cupula)
sensedMaxima['deflection_Min'] = min(cupula)
# Then for linear acceleration ----------------------------
onDir = np.array([0., 1., 0.])
accSensed = sensor.accReHead.dot(onDir)
# Acceleration maxima
sensedMaxima['acc_Max'] = max(accSensed)
sensedMaxima['acc_Min'] = min(accSensed)
return sensedMaxima
def siggen_model(s, rad, phi, z, e, temp):
out = np.zeros_like(data)
detector.SetTemperature(temp)
siggen_wf= detector.GetSiggenWaveform(rad, phi, z, energy=2600)
if siggen_wf is None:
return np.ones_like(data)*-1.
if np.amax(siggen_wf) == 0:
print "wtf is even happening here?"
return np.ones_like(data)*-1.
siggen_wf = np.pad(siggen_wf, (detector.zeroPadding,0), 'constant', constant_values=(0, 0))
tout, siggen_wf, x = signal.lsim(system, siggen_wf, t)
siggen_wf /= np.amax(siggen_wf)
siggen_data = siggen_wf[detector.zeroPadding::]
siggen_data = siggen_data*e
#ok, so the siggen step size is 1 ns and the
#WARNING: only works for 1 ns step size for now
#TODO: might be worth downsampling BEFORE applying transfer function
siggen_start_idx = np.int(np.around(s, decimals=1) * data_to_siggen_size_ratio % data_to_siggen_size_ratio)
switchpoint_ceil = np.int( np.ceil(s) )
samples_to_fill = (len(data) - switchpoint_ceil)
sampled_idxs = np.arange(samples_to_fill, dtype=np.int)*data_to_siggen_size_ratio+siggen_start_idx
out[switchpoint_ceil:] = siggen_data[sampled_idxs]
return out
def siggen_model(s, rad, phi, z, e, temp, num_1, num_2, num_3, den_1, den_2, den_3):
out = np.zeros_like(data)
detector.SetTemperature(temp)
siggen_wf= detector.GetSiggenWaveform(rad, phi, z, energy=2600)
if siggen_wf is None:
return np.ones_like(data)*-1.
if np.amax(siggen_wf) == 0:
print "wtf is even happening here?"
return np.ones_like(data)*-1.
siggen_wf = np.pad(siggen_wf, (detector.zeroPadding,0), 'constant', constant_values=(0, 0))
num = [num_1, num_2, num_3]
den = [1, den_1, den_2, den_3]
# num = [-1.089e10, 5.863e17, 6.087e15]
# den = [1, 3.009e07, 3.743e14,5.21e18]
system = signal.lti(num, den)
t = np.arange(0, len(siggen_wf)*10E-9, 10E-9)
tout, siggen_wf, x = signal.lsim(system, siggen_wf, t)
siggen_wf /= np.amax(siggen_wf)
siggen_data = siggen_wf[detector.zeroPadding::]
siggen_data = siggen_data*e
out[s:] = siggen_data[0:(len(data) - s)]
return out
def vestibularStimulation(self, sensor):
'''Stimulation of canals and otoliths.'''
# First for the angular velocity -----------------------
ReidangVel = np.dot(RotMat.R2(15), sensor.spaceAngVel.transpose())
# sensed angular velocity
omega = np.dot(ReidangVel.transpose(), self.n_HorScc)
# mpl.plot(sensor.time, omega)
# mpl.show()
# raw_input()
# Canal dynamics
tout, cupulaTheta, xout = ss.lsim(self.scc, omega, sensor.time)
#mpl.hold
#mpl.plot(tout, yout,'r')
# Displacement maxima
cupula = cupulaTheta * self.r_scc
sensedMaxima = {}
sensedMaxima['deflection_Max'] = max(cupula)
sensedMaxima['deflection_Min'] = min(cupula)
# Then for linear acceleration ----------------------------
onDir = np.array([0., 1., 0.])
accSensed = np.dot(sensor.accReHead, onDir)
# Acceleration maxima
sensedMaxima['acc_Max'] = max(accSensed)
sensedMaxima['acc_Min'] = min(accSensed)
return sensedMaxima
def _test_system():
"""Test PID algorithm."""
import scipy.signal as sig
# transfer function in s-space describes sys
tf = sig.tf2ss([10], [100, 10])
times = np.arange(1, 200, 5.0)
#step = 1 * np.ones(len(times))
# initialize PID
pid = PidController(2.0, 10.0, 0.0)
pid.anti_windup = 0.2
pid.vmin, pid.vmax = -200.0, 200.0
pid.setpoint = 50.0
pid._prev_time = 0.0
sysout = [0.0]
pidout = [0.0]
real_time = [0.0]
for time in times:
real_time.append(time)
pidout.append(pid.compute_output(sysout[-1], real_time[-1]))
t, sysout, xout = sig.lsim(tf, pidout, real_time)
fig = plt.figure()
ax = fig.add_subplot(111)
ax.plot(real_time, sysout, 'r', real_time, pidout, 'b--')
plt.show()
def exp_sin_respLTI(decay, zeta, freq, tvec):
H = sp.lti([1], poly1d([1, 2 * zeta * 1.5, 2.25]).coeffs)
u = cos(freq * tvec) * exp(-1 * decay * tvec)
t, x, svec = sp.lsim(H, u, tvec)
plot(t, x)
title("Complete Response at " + str(freq) + "Hz")
savefig("./Images/expsinLTI_" + str(freq) + ".png")
close()
return 0
def plot_response(system, u, t, name=""):
_, y, _= signal.lsim(system, u, t)
fig = go.Figure()
fig.add_trace(go.Scatter(x=t, y=u, name="input"))
fig.add_trace(go.Scatter(x=t, y=y, name="output"))
fig.add_trace(go.Scatter(x=t, y=y-u, name="error"))
fig.update_xaxes(title="Time (s)")
fig.update_layout(title=name)
fig.show()
def FoldedCascodeFilter(anInput, c1, c2, r): num = [c1*r,0] den = [c2*r, 1] system = signal.TransferFunction(num, den) t = np.arange(0, len(anInput)) tout, y, x = signal.lsim(system, anInput, t) return y
def test_integrator(self):
# integrator: y' = u
system = self.lti_nowarn(0., 1., 1., 0.)
