def graficado(valor_ajustado_de_la_deslizadera_del_tiempo, tamaño_impulso,
tamaño_escalon, tamaño_rampa, boton_pulsado, G0):
fig.clf()
retardo = eval(input_del_retardo_en_la_ventana.get())
if boton_pulsado == 'Impulso':
t, y = control.impulse_response(
G0 * tamaño_impulso,
T=(valor_ajustado_de_la_deslizadera_del_tiempo))
if boton_pulsado == 'Escalon':
t, y = control.step_response(
G0 * tamaño_escalon,
T=(valor_ajustado_de_la_deslizadera_del_tiempo))
if boton_pulsado == 'Rampa':
t, y = control.step_response(
G0 * tamaño_rampa / s,
T=(valor_ajustado_de_la_deslizadera_del_tiempo))
if boton_pulsado == 'Arbitraria':
t, y, xout = control.forced_response(G0,
T=(t_experimental),
U=(u_experimental))
t_a_dibujar, y_a_dibujar = ajusta_el_retardo_segun_el_input_de_la_ventana(
t, y, retardo)
fig.add_subplot(111).plot(t_a_dibujar, y_a_dibujar)
canvas.draw()
def pidplot1(num, den, kp, ki, kd):
G = control.tf(num, den)
if ki != 0:
g2 = control.tf([kd, kp, ki], [1, 0])
else:
g2 = control.tf([kd, kp], [1])
k = control.series(G, g2)
v = control.feedback(k, 1)
t1, y1 = control.step_response(G)
t2, y2 = control.step_response(v)
plt.plot(t2, y2, 'r', linewidth=1, label='G(s) with PID control')
plt.grid(True)
s = '(Kp=' + str(kp) + ',Ki=' + str(ki) + ',Kd=' + str(kd) + ')'
plt.title('Time response of G(s) with PID control' + s)
plt.xlabel('Time(sec)')
plt.ylabel('Amplitude')
if not os.path.isdir('static'):
os.mkdir('static')
else:
# Remove old plot files
for filename in glob.glob(
os.path.join('static', 'pidcontrol', 'pidc1.png')):
os.remove(filename)
pidc1 = os.path.join('static', 'pidcontrol', 'pidc1.png')
plt.savefig(pidc1)
plt.clf()
plt.cla()
plt.close()
return pidc1
def Controlador(X):
#Atribuição dos paramentros Kp, Ki e Kd
Kp = Kpi + X[0] / 100
Ki = Kii + X[1] / 100
Kd = Kdi + X[2] / 100
#Função Transferência dos termos do controlador
P = Kp
I = tf(Ki, [1, 0])
D = tf([Kd, 0], [0.1 * Kd, 1])
#União dos blocos PID
C = parallel(P, I, D)
# Função Transferência com o Controlador
F = series(C, G)
# Penalidade para o valor do sinal de Entrada na planta
# ou seja penalidade para o sinal de Controle alto
tc = feedback(C, G)
_, yc = step_response(tc, time)
if max(yc) > maxcontrolador:
#SE1 = np.square(np.subtract(1,yc))
ISE = tdiv + max(yc)
else:
# Realizando a Integral do erro quadrado
t1 = feedback(F, 1)
_, y1 = step_response(t1, time)
SE = np.square(np.subtract(1, y1))
ISE = np.sum(SE)
return (ISE)
def test_response_copy():
# Generate some initial data to use
sys_siso = ct.rss(4, 1, 1)
response_siso = ct.step_response(sys_siso)
siso_ntimes = response_siso.time.size
sys_mimo = ct.rss(4, 2, 1)
response_mimo = ct.step_response(sys_mimo)
mimo_ntimes = response_mimo.time.size
# Transpose
response_mimo_transpose = response_mimo(transpose=True)
assert response_mimo.outputs.shape == (2, 1, mimo_ntimes)
assert response_mimo_transpose.outputs.shape == (mimo_ntimes, 2, 1)
assert response_mimo.states.shape == (4, 1, mimo_ntimes)
assert response_mimo_transpose.states.shape == (mimo_ntimes, 4, 1)
# Squeeze
response_siso_as_mimo = response_siso(squeeze=False)
assert response_siso_as_mimo.outputs.shape == (1, 1, siso_ntimes)
assert response_siso_as_mimo.states.shape == (4, 1, siso_ntimes)
assert response_siso_as_mimo._legacy_states.shape == (4, siso_ntimes)
response_mimo_squeezed = response_mimo(squeeze=True)
assert response_mimo_squeezed.outputs.shape == (2, mimo_ntimes)
assert response_mimo_squeezed.states.shape == (4, mimo_ntimes)
assert response_mimo_squeezed._legacy_states.shape == (4, 1, mimo_ntimes)
# Squeeze and transpose
response_mimo_sqtr = response_mimo(squeeze=True, transpose=True)
assert response_mimo_sqtr.outputs.shape == (mimo_ntimes, 2)
assert response_mimo_sqtr.states.shape == (mimo_ntimes, 4)
assert response_mimo_sqtr._legacy_states.shape == (mimo_ntimes, 4, 1)
# Return_x
t, y = response_mimo
t, y = response_mimo()
t, y, x = response_mimo(return_x=True)
with pytest.raises(ValueError, match="too many"):