t = np.linspace(0,5)
u = t
tout, y, x = lsim(system, u, t)
expected_x = 0.5 * tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def RLCFilter(anInput, rc, lc): num = [1] den = [lc, rc, 1] system = signal.TransferFunction(num, den) t = np.arange(0, len(anInput)) tout, y, x = signal.lsim(system, anInput, t) return y
def OpAmpFilter(anInput, r1, r2, c): num = [r2] den = [r1*r2*c, r1] system = signal.TransferFunction(num, den) t = np.arange(0, len(anInput)) tout, y, x = signal.lsim(system, anInput, t) return y
def test_integrator(self):
# integrator: y' = u
system = self.lti_nowarn(0., 1., 1., 0.)
t = np.linspace(0,5)
u = t
tout, y, x = lsim(system, u, t)
expected_x = 0.5 * tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def calc_inverse_Al_dynamics(t, T_targ, K, t0, zeta, n_per=1):
'''
Inverse of the second order dynamical model for tha Al cell
Gives the temperature input required for a target temperature output
t is the time signal (Assumes t is equally spaced!)
The rest of the inputs are constants defining the dynamic response
n_per is the number of repetitions. E.g., n_per = 10 will give the response after the input has already been applied 9 times
Useful for approximating a periodic system
'''
T_init = T_targ[0]
# Extend over n_per periods
if n_per > 1:
T_targ_ext = np.concatenate([T_targ[:-1]
for n in range(n_per)] + [T_targ[-1:]])
t_ext = np.concatenate([t[:-1] + n * t[-1]
for n in range(n_per)] + [t[-1:] * n_per])
else:
T_targ_ext = T_targ[:]
t_ext = t[:]
# Subtract initial value
T_targ_ext -= T_init
w0 = 2 * np.pi / t0
kz = K * zeta
a = 1 / (kz * w0)
b = (2 * kz * zeta - 1) / (kz**2)
c = (kz**2 - 2 * kz * zeta + 1) * w0 / (kz**3)
tau = kz / w0
# Derivative part
dt = t[1] - t[0]
#print(A, B, C, tau)
T_der = a * np.gradient(T_targ_ext, dt, edge_order=2)
# Gain part
T_gain = b * T_targ_ext
# Integral part
num = [c]
den = [1.0, 1.0 / tau]
int_sys = sig.lti(num, den)
t_int, T_int, x_out = sig.lsim(int_sys, T_targ_ext, t_ext)
T_in = T_der + T_gain + T_int + T_init
return T_in[-len(t):]
def test_first_order(self):
# y' = -y
# exact solution is y(t) = exp(-t)
system = self.lti_nowarn(-1., 1., 1., 0.)
t = np.linspace(0, 5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0])
expected_x = np.exp(-tout)
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def test_first_order(self):
# y' = -y
# exact solution is y(t) = exp(-t)
system = self.lti_nowarn(-1.,1.,1.,0.)
t = np.linspace(0,5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0])
expected_x = np.exp(-tout)
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_x)
def simulate(kp, ki, kd, time_arr, reference_arr, ax):
a = 0.94
b = 9
c = 0.4
system = sig.lti([0, 0, b * kp, b * ki],
[1, a + b * kd, c + b * kp, b * ki])
time_arr = np.linspace(9, 19.9, 500)
reference_arr = [90 if x > 10 else 0 for x in time_arr]
tout, response, _ = sig.lsim(system, reference_arr, time_arr, interp=0)
return time_arr, response
def simulate(self, u: np.ndarray, t: np.ndarray) -> np.ndarray:
"""
Simulate filter
:param u: filter input
:param t: timeseries
:return: filter output
"""
_, y, x = lsim(self.filter, U=u, T=t, X0=self.x)
self.x = x[-1]
return y
def graph_pid(kp, ki, kd, col):
a = 0.94
b = 9
c = 0.4
system = sig.lti([0, 0, b * kp, b * ki],
[1, a + b * kd, c + b * kp, b * ki])
time_arr = np.linspace(0, 10, 500)
reference_arr = np.repeat(90, 500)
tout, response, _ = sig.lsim(system, reference_arr, time_arr, interp=0)
pp.plot(time_arr, response, color=(col, 0, 1 - col))
def apply_to_signal(self, signal_in):
returning_signal = Signal(None)
returning_signal.copy_signal(signal_in)
if self.blockActivated:
if 1 / signal_in.period <= 3.9:
tout, y, ni = signal.lsim(
(self.b1, self.a1), signal_in.yValues, signal_in.timeArray)
returning_signal.set_x_y_values(tout, y)
returning_signal.cut_first_period()
elif 3510 >= 1 / signal_in.period > 3.9:
tout, y, ni = signal.lsim(
(self.b2, self.a2), signal_in.yValues, signal_in.timeArray)
returning_signal.set_x_y_values(tout, y)
returning_signal.cut_first_period()
else:
tout, y, ni = signal.lsim(
(self.b3, self.a3), signal_in.yValues, signal_in.timeArray)
returning_signal.set_x_y_values(tout, y)
returning_signal.cut_first_period()
return returning_signal
def ProcessWaveform(self, siggen_wf, outputLength, scale, switchpoint):
'''Use interpolation instead of rounding'''
siggen_len = self.num_steps #+ self.zeroPadding
# #TODO: i don't think zero padding actually does anything anyway
# if self.zeroPadding == 0:
# zeroPaddingIdx = 0
# else:
# siggen_wf = np.pad(siggen_wf, (self.zeroPadding,0), 'constant', constant_values=(0, 0))
# zeroPaddingIdx = self.zeroPadding
#actual wf gen
tout, siggen_data, x = signal.lsim(self.tfSystem, siggen_wf,
self.time_steps)
smax = np.amax(siggen_data)
# if smax == 0:
# print "waveform max is 0 -- something went wrong"
# exit(0)
siggen_data /= smax
# siggen_data = siggen_wf[zeroPaddingIdx::]
siggen_data *= scale
#resample the siggen wf to the 10ns digitized data frequency w/ interpolaiton
switchpoint_ceil = np.int(np.ceil(switchpoint))
samples_to_fill = (outputLength - switchpoint_ceil)
siggen_interp_fn = interpolate.interp1d(np.arange(self.num_steps),
siggen_data,
kind="linear",
copy="False",
assume_sorted="True")
siggen_start_idx = (switchpoint_ceil -
switchpoint) * self.data_to_siggen_size_ratio
sampled_idxs = np.arange(
samples_to_fill) * self.data_to_siggen_size_ratio + siggen_start_idx
out = np.zeros(outputLength)
try:
out[switchpoint_ceil:] = siggen_interp_fn(sampled_idxs)
except ValueError:
print "Something goofy happened here during interp"
print outputLength
print siggen_wf.size
print sampled_idxs[-10:]
return None
return out
def sin_paNotch():
w, f, dB, phase, sys, w0 = pasa_alto_notch.pa_notch()
A = float(input()) # amplitud del seno de mi señal
w1 = float(input()) # frecuencia de mi señal
t = np.linspace(0, 5, 500)
u = A * np.sin(w1 * t)
tout, y, x = signal.lsim(sys, u, t)
plt.plot(t, y)
plt.xlabel('seg')
plt.ylabel('A (amplitud)')
plt.grid()
plt.show()
def processInput(self, inputSignal, loadingModel, fraction):
actual = inputSignal
tfList = tf.getTf()
paso = fraction / len(tfList)
for tfi in tfList:
t, y, x = signal.lsim(tfi, actual.values, actual.xvar)
actual = Senial(t, y)
if loadingModel:
loadingModel.update(paso)
return actual
def RLC(time, inp=func, bode=False, R=100, L=1e-6, C=1e-6):
H = sp.lti([1], [L * C, R * C, 1])
if bode:
w, S, phi = H.bode()
fig, (ax1, ax2) = plt.subplots(2, 1)
ax1.set_title("Magnitude response")
ax1.semilogx(w, S)
ax2.set_title("Phase response")
ax2.semilogx(w, phi)
plt.show()
return sp.lsim(H, inp(time), time)
def fullModel(IsPfc, angles, Rc, time):
Is2Bpol2 = buildIs2BpolB(isttok_mag_2)
RIc = isttok_mag['RM'] + isttok_mag['Rcopper'] * np.cos(anglesIc)
ZIc = isttok_mag['Rcopper'] * np.sin(anglesIc)
A2, Bs2, C2, Ds2 = buildLtiModelB(RIc, ZIc, isttok_mag_2, Rc)
Ic2Bpol = buildIc2Bpol(RIc, ZIc)
magSys2 = signal.StateSpace(A2, Bs2, C2, Ds2)
bPolIs2 = np.matmul(Is2Bpol2, IsPfc)
tout2, Ic2, x2 = signal.lsim(magSys2, IsPfc.T, time)
bPolIc2 = np.matmul(Ic2Bpol, Ic2.T)
bPolTot2 = (bPolIs2.T + bPolIc2.T) * 50 * 49e-6
return bPolTot2, (RIc, ZIc)
def grafSignal(self, sys2, w0):
if senhal['senoide']:
amp = senhalparams['Amplitud']
w1 = senhalparams['frecuencia']
t = np.linspace(0, 5, 500)
u = amp * np.sin(w1 * t)
tout, y, x = signal.lsim(sys2, u, t)
self.ax1.plot(tout, y)
self.ax1.set_xlabel('seg')
self.ax1.set_ylabel('A (ammplitud)')
self.ax1.grid(True)
elif senhal['pulso']:
amp = senhalparams['Amplitud']
t = np.linspace(0, 5 * (1 / w0), 5000)
u = amp * (np.sign(t) + 1)
tout, y, x = signal.lsim(sys2, u, t)
self.ax1.plot(tout, y)
self.ax1.set_xlabel('seg')
self.ax1.set_ylabel('A (ammplitud)')
self.ax1.grid(True)
else:
amp = senhalparams['Amplitud']
duty = senhalparams['DutyCicle']
f1 = senhalparams['frecuencia']
w1 = f1 * 2 * np.pi
t = np.linspace(0, 2, 500)
u = amp * signal.square(2 * np.pi * w1 * t, duty)
tout, y, x = signal.lsim(sys2, u, t)
self.ax1.plot(tout, y)
self.ax1.set_xlabel('seg')
self.ax1.set_ylabel('A (ammplitud)')
self.ax1.grid(True)
def rspect(A, z, fs):
"""
by Omar
A: Señal de acceleraciones
z: amortiguamiento
fs: Frecuencia de adqusición o muestreo
"""