t, y = response_mimo(return_x=True)
with pytest.raises(ValueError, match="not enough"):
t, y, x = response_mimo
# Labels
assert response_mimo.output_labels is None
assert response_mimo.state_labels is None
assert response_mimo.input_labels is None
response = response_mimo(
output_labels=['y1', 'y2'], input_labels='u',
state_labels=["x[%d]" % i for i in range(4)])
assert response.output_labels == ['y1', 'y2']
assert response.state_labels == ['x[0]', 'x[1]', 'x[2]', 'x[3]']
assert response.input_labels == ['u']
# Unknown keyword
with pytest.raises(ValueError, match="Unknown parameter(s)*"):
response_bad_kw = response_mimo(input=0)
def testSimulation(self):
T = range(100)
U = np.sin(T)
# For now, just check calling syntax
# TODO: add checks on output of simulations
tout, yout = step_response(self.siso_ss1d)
tout, yout = step_response(self.siso_ss1d, T)
tout, yout = impulse_response(self.siso_ss1d, T)
tout, yout = impulse_response(self.siso_ss1d)
tout, yout, xout = forced_response(self.siso_ss1d, T, U, 0)
tout, yout, xout = forced_response(self.siso_ss2d, T, U, 0)
tout, yout, xout = forced_response(self.siso_ss3d, T, U, 0)
def test_div(self):
fb_sys = self.sys1 / (1 + self.sys1 * self.sys2)
fb_m = self.m1 / self.m2
t, y2 = ps.step_response(fb_m)
_, y1 = ctrl.step_response(fb_sys, t)
self.assertTrue(np.allclose(y1, y2, rtol=1e-2), "feedback is broken")
fb_sys = ctrl.feedback(self.sys1, 1)
fb_m = self.m1 / 1
t, y2 = ps.step_response(fb_m)
_, y1 = ctrl.step_response(fb_sys, t)
self.assertTrue(np.allclose(y1, y2, rtol=1e1), "scalar feedback is"
"broken")
def analyze_sys(sys,H):
Go = sys*H
Gc = control.feedback(Go)
control.root_locus(Go)
plt.figure()
plt.title('system')
t1,x1 = control.step_response(sys)
plt.plot(t1,x1)
plt.figure()
plt.title('controlled system w/ step response')
t2,x2 = control.step_response(Gc)
print(x2)
plt.plot(t2,x2)
def pt1(smooth, time):
smoothed_df = pd.concat([pd.DataFrame(smooth, columns = ['smoothed']), \
pd.DataFrame(time, columns = ['time'])], axis = 1)
steady_state = smooth[-1]
#last element of the smoothed data is passed as steady state value
standard_output = steady_state * (1 - np.exp(-1))
#case when t = time_constant in the eqn.
#############################################################################
# standard_output = steady_state * (1 - e ^ (−t / time_constant)) #
#############################################################################
delay = smoothed_df.time[smoothed_df.smoothed < 0.02].values[-1]
#returns the time at which the step change occurs i.e a transition from 0 to some value.
#Values lesser than 0.02 were treatred as zero.
time_constant = smoothed_df.time[smoothed_df.index == abs(smoothed_df.smoothed - standard_output)\
.sort_values().index[0]].values[0]
#derived from the equation of standard_output
tf_pt1 = con.tf(steady_state, [time_constant, 1])
numerator, denominator = con.pade(delay, 1)
delay_tf_pt1 = con.tf(numerator, denominator)
t_pt1, yout_pt1 = con.step_response(tf_pt1 * delay_tf_pt1)
#first order transfer function is given by
###############################################################################
# steady_state * (e ^ - (delay * s)) #
# transfer_function(s) = ------------------------------------ #
# (time_constant * s + 1 ) #
###############################################################################
return tf_pt1 * delay_tf_pt1, yout_pt1, t_pt1, delay, time_constant, steady_state, tf_pt1
def test_import_export(self):
sys = ctrl.tf([1], [100, 1])
sim_duration = 2000
time = np.zeros(sim_duration)
i = 0
while (i < sim_duration):
time[i] = i
i += 1
_, output = ctrl.step_response(sys, time)
m = ps.FsrModel(output, t=time)
# testing our model with a test signal
test_sgnl_len = int(2500)
u = np.zeros(test_sgnl_len)
for i in range(test_sgnl_len):
u[i] = 1
time = np.zeros(test_sgnl_len)
for i in range(test_sgnl_len):
time[i] = i
_, comp, _ = ctrl.forced_response(sys, time, u)