# ¿Qué es T?
T = [(x * 1 / fs) for x in range(0, len(A))]
# Pseudo acceleration response spectrum
Pa = []
# Oscilator periods for start=0.0,stop=4.0,step=0.02
Ts = spec_period_serie()
for i in range(len(Ts)):
t = Ts[i]
wn = (2.0 * numpy.pi) / t
# H = sg.TransferFunction(num=[0.0, 0.0, -1.0], den=[1.0, 2.0*z*wn, wn**2])
# H2 = sg.TransferFunction(num=[-1.0, 0.0, 0.0], den=[1.0, 2.0*z*wn, wn**2])
H = sg.TransferFunction([-1.0, 0.0, 0.0], [wn, 2.0 * z * wn, 1.0])
H2 = sg.TransferFunction([0.0, 0.0, -1.0], [wn, 2.0 * z * wn, 1.0])
# tout, a 1D array, time values for the output
# yout, 1D array system response
# xout, time evolution of the state vector
# displacement response
Tout, Yout, Xout = sg.lsim(system=H, U=A, T=T)
# acceleration response
Tout1, Yout1, Xout1 = sg.lsim(system=H2, U=A, T=T)
D = max(map(lambda x: abs(x), Yout))
EA = max(map(lambda x: abs(x),
Yout1)) # No sé donde se usa esta variable
Pa.append(D * (2 * numpy.pi / Ts[i])**2 /
9.81) # ¿Es acceleración o desplazamiento?
return Ts, Pa
def test_double_integrator(self):
# double integrator: y'' = 2u
A = np.mat("0. 1.; 0. 0.")
B = np.mat("0.; 1.")
C = np.mat("2. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0, 5)
u = np.ones_like(t)
tout, y, x = lsim(system, u, t)
expected_x = np.transpose(np.array([0.5 * tout**2, tout]))
expected_y = tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_y)
def get_output_with_lsim(H, x, t):
simplH = simplify(H)
num = fraction(simplH)[0]
den = fraction(simplH)[1]
num2, den2 = get_numpy_array_from_Poly(num, den)
num2 = np.poly1d(num2)
den2 = np.poly1d(den2)
H = sp.lti(num2, den2)
t, y, sec = sp.lsim(H, x, t)
return t, y
def test_double_integrator(self):
# double integrator: y'' = 2u
A = matrix([[0., 1.], [0., 0.]])
B = matrix([[0.], [1.]])
C = matrix([[2., 0.]])
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0, 5)
u = np.ones_like(t)
tout, y, x = lsim(system, u, t)
expected_x = np.transpose(np.array([0.5 * tout**2, tout]))
expected_y = tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_y)
def test_double_integrator(self):
# double integrator: y'' = 2u
A = np.mat("0. 1.; 0. 0.")
B = np.mat("0.; 1.")
C = np.mat("2. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0,5)
u = np.ones_like(t)
tout, y, x = lsim(system, u, t)
expected_x = np.transpose(np.array([0.5 * tout**2, tout]))
expected_y = tout**2
assert_almost_equal(x, expected_x)
assert_almost_equal(y, expected_y)
def getFitWaveformRLC(step):
lc = 10.
rc = 10.
num = [1]
den = [lc, rc, 1]
system = signal.TransferFunction(num, den)
t = np.arange(0, len(step))
tout, y, x = signal.lsim(system, step, t)
return (y)
def getFitWaveformRLC(step): lc = 10. rc = 10. num = [1] den = [lc, rc, 1] system = signal.TransferFunction(num, den) t = np.arange(0, len(step)) tout, y, x = signal.lsim(system, step, t) return (y)
def ProcessWaveform(self, siggen_wf, outputLength, scale, switchpoint):
'''Use interpolation instead of rounding'''
siggen_len = self.num_steps #+ self.zeroPadding
# #TODO: i don't think zero padding actually does anything anyway
# if self.zeroPadding == 0:
# zeroPaddingIdx = 0
# else:
# siggen_wf = np.pad(siggen_wf, (self.zeroPadding,0), 'constant', constant_values=(0, 0))
# zeroPaddingIdx = self.zeroPadding
#actual wf gen
tout, siggen_data, x = signal.lsim(self.tfSystem, siggen_wf, self.time_steps)
smax = np.amax(siggen_data)
# if smax == 0:
# print "waveform max is 0 -- something went wrong"
# exit(0)
siggen_data /= smax
# siggen_data = siggen_wf[zeroPaddingIdx::]
siggen_data *= scale
#resample the siggen wf to the 10ns digitized data frequency w/ interpolaiton
switchpoint_ceil= np.int( np.ceil(switchpoint) )
samples_to_fill = (outputLength - switchpoint_ceil)
siggen_interp_fn = interpolate.interp1d(np.arange(self.num_steps ), siggen_data, kind="linear", copy="False", assume_sorted="True")
siggen_start_idx = (switchpoint_ceil - switchpoint) * self.data_to_siggen_size_ratio
sampled_idxs = np.arange(samples_to_fill)*self.data_to_siggen_size_ratio + siggen_start_idx
out = np.zeros(outputLength)
try:
out[switchpoint_ceil:] = siggen_interp_fn(sampled_idxs)
except ValueError:
print "Something goofy happened here during interp"
print outputLength
print siggen_wf.size
print sampled_idxs[-10:]
return None
return out
def getFitWaveformFoldedCascode(step):
r = 1.
c1 = 1.
c2 = 2000.
num = [c1 * r, 0]
den = [c2 * r, 1]
system = signal.TransferFunction(num, den)
t = np.arange(0, len(step))
tout, y, x = signal.lsim(system, step, t)
return (y)
def getFitWaveformOpAmp(step):
r1 = 5
r2 = 5
c = 2.
num = [r2]
den = [r1 * r2 * c, r1]
system = signal.TransferFunction(num, den)
t = np.arange(0, len(step))
tout, y, x = signal.lsim(system, step, t)
return (y)
def getFitWaveformFoldedCascode(step): r = 1. c1 = 1. c2 = 2000. num = [c1*r,0] den = [c2*r, 1] system = signal.TransferFunction(num, den) t = np.arange(0, len(step)) tout, y, x = signal.lsim(system, step, t) return (y)
def time_response(self, F, t, ic=None):
r"""Time response for a mdof system.
This method returns the time response for a mdof system
given a force, time and initial conditions.
Parameters
----------
F : array
Force array (needs to have the same length as time array).
t : array
Time array.
ic : array, optional
The initial conditions on the state vector (zero by default).
Returns
----------
t : array
Time values for the output.
yout : array
System response.
xout : array
Time evolution of the state vector.
Examples
--------
>>> m0, m1 = 1, 1
>>> c0, c1, c2 = 1, 1, 1
>>> k0, k1, k2 = 1e3, 1e3, 1e3
>>> M = np.array([[m0, 0],
... [0, m1]])
>>> C = np.array([[c0+c1, -c2],
... [-c1, c2+c2]])
>>> K = np.array([[k0+k1, -k2],
... [-k1, k2+k2]])
>>> sys = VibeSystem(M, C, K) # create the system
>>> t = np.linspace(0, 25, 1000) # time array
>>> F1 = np.zeros((len(t), 2))
>>> F1[:, 1] = 1000*np.sin(40*t) # force applied on m1
>>> t, yout, xout = sys.time_response(F1, t)
>>> # response on m0
>>> yout[:5, 0]
array([ 0. , 0. , 0.07, 0.32, 0.61])
>>> # response on m1
>>> yout[:5, 1]
array([ 0. , 0.08, 0.46, 0.79, 0.48])
"""
return signal.lsim(self.lti, F, t, X0=ic)
def getFitWaveformOpAmp(step): r1 = 5 r2 = 5 c = 2. num = [r2] den = [r1*r2*c, r1] system = signal.TransferFunction(num, den) t = np.arange(0, len(step)) tout, y, x = signal.lsim(system, step, t) return (y)
def test_jordan_block(self):
# Non-diagonalizable A matrix
# x1' + x1 = x2
# x2' + x2 = u
# y = x1
# Exact solution with u = 0 is y(t) = t exp(-t)
A = np.mat("-1. 1.; 0. -1.")
B = np.mat("0.; 1.")
C = np.mat("1. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0, 5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[0.0, 1.0])
expected_y = tout * np.exp(-tout)
assert_almost_equal(y, expected_y)
def test_jordan_block(self):
# Non-diagonalizable A matrix
# x1' + x1 = x2
# x2' + x2 = u
# y = x1
# Exact solution with u = 0 is y(t) = t exp(-t)
A = np.mat("-1. 1.; 0. -1.")
B = np.mat("0.; 1.")
C = np.mat("1. 0.")
system = self.lti_nowarn(A, B, C, 0.)
t = np.linspace(0,5)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[0.0, 1.0])
expected_y = tout * np.exp(-tout)
assert_almost_equal(y, expected_y)
def create_initial(pop_num, pop, kd_min, kd_max, kp_min, kp_max, ki_min,
ki_max, desired_x, system_force, dt, MSDnum, MSDden, times):
"""Creates the initial population of the genetic algorithm while making sure it adheres to force constraints"""
for s in range(pop_num):
flag = True
while flag == True:
flagged = 0
#Creating the random PID values
kd_cur = round(random.uniform(kd_min, kd_max), 2)
kp_cur = round(random.uniform(kp_min, kp_max), 2)
ki_cur = round(random.uniform(ki_min, ki_max), 2)
#Simulate for PID values
GAnum = [kd_cur, kp_cur, ki_cur] # kd, kp, ki
GAden = [0, 1, 0]
GHs_num = signal.convolve(GAnum, MSDnum)
GHs_den = signal.convolve(GAden, MSDden)
#Create CLTF
cltf_num = GHs_num
cltf_den = GHs_den + GHs_num
cltf = signal.TransferFunction(cltf_num, cltf_den)
#Simulates the current system [s].