# 'rb' and 'wb' to avoid problems under Windows!
with open("temp", "w") as fh:
ps.export_csv(m, fh)
with open("temp", "r") as fh:
m = ps.import_csv(fh)
os.remove("temp")
_, y = ps.forced_response(m, time, u)
self.assertTrue(np.allclose(y, comp, rtol=1e-2), "import/export broke")
def pidplot(nlg,dlg,nlh,dlh):
G = control.tf(nlg,dlg)
s1="("
s2="("
s=str(G)
s=s.split('\n')
s[1]=s[1].strip()
s[3]=s[3].strip()
s1=s1+s[1]+')'
s2=s2+s[3]+')'
t1,y1 =control.step_response(G)
plt.plot(t1,y1,'b',linewidth=1,label='G(s)')
plt.grid(True)
plt.title('Time response of G(s)='+(s1)+'/'+(s2))
plt.xlabel('Time(sec)')
plt.ylabel('Amplitude')
if not os.path.isdir('static'):
os.mkdir('static')
else:
# Remove old plot files
for filename in glob.glob(os.path.join('static', 'Feedback','pidc.png')):
os.remove(filename)
pidc=os.path.join('static', 'Feedback' ,'pidc.png')
plt.savefig(pidc)
plt.clf()
plt.cla()
plt.close()
return pidc
def plot_step(self, fig):
if self.settings.is_step_default():
t, y = control.step_response(self.tf)
else:
tmax = self.settings.get_step_time_max()
step = self.settings.get_step_step()
t = np.arange(0, tmax, step)
_, y = control.step_response(self.tf, t)
fig.clf()
ax = fig.add_subplot(1, 1, 1)
ax.plot(t, y)
ax.set_xlabel('Time')
ax.set_ylabel('Amplitude (s)')
return fig
def plot_loops(name, G_ol, G_cl):
# type: (str, control.tf, control.tf) -> None
"""
Plot loops
:param name: Name of axis
:param G_ol: open loop transfer function
:param G_cl: closed loop transfer function
"""
plt.figure()
plt.plot(*control.step_response(G_cl, np.linspace(0, 1, 1000)))
plt.title(name + ' step response')
plt.grid()
plt.figure()
control.bode(G_ol)
print('margins', control.margin(G_ol))
plt.subplot(211)
plt.title(name + ' open loop bode plot')
plt.figure()
control.rlocus(G_ol, np.logspace(-2, 0, 1000))
for pole in G_cl.pole():
plt.plot(np.real(pole), np.imag(pole), 'rs')
plt.title(name + ' root locus')
plt.grid()
def pidplot1(nlg, dlg, nlh, dlh):
G = control.tf(nlg, dlg)
H = control.tf(nlh, dlh)
s = str(H)
s1 = "("
s2 = "("
s = s.split('\n')
s[1] = s[1].strip()
s[3] = s[3].strip()
s1 = s1 + s[1] + ')'
s2 = s2 + s[3] + ')'
v = control.feedback(G, H)
t2, y2 = control.step_response(v)
plt.plot(t2, y2, 'r', linewidth=1, label='G(s) with Feedback H(s)')
plt.grid(True)
plt.title('Time response of G(s) with feedback H(s)=G(s)/(1+G(s)H(s))')
plt.xlabel('Time(sec)')
plt.ylabel('Amplitude')
if not os.path.isdir('static'):
os.mkdir('static')
else:
# Remove old plot files
for filename in glob.glob(
os.path.join('static', 'Feedback', 'pidc1.png')):
os.remove(filename)
pidc1 = os.path.join('static', 'Feedback', 'pidc1.png')
plt.savefig(pidc1)
plt.clf()
plt.cla()
plt.close()
return pidc1
def creation_example():
"""Example for creation of a FSR model with python-control."""
# creating a step response for our model
sys = ctrl.tf([1], [100, 1])
sim_duration = 2000
time = np.arange(sim_duration)
_, output = ctrl.step_response(sys, time)
# creating the model
model = ps.FsrModel(output, t=time)
# creating a test input signal
u = np.ones(sim_duration)
for i in range(len(u)):
if i < 500:
u[i] = 0.001 * i
# getting response from our model
t1, y1 = ps.forced_response(model, time, u)
# simulating a reference with control
t2, y2, _ = ctrl.forced_response(sys, time, u)
# show everything
ax = plt.subplot(111)
plt.plot(t1, y1, label="Model response")
plt.plot(t2, y2, label="Reference response")
plt.plot(t1, u, label="Input signal")
ax.legend()
plt.title("pystrem example")
plt.show()
def Bode_Margin(sys, omega):
w = omega
mag, phaserad, w = ctrl.bode(sys, w)
magdb = 20 * log(mag)
phasedeg = phaserad * 180 / pi
gm, pm, wg, wp = ctrl.margin(sys)
a1 = f.add_subplot(221)
a1.set_xscale("log")
a1.plot(w, magdb)
a1.plot(wp, 0, '.y')
a1.text(wp, 0 + 25, "wc=%.2f" % wp)
# a1.title = "Bode"
# a1.ylabel = "Magnitude dB "
# a1.xlabel = "Angular frequency"
a2 = f.add_subplot(223)
a2.set_xscale("log")
a2.plot(w, phasedeg)
a2.plot(wp, pm - 180, '.y')
a2.text(wp, pm - 180 + 25, "phase=%.2f" % (pm - 180))
# a2.ylabel = "Phase (degree) "
# a2.xlabel = "Angular frequency"
a3 = f.add_subplot(122)
sysF = sys / (1 + sys)
T = np.arange(0, 30, 0.5)
T, yout = ctrl.step_response(sysF, T)
a3.plot(T, yout)
# a3.title = "step response"
# a3.xlabel = "time"
# a3.ylabel = "Magnitude"
return wp, pm
def test_response_transpose(self, nstate, nout, ninp, squeeze, ysh_in,
ysh_no, xsh_in):
sys = ct.rss(nstate, nout, ninp)
T = np.linspace(0, 1, 8)
# Step response - input indexed
t, y, x = ct.step_response(sys,
T,
transpose=True,
return_x=True,
squeeze=squeeze)
assert t.shape == (T.size, )
assert y.shape == ysh_in
assert x.shape == xsh_in
# Initial response - no input indexing
t, y, x = ct.initial_response(sys,
T,
1,
transpose=True,
return_x=True,
squeeze=squeeze)
assert t.shape == (T.size, )
assert y.shape == ysh_no
assert x.shape == (T.size, sys.nstates)
def calculating_params(self, populations):
calculatedParams = []
for population in populations:
kp = population[0]
ti = population[1]
td = population[2]
G = kp * control.tf([ti * td, ti, 1], [ti, 0])
F = control.tf(1, [1, 6, 11, 6, 0])
system = control.feedback(control.series(G, F), 1)
t = []
i = 0
while i < 100:
t.append(i)
i += 0.01
try:
systemInfo = control.step_info(system)
except IndexError:
calculatedParams.append([10000000, 1, 100, 200])
continue
T, output = control.step_response(system, T=t)
ISE = round(sum((output - 1)**2), 2)
timeRise = round(systemInfo['RiseTime'], 2)
timeSettle = round(systemInfo['SettlingTime'], 2)
overshoot = round(systemInfo['Overshoot'], 2)
calculatedParams.append([ISE, timeRise, timeSettle, overshoot])
return calculatedParams
def test_forced_response_legacy(self):
# Define a system for testing
sys = ct.rss(2, 1, 1)
T = np.linspace(0, 10, 10)
U = np.sin(T)
"""Make sure that legacy version of forced_response works"""
ct.config.use_legacy_defaults("0.8.4")
# forced_response returns x by default
t, y = ct.step_response(sys, T)
t, y, x = ct.forced_response(sys, T, U)
ct.config.use_legacy_defaults("0.9.0")
# forced_response returns input/output by default
t, y = ct.step_response(sys, T)
t, y = ct.forced_response(sys, T, U)
t, y, x = ct.forced_response(sys, T, U, return_x=True)
def step(tf_list=[], N=100, T=None, name=None):
data = []
T_max = get_T_max(tf_list, T=T, N=N)
for index, tf in enumerate(tf_list):
if ctl.isctime(tf):
T = np.linspace(0, T_max, N)
line_shape = "linear"
else:
T = np.arange(0, T_max, tf.dt)
line_shape = "hv"
t, y = ctl.step_response(tf, T=T)
tf_name = "tf {}".format(index + 1)
data.append({
"x": np.ravel(t),
"y": np.ravel(y),
"name": tf_name,
"mode": "lines",
"showlegend": False,
"line_shape": line_shape
})
layout = default_layout("time (s)", "response", name)
fig = go.Figure(data, layout=layout)
return fig
def tr2(numG, denG, numH, denH):
G = control.tf(numG, denG)
H = control.tf(numH, denH)
k = control.parallel(G, H)
s1 = "("
s2 = "("
s = str(k)
s = s.split('\n')
s[1] = s[1].strip()
s[3] = s[3].strip()
s1 = s1 + s[1] + ')'
s2 = s2 + s[3] + ')'
t1, y1 = control.step_response(k)
plt.plot(t1, y1, 'b', linewidth=1, label='G(s)')
plt.grid(True)
plt.title('Time response of Parallel Operation\n' + (s1) + '/' + (s2))
plt.xlabel('Time(sec)')
plt.ylabel('Amplitude')
if not os.path.isdir('static'):
os.mkdir('static')
else:
# Remove old plot files
for filename in glob.glob(
os.path.join('static', 'SeriesParallel', 'sp2.png')):
os.remove(filename)
sp2 = os.path.join('static', 'SeriesParallel', 'sp2.png')
plt.savefig(sp2)
plt.clf()
plt.cla()
plt.close()
return sp2
def grstep(sys, T=None):
"""get step response graphically
Usage
=====
grstep(sys)
Inputs
------
sys: system
"""
if np.isscalar(T):
if sys.isctime():
T = np.linspace(0, T)
else:
T = np.arange(0, T, sys.dt)
t, y = ct.step_response(sys, T)
if len(y.shape) == 2:
N = y.shape[0]
for n in range(0, N):
plt.plot(t, y[n])
else:
plt.plot(t, y)
plt.grid()
plt.show()
def classic():
# PI controller
Kp = 1.5
Ki = 30.