t_out, y_out, state = signal.lsim(cltf, U=desired_x, T=times)
err_sig = []
for y in range(len(times)):
err_sig.append(desired_x[y] - y_out[y])
for y in range(1, len(err_sig)):
y_curr = []
y_curr = [err_sig[y - 1], err_sig[y]]
err_int = np.trapz(y_curr, dx=dt)
err_diff = (y_curr[1] - y_curr[0]) / dt
#pid force = kp * e ki * i_e kd * d_e
pid_force = kp_cur * err_sig[
y] + ki_cur * err_int + kd_cur * err_diff
#if PID values exceeds requirements for time step, flag it.
if system_force < pid_force:
flagged = flagged + 1
#If system never exceeds max force then continue.
if flagged == 0:
flag = False
#Into 2-D List. Access via pop[i][j]
pop.insert(s, [kd_cur, kp_cur, ki_cur])
return pop
def crossover(a, b, system_force, desired_x, times, dt, MSDnum, MSDden):
"""Finding cut-points for crossover
and joining the two parts of the two members
of the population together. """
new_a = [] #Clearing previous
cut_a = random.randint(1, len(a) - 1) #Makes sure there is always a cut
new_a1 = a[0:cut_a]
new_a2 = b[cut_a:len(b)]
#Creates the new crossed-over list
new_a = new_a1 + new_a2
#trying to keep force constraints upheld
#Simulate for PID values
GAnum = [new_a[0], new_a[1], new_a[2]] # kd, kp, ki
GAden = [0, 1, 0]
GHs_num = signal.convolve(GAnum, MSDnum)
GHs_den = signal.convolve(GAden, MSDden)
#Create CLTF
cltf_num = GHs_num
cltf_den = GHs_den + GHs_num
cltf = signal.TransferFunction(cltf_num, cltf_den)
#Simulates the current system [s].
t_out, y_out, state = signal.lsim(cltf, U=desired_x, T=times)
err_sig = []
for y in range(len(times)):
err_sig.append(desired_x[y] - y_out[y])
flagged = 0
for y in range(1, len(err_sig)):
y_curr = []
y_curr = [err_sig[y - 1], err_sig[y]]
err_int = np.trapz(y_curr, dx=dt)
err_diff = (y_curr[1] - y_curr[0]) / dt
#pid force = kp * e ki * i_e kd * d_e
pid_force = new_a[1] * err_sig[y] + new_a[2] * err_int + new_a[
0] * err_diff
#if PID values exceeds requirements for time step, flag it.
if system_force < pid_force:
flagged = flagged + 1
#If system exceeds max force then crossover is aborted.
if flagged > 0:
new_a = a
return new_a
def run():
# Generate 2nd order transfer function
zeta = 0.2 # damping ratio
f_n = 2.0 # natural frequency
w_n = f_n * 2.0*np.pi
num = [w_n**2]
den = [1, 2.0*zeta*w_n, w_n**2]
Gs = signal.TransferFunction(num, den)
# Simulation parameters
n_steps = 1000
t = np.linspace(0, 5, n_steps)
u = np.ones(n_steps) # input signal
u[int(n_steps/2):-1] = -1
# Simulate the output of the continuous-time system
t, y, x = signal.lsim(Gs, U=u, T=t)
dt = t[1]
# Identification
n = 2 # order of the denominator (a_1,...,a_n)
m = 2 # order of the numerator (b_0,...,b_m)
d = 1
rls = ArxRls(n, m, d)
for k in range(n_steps):
rls.update(u[k], y[k])
theta_hat = rls._theta_hat
# Construct discrete-time TF from vector of estimated parameters
num = [theta_hat.item(i) for i in range(n, n+m+1)] # b0 .. bm
den = [theta_hat.item(i) for i in range(0, n)] # a1 .. an
den.insert(0, 1.0) # add 1 to get [1, a1, .., an]
Gz = signal.TransferFunction(num, den, dt=dt)
# TODO: add delay of d
# Simulate the output and compare with the true system
t, y_est = signal.dlsim(Gz, u, t=t)
plt.plot(t, y, t, y_est)
plt.legend(["True", "Estimated"])
plt.xlabel("Time (s)")
plt.ylabel("Amplitude (-)")
plt.show()
# design controller
(kc, ki, kd) = computePidGmvc(num, den, dt, sigma=0.1, delta=0.0, lbda=0.5)
print("kc = {}, ki = {}, kd = {}\n".format(kc, ki, kd))
return
def plot_prefilter(system, prefilter, u, t, name=""):
print(prefilter.shape)
print(u.shape)
y = signal.convolve(u, prefilter, mode="same")
print(y.shape)
fig = go.Figure()
fig.add_trace(go.Scatter(x=t, y=u, name="input"))
fig.add_trace(go.Scatter(x=t, y=y, name="prefiltered"))
_, y, _= signal.lsim(system, y, t)
#fig = go.Figure()
fig.add_trace(go.Scatter(x=t, y=y, name="output"))
fig.add_trace(go.Scatter(x=t, y=y-u, name="error"))
#fig.add_trace(go.Scatter(x=t, y=y-u, name="error"))
fig.update_xaxes(title="Time (s)")
fig.update_layout(title=name)
fig.show()
def ltisys(T, U):
tf = transfunc()
t, yout, xout = scisig.lsim(tf, U=U, T=T)
# t, s = scisig.step(tf, T=T)
# t, i = scisig.impulse(tf, T)
# data = (t, (yout, U, xout[:, 0], xout[:, 1]))
# params = ({'label': 'response'},
# {'label': 'input'},
# {'label': 'xout[:, 0]'},
# {'label': 'xout[:, 1]'})
# smdplt.basicplot(data, params, xlabel='time, [s]', ylabel='response',
# suptitle=' ', title='Spring-Mass-Damper Time Response',
# xmax=np.max(T), filename='smd_response_ltisys.png')
return yout
def plotter(f,t):
transfer_function = sp.lti([1],[1,0,2.25])
t,h_t = sp.impulse(transfer_function,None,t)
t,y,svec = sp.lsim(transfer_function, f, t)
plt.subplot(3,1,1)
plt.plot(t,f, 'r')
plt.grid(True)
plt.title("Input")
plt.subplot(3,1,2)
plt.plot(t, h_t, 'y')
plt.grid(True)
plt.title('Impulse response')
plt.subplot(3,1,3)
plt.plot(t,y,'b')
plt.title('Output')
plt.grid(True)
plt.show()
def test_miso(self):
# A system with two state variables, two inputs, and one output.
A = np.array([[-1.0, 0.0], [0.0, -2.0]])
B = np.array([[1.0, 0.0], [0.0, 1.0]])
C = np.array([1.0, 0.0])
D = np.zeros((1, 2))
system = self.lti_nowarn(A, B, C, D)
t = np.linspace(0, 5.0, 101)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0, 1.0])
expected_y = np.exp(-tout)
expected_x0 = np.exp(-tout)
expected_x1 = np.exp(-2.0 * tout)
assert_almost_equal(y, expected_y)
assert_almost_equal(x[:, 0], expected_x0)
assert_almost_equal(x[:, 1], expected_x1)
def test_miso(self):
# A system with two state variables, two inputs, and one output.
A = np.array([[-1.0, 0.0], [0.0, -2.0]])
B = np.array([[1.0, 0.0], [0.0, 1.0]])
C = np.array([1.0, 0.0])
D = np.zeros((1,2))
system = self.lti_nowarn(A, B, C, D)
t = np.linspace(0, 5.0, 101)
u = np.zeros_like(t)
tout, y, x = lsim(system, u, t, X0=[1.0, 1.0])
expected_y = np.exp(-tout)
expected_x0 = np.exp(-tout)
expected_x1 = np.exp(-2.0*tout)
assert_almost_equal(y, expected_y)
assert_almost_equal(x[:,0], expected_x0)
assert_almost_equal(x[:,1], expected_x1)
def lsim(self, u, t, interp=0, returnall=False, X0=None, hmax=None):
"""Find the response of the TransferFunction to the input u
with time vector t. Uses signal.lsim.
return y the response of the system."""
try:
out = signal.lsim(self, u, t, interp=interp, X0=X0)
except LinAlgError:
#if the system has a pure integrator, lsim won't work.
#Call lsim2.
out = self.lsim2(u, t, X0=X0, returnall=True, hmax=hmax)
#override returnall because it is handled below
if returnall:#most users will just want the system output y,
#but some will need the (t, y, x) tuple that
#signal.lsim returns
return out
else:
return out[1]
def NLsysSimulate(self,R):
"""
R is the input vector.
"""
y_out = numpy.zeros(self.N)
for i in numpy.arange(0,self.N):
# Calculates the error signal:
if (self.Malha == 'Fechada'):
e = self.K * (R[i] - self.y0[0])
else:
e = self.K * R[i]
# Check if C(s) is defined.
if (len(self.Cden) > 1):
# Solve one step of the C(s) differential equation:
t, yc, xout = signal.lsim((self.Cnum,self.Cden),numpy.array([self.e0,e]),numpy.array([0,self.delta_t]),self.X0)
self.u = yc[1]
self.X0 = xout[1] # Save the last state.