P = tf([Kp], [1])
I = tf([Ki], [1, 0])
Gc = parallel(P, I)
# Power convertor
Gpc = synthesize_2pole_filter(50, 0.707)
# Plant
Gp = tf([50], [1, 0])
# Sensor
# если выбросить из петли становится лучше
# "remove sensor lag"
Gs = synthesize_1pole_filter(20)
# Openloop
Gol = series(series(Gc, Gpc), Gp)
# Closed loop
Gcl = feedback(Gol)
ts, xs = step_response( Gcl )
grid()
plot(ts, xs)
def execute(self):
# Realimentando a malha
sysFechada = con.feedback(self.sys, 1)
# Resposta ao degrau
[self.xout, self.yout] = con.step_response(sysFechada,
const.TEMPO_CALCULO)
# "Alterando" amplitude do degrau
self.yout = self.yout * const.SP
# Pegando as informações sobre o sistema
info = con.step_info(sysFechada, self.xout)
# Pegando o valor de estado estacionário
self.valorEstacionario = info['SteadyStateValue'] * const.SP
# Ponto de acomodação
self.tempo_acomodacao = info['SettlingTime']
self.valor_acomodacao = accommodationPoint(self.yout,
self.valorEstacionario)
# Overshoot
self.overshootX = info['PeakTime']
self.overshootY = info['Peak'] * const.SP
self.overshoot = info['Overshoot']
# Erro em regime permanente
self.erroRegimePermanente = errorCalculate(const.SP,
self.valorEstacionario)
def f(X): #F(Kp, Ki, Kd)
#Obtendo as constantes a partir da entrada
Kp = X[0]
Ki = X[1]
Kd = X[2]
#Definindo as constantes do processo
K = 2
CT = 4
s = ct.TransferFunction.s
#Equação do sistema de Controle
C = Kp + Ki / s + Kd * s
#Equação do processo a ser controlado
P = K / (CT * s + 1)
#Fazendo a retroalimentação
T = ct.TransferFunction.feedback(C * P, 1)
tempo, resposta = ct.step_response(T)
erro = [TARGET_VALUE - resp for resp in resposta]
#Cálculo da integral de erro quadratico multiplicado pelo tempo
# print(tempo)
# print(erro)
itse = np.sum(tempo * np.power(erro, 2))
return itse
def assignment2(Kc=Kc, Ki=Ki): #Kc has to be a list; Ki has to be a float
# Defining the transfer functions
sysgp = control.tf(4, [500, 2]) #Process
sysgv = control.tf(2, [1, 10, 1]) #Valve
sysgt = control.tf(2, 1) # Sensor
syspi_list = []
# Loop to iterate among the different values of Kc
for i in Kc:
syspi = control.tf([i, i * Ki], [1, 0])
syspi_list.append(syspi)
# Plotting the figures with the different values of Kc
plt.figure()
for i in range(len(syspi_list)):
#Defining the closed loop
syslc = control.feedback(syspi_list[i] * sysgv * sysgp, sysgt)
consig = 1 / 2 # The setpoint is 0.5, because the sensor
# transfer function is equal to 2
t, y = control.step_response(syslc, 200)
error = np.abs(y - consig) # The error while achieving the setpoint
plt.plot(t, y, label=f'Kc= {Kc[i]:.2f}')
# plt.plot(t, error, label=f'Error para Kc={Kc[i]:.2f}')
plt.title(f'Ki= {Ki:.4f}')
plt.legend()
plt.xlabel('Time (s)')
plt.ylabel('Value')
plt.show()
return syspi_list
def execute(self):
# Resposta ao degrau
[self.xout, self.yout] = con.step_response(self.sys, const.TEMPO)
# Pegando as informações do sistema
info = con.step_info(self.sys, self.xout)
# "Alterando" amplitude do degrau
self.yout = self.yout * self.VALOR_ENTRADA
# Pegando o valor de estado estacionário
self.valorEstacionario = info['SteadyStateValue'] * self.VALOR_ENTRADA
# Ponto de acomodação
self.tempo_acomodacao = info['SettlingTime']
self.valor_acomodacao = accommodationPoint(self.yout,
self.valorEstacionario)
# Overshoot
self.overshootX = info['PeakTime']
self.overshootY = info['Peak'] * self.VALOR_ENTRADA
self.overshoot = info['Overshoot']
# Erro em regime permanente
self.erroRegimePermanente = errorCalculate(self.VALOR_ENTRADA,
self.valorEstacionario)
def KpKi(sys):
# Pegando os valores do OVERSHOOT e Tempo de acomodação desejados
mp = const.OVERSHOOT
ts = const.TS
# Resposta ao degrau
[xout, yout] = con.step_response(sys, const.TEMPO)
# "Alterando" amplitude do degrau
yout = yout * const.SP
# Pegando as informações sobre o sistema
info = con.step_info(sys, xout)
# Pegando o valor de estado estacionário
valorEstacionario = info['SteadyStateValue'] * const.SP
# Calculando valor de K e tall
k = K(const.SP, valorEstacionario)
tal = tall(yout, valorEstacionario, const.TEMPO_AMOSTRAGEM)
# Calculando valores de Kp e Ki
kp, ki = calculateKpKi(mp, ts, k, tal)
return kp, ki
def exercise_2():
# get unknown step response
t, y = sr1.unknown_step()
# plot unknown step response
plt.figure()
plt.grid(True)
plt.xlabel("$t$ in s")
plt.ylabel("$y(t)$")
plt.plot(t, y)
# create system
k_s = 1.38
T = 1.1
T_t = 2.2
sys_2 = system_2(k_s, T, T_t)
# plot system step response
t = np.linspace(0, 50, 100)
t, y = ctl.step_response(sys_2, t)
plt.plot(t, y)
# plot PID controlled system step response
K_P = 1.2 * T / (k_s * T_t)
K_I = 0.6 * T / (k_s * T_t**2)
K_D = 0.6 * T / k_s
t, y = sr1.unknown_step(K_P, K_I, K_D)
plt.plot(t, y)
# save plot
plt.savefig("plots/step_response.png")
plt.clf()
def pt2(smooth, time):
def fourpoint(z):
f1_zeta = 0.451465 + (0.066696 * z) + (0.013639 * z**2)
f3_zeta = 0.800879 + (0.194550 * z) + (0.101784 * z**2)
f6_zeta = 1.202664 + (0.288331 * z) + (0.530572 * z**2)
f9_zeta = 1.941112 - (1.237235 * z) + (3.182373 * z**2)
return f1_zeta, f3_zeta, f6_zeta, f9_zeta
def method():
#the second method from the article is adopted, as the response/data handled strictly follows this method.
zeta = np.sqrt(
(np.log(overshoot)**2) / ((np.pi**2) + (np.log(overshoot)**2)))
f1_zeta, f3_zeta, f6_zeta, f9_zeta = fourpoint(zeta)
time_constant = (t9 - t1) / (f9_zeta - f1_zeta)
#delay = t1 - time_constant*f1_zeta #based on article.
delay = smoothed_df.time[smoothed_df.smoothed < 0.02].values[-1]
return zeta, time_constant, delay
smoothed_df = pd.concat([pd.DataFrame(smooth, columns = ['smoothed']), \
pd.DataFrame(time, columns = ['time'])], axis = 1)
steady_state = smooth[-1]
#ssn = steady state at n/10th instant of time
ss1 = steady_state * 0.1
ss3 = steady_state * 0.3
ss6 = steady_state * 0.6
ss9 = steady_state * 0.9
#tn = time at n/10th instant
t1 = smoothed_df.time[smoothed_df.index == abs(
smoothed_df.smoothed - ss1).sort_values().index[0]].values[0]
t3 = smoothed_df.time[smoothed_df.index == abs(
smoothed_df.smoothed - ss3).sort_values().index[0]].values[0]
t6 = smoothed_df.time[smoothed_df.index == abs(
smoothed_df.smoothed - ss6).sort_values().index[0]].values[0]
t9 = smoothed_df.time[smoothed_df.index == abs(
smoothed_df.smoothed - ss9).sort_values().index[0]].values[0]
peak = smoothed_df.smoothed.max()
#returns the highest output in the response
overshoot = (peak - steady_state) / steady_state
#represented as Mp in article
zeta, time_constant, delay = method()
tf_pt2 = con.tf(steady_state,
[time_constant**2, 2 * zeta * time_constant, 1])
n_2, d_2 = con.pade(delay, 1)
delay_tf_pt2 = con.tf(n_2, d_2)
t_pt2, yout_pt2 = con.step_response(tf_pt2 * delay_tf_pt2)
#second order transfer function is given by
########################################################################################################
# steady_state * (e ^ - (delay * s)) #
# transfer_function(s) = ---------------------------------------------------------------------- #
# ((time_constant ^ 2) * (s ^ 2)) + (2 * zeta * time_constant * s) + 1 ) #
########################################################################################################