else:
self.u = e
self.e0 = e
# Solve one step of the non-linear differential equation:
if (self.order == 1):
y = odeint(self.NLsysODE1,self.y0[0],numpy.array([0,self.delta_t]))
self.y0[0]=y[1]
y_out[i] = y[0]
elif (self.order == 2):
y = odeint(self.NLsysODE2,self.y00,numpy.array([0,self.delta_t]))
self.y00=y[1]
y_out[i] = y[0][0]
#self.tfinal = t[-1]
#self.Rfinal = u[-1]
#self.Wfinal = w[-1]
return y_out
def plotWaveform(wfFig, np_data_early, wfScale, offset):
plt.figure(wfFig.number)
plt.clf()
plt.title("Charge waveform")
plt.xlabel("Sample number [10s of ns]")
plt.ylabel("Raw ADC Value [Arb]")
plt.plot( np_data_early ,color="red" )
siggen_wf= det.GetSiggenWaveform(10, 0, 10, energy=1)
#siggen_fit = det.ProcessWaveform(siggen_fit)
siggen_wf = np.pad(siggen_wf, (det.zeroPadding,0), 'constant', constant_values=(0, 0))
num = [-1.089e10, 5.863e17, 6.087e15]
den = [1, 3.009e07, 3.743e14,5.21e18]
system = signal.lti(num, den)
t = np.arange(0, len(siggen_wf)*10E-9, 10E-9)
tout, siggen_wf, x = signal.lsim(system, siggen_wf, t)
# siggen_wf /= np.amax(siggen_wf)
siggen_wf /= np.amax(siggen_wf)
siggen_wf *= wfScale
siggen_wf = siggen_wf[500::]
plt.plot(np.arange(offset, len(siggen_wf)+offset), siggen_wf ,color="blue" )
# plt.axvline(x=lastFitSampleIdx, linewidth=1, color='r',linestyle=":")
# plt.axvline(x=startGuess, linewidth=1, color='g',linestyle=":")
plt.xlim(0, len(np_data_early))
value = raw_input(' --> Press s to skip, q to quit, any other key to continue with fit\n')
if value == 'q':
exit(0)
if value == 's':
return 0
return 1
def get_next_state(self,rtl_result):
#ex. divide_num=2 and time_step = 1
# t_in = [0,0.5,1]
t_in = np.linspace(self.current_time, self.current_time + self.time_step, self.divide_num + 1)
if debug:
print(t_in)
sig_t = self.sig_h.val_t(t_in)
noise_t = self.noise_h.val_t(t_in)
_, out_t,__ = signal.lsim((self.filter1_b,self.filter1_a),sig_t+noise_t,t_in,self.sig_h.current_val)
#late: >2s for 500step
#_, out_t,__ = signal.lsim2((np.real(self.filter1_b),np.real(self.filter1_a)),sig_t+noise_t,t_in,self.sig_h.current_val,atol=1.0e-3,rtol=1.0e-3)
self.dsm.get_next_state(out_t[-1])
self.sinc.get_next_state(self.dsm.out)
#log data
self.inmonitor.add_new_data(self.current_time+self.time_step,sig_t[-1]+noise_t[-1])
self.monitor.add_new_data(self.current_time+self.time_step,out_t[-1])
self.dsmonitor.add_new_data(self.current_time+self.time_step,self.dsm.out)
self.sincmonitor.add_new_data(self.current_time+self.time_step,self.sinc.dif3)
#cation! time = current_time
self.rtlsincmonitor.add_new_data(self.current_time,rtl_result)
#step end process
self.current_time += self.time_step
if debug:
print("sig: "+str(sig_t[-1])+"@python")
print("noise: "+str(sig_t[-1])+"@python")
print("dt: "+str(self.dt)+"@python")
print("filter_b: "+str(self.filter1_b)+"@python")
print("return to: "+str(out_t[-1])+"@python")
return self.dsm.out
def ProcessWaveform(self, siggen_wf, outputLength, scale, switchpoint):
'''Use interpolation instead of rounding'''
siggen_len = self.num_steps #+ self.zeroPadding
# #TODO: i don't think zero padding actually does anything anyway
# if self.zeroPadding == 0:
# zeroPaddingIdx = 0
# else:
# siggen_wf = np.pad(siggen_wf, (self.zeroPadding,0), 'constant', constant_values=(0, 0))
# zeroPaddingIdx = self.zeroPadding
#actual wf gen
tout, siggen_data, x = signal.lsim(self.tfSystem, siggen_wf, self.time_steps)
siggen_data /= np.amax(siggen_data)
# siggen_data = siggen_wf[zeroPaddingIdx::]
siggen_data *= scale
#resample the siggen wf to the 10ns digitized data frequency w/ interpolaiton
switchpoint_ceil= np.int( np.ceil(switchpoint) )
samples_to_fill = (outputLength - switchpoint_ceil)
siggen_interp_fn = interpolate.interp1d(np.arange(self.num_steps ), siggen_data, kind="linear", copy="False", assume_sorted="True")
siggen_start_idx = switchpoint_ceil - switchpoint
sampled_idxs = np.arange(samples_to_fill)*self.data_to_siggen_size_ratio + siggen_start_idx
# print sampled_idxs
out = np.zeros(outputLength)
out[switchpoint_ceil:] = siggen_interp_fn(sampled_idxs)
return out
# the solution of wc: 10 is an estimate in the handbook
s = tf([1, 0], 1)
G = funG(s)
Gd = funGd(s)
G2 = (200 * (0.01 * s + 1)) / ((10 * s + 1) * (0.1 * s + 1)) # simplified G
K = wc / s / G2
L = G * K
S = 1 / (1 + L)
T = 1 - S
Sd = S * Gd
t = np.linspace(0, 3)
u = np.ones(np.size(t))
[t, yr, x] = sc.lsim((T.numerator, T.denominator), u, t)
[t, yd, x] = sc.lsim((Sd.numerator, Sd.denominator), u, t)
plt.figure('Figure 2.22')
plt.subplot(1, 2, 1)
plt.title('Tracking response')
plt.plot(t, yr)
plt.plot(t, u, '--')
plt.axis([0, 3, -0.2, 1.2])
plt.ylabel('y(t)')
plt.xlabel('Time (s)')
plt.subplot(1, 2, 2)
plt.title('Disturbance response')
plt.plot(t, yd)
plt.plot(t, u * 0, '--')