return tf_pt2 * delay_tf_pt2, yout_pt2, t_pt2, delay, time_constant, steady_state, zeta, tf_pt2
def plot_response(sys, T=None, U=0.0, impulse=True, step=True) -> None:
if impulse:
t, yout = control.impulse_response(sys, T=T, X0=U)
plot_params(t, yout)
if step:
t, yout = control.step_response(sys, T=T, X0=U)
plot_params(t, yout)
return
def Q2_perfFCN(Kp, Ti, Td): G = Kp * tf([Ti * Td, Ti, 1.0], [Ti, 0]) sys = feedback(series(G,F),1) res = step_response(sys, t) ISE = sum((val - 1)**2 for val in res[1]) return (ISE,) + stepinfo(res)
def test_IT2_forced_response(self):
sys = ctrl.tf([100], [50, 1000, 150, 0]) # IT2
_, o = ctrl.step_response(sys, self.time)
m = ps.FsrModel(o, t=self.time, optimize=False)
_, y = ps.forced_response(m, self.t, self.u)
_, o, _ = ctrl.forced_response(sys, self.t, self.u)
self.assertTrue(np.allclose(y, o, rtol=1e-2), "it2 response broke")
def analysis():
"""Plot open-loop responses for various inputs"""
g = plant()
t = np.linspace(0, 10, 101)
_, yu1 = step_response(g, t, input=0)
_, yu2 = step_response(g, t, input=1)
yu1 = yu1
yu2 = yu2
# linear system, so scale and sum previous results to get the
# [1,-1] response
yuz = yu1 - yu2
plt.figure(1)
plt.subplot(1, 3, 1)
plt.plot(t, yu1[0], label='$y_1$')
plt.plot(t, yu1[1], label='$y_2$')
plt.xlabel('time')
plt.ylabel('output')
plt.ylim([-1.1, 2.1])
plt.legend()
plt.title('o/l response\nto input [1,0]')
plt.subplot(1, 3, 2)
plt.plot(t, yu2[0], label='$y_1$')
plt.plot(t, yu2[1], label='$y_2$')
plt.xlabel('time')
plt.ylabel('output')
plt.ylim([-1.1, 2.1])
plt.legend()
plt.title('o/l response\nto input [0,1]')
plt.subplot(1, 3, 3)
plt.plot(t, yuz[0], label='$y_1$')
plt.plot(t, yuz[1], label='$y_2$')
plt.xlabel('time')
plt.ylabel('output')
plt.ylim([-1.1, 2.1])
plt.legend()
plt.title('o/l response\nto input [1,-1]')
def time (tf, method = 'step', plot = False):
print "==================================================================";
print "Poles: ", ctrl.pole (tf);
print "Zeros: ", ctrl.zero (tf);
dc = ctrl.dcgain (tf);
print "DC gain: ", dc;
if (method == 'step'):
t, y = ctrl.step_response (tf);
if (method == 'impulse'):
t, y = ctrl.impulse_response (tf);
ys = filter (lambda l: l >= 0.98 * dc, y);
i = np.ndarray.tolist(y).index (min (ys));
print "Ts: ", t[i];
print "Overshoot: ", (max (y) / dc) - 1;
i = np.ndarray.tolist(y).index (max (y));
print "Tr: ", t[i];
if (plot == True):
p = Plotter ({'grid' : True});
p.plot ([(t, y)]);
return t, y
def step_opposite(g, t):
"""reponse to step of [-1,1]"""
_, yu1 = step_response(g, t, input=0)
_, yu2 = step_response(g, t, input=1)
return yu1 - yu2
cls()
Kt = 1.0
Jt = 1.0 # [?]
u1 = tf([Kt], [1])
u2 = tf([1 / Jt], [1])
# fixme: как добавить сигнал шума?
u12 = series(u1, u2)
u3 = tf([1], [1, 0])
u4 = copy.deepcopy(u3)
u34 = series(u3, u4)
# похоже нельзя соединить аналоговую и дискретную
u34_d0 = c2d(u3, Ts=0.5)
u34_d = c2d(u3, Ts=0.5)
print series(u34_d0, u34_d)
u14 = series(u12, u34)
print u14
ts, xs = step_response(u14)
# print (c2d(u14, Ts=0.5))
plot(ts, xs)
grid()
show()
# #### additional code for comparision
A, B, C, D = get_linear_ct_model(theStateAdmin, sys_output)
# create a control system with the python-control-toolbox, see
# https://github.com/python-control/python-control
import control
cs = control.StateSpace(A, B, C, D)
# use default method (zero oder hold (zoh))
cs_dt = control.sample_system(cs, 0.05)
# calculate step-response for first input
__, yy_dt = control.step_response(cs_dt, T=tt, input=0)
# in the time-discrete case the result is shortened by one value. -> repeat the last one.
yy_dt = np.column_stack((yy_dt, yy_dt[:, -1]))
# __, yy_dt = control.step_response(cs,T=tt, input=0)
# #### end of additional code
if __name__ == "__main__":
pl.plot(tt, bo[SUM1], "b-", lw=3, label="$y_1$ (pyblocksim)")
pl.plot(tt, bo[SUM2], "r-", lw=3, label="$y_2$ (pyblocksim)")
# +1 because the step_response starts the step at t=0
# Define the system to use in simulation - in transfer function form here
num = [2.*z*wn,wn**2];
den = [1,2.*z*wn,wn**2];
sys = control.tf(num,den);
# Set up simulation parameters
t = np.linspace(0,5,500) # time for simulation, 0-5s with 500 points in-between
# run the simulation - utilize the built-in initial condition response function
[T,yout] = control.step_response(sys,t)
# Make the figure pretty, then plot the results
# "pretty" parameters selected based on pdf output, not screen output
# Many of these setting could also be made default by the .matplotlibrc file
fig = figure(figsize=(6,4))
ax = gca()
subplots_adjust(bottom=0.17,left=0.17,top=0.96,right=0.96)
setp(ax.get_ymajorticklabels(),family='CMU Serif',fontsize=18)
setp(ax.get_xmajorticklabels(),family='CMU Serif',fontsize=18)
ax.spines['right'].set_color('none')
ax.spines['top'].set_color('none')
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
ax.grid(True,linestyle=':',color='0.75')
ax.set_axisbelow(True)
# 超调量
print("Mp (%): ", (yout.max() / yout[-1] - 1) * 100)
# 峰值时间
print("Tp: ", t[numpy.argmax(yout)])
# 上升时间
print("Tr: ", t[next(i for i in range(0, len(yout) - 1) if yout[i] > yout[-1])])
# 调整时间
offset = 0.05 # 最大误差容许范围
print("Ts: ", t[next(len(yout) - i for i in range(2, len(yout) - 1) if abs(yout[-i] / yout[-1] - 1) > offset)])
# 化简分母
S = sympy.symbols('S')
denominator = (S**2 + 0.6*S + 1) * (S**2 + 3*S + 9) * (S + 5)
denominator = denominator.expand() # 化简表达式
denominator = sympy.poly(denominator, S).all_coeffs() # 转成多项式 list
denominator = list(map(float, denominator)) # convert sympy.core.numbers.Float to float
numerator = [45.]
sys = control.matlab.tf(numerator, denominator)
# 阶跃
T, yout = control.step_response(sys)
step_info(T, yout)
# 绘图
plot(T, yout)
title("System Step Response")
xlabel("time / sec")
ylabel("response / value")
show()
plt.semilogx(omega, 20 * np.log10(s1mag.flat), label='$S_1$')
plt.semilogx(omega, 20 * np.log10(s2mag.flat), label='$S_2$')
# -1 in logspace is inverse
plt.semilogx(omega, -20 * np.log10(ws1mag.flat), label='$1/w_{P1}$')
plt.semilogx(omega, -20 * np.log10(ws2mag.flat), label='$1/w_{P2}$')
plt.ylim([-80, 10])
plt.xlim([1e-2, 1e2])
plt.xlabel('freq [rad/s]')
plt.ylabel('mag [dB]')
plt.legend()
plt.title('Sensitivity and sensitivity weighting frequency responses')
# time response
time = np.linspace(0, 3, 201)
_, y1 = step_response(t1, time)
_, y2 = step_response(t2, time)
# gd injects into the output (that is, g and gd are summed), and the
# closed loop mapping from output disturbance->output is S.
_, y1d = step_response(s1 * gd, time)
_, y2d = step_response(s2 * gd, time)
plt.figure(2)
plt.subplot(1, 2, 1)
plt.plot(time, y1, label='$y_1(t)$')
plt.plot(time, y2, label='$y_2(t)$')
plt.ylim([-0.1, 1.5])
plt.xlim([0, 3])
plt.xlabel('time [s]')
def plot_loops(name, G_ol, G_cl):
"""
Plot loops
:param name: Name of axis
:param G_ol: open loop transfer function
:param G_cl: closed loop transfer function
"""
plt.figure()
plt.plot(*control.step_response(G_cl, np.linspace(0, 1, 1000)))
plt.title(name + ' step resposne')
plt.grid()
plt.figure()
control.bode(G_ol)
print('margins', control.margin(G_ol))
plt.subplot(211)
plt.title(name + ' open loop bode plot')
plt.figure()
control.rlocus(G_ol, np.logspace(-2, 0, 1000))
for pole in G_cl.pole():
plt.plot(np.real(pole), np.imag(pole), 'rs')
plt.title(name + ' root locus')
plt.grid()