def test_impulse(self):
A, B, C, D = self.make_SISO_mats()
sys = ss(A, B, C, D)
figure()
#everything automatically
t, y = impulse(sys)
plot(t, y, label='Simple Case')
#supply time and X0
T = linspace(0, 2, 100)
X0 = [0.2, 0.2]
t, y = impulse(sys, T, X0)
plot(t, y, label='t=0..2, X0=[0.2, 0.2]')
#Test system with direct feed-though, the function should print a warning.
D = [[0.5]]
sys_ft = ss(A, B, C, D)
t, y = impulse(sys_ft)
plot(t, y, label='Direct feedthrough D=[[0.5]]')
#Test MIMO system
A, B, C, D = self.make_MIMO_mats()
sys = ss(A, B, C, D)
t, y = impulse(sys)
plot(t, y, label='MIMO System')
legend(loc='best')
def process_data(num11, den11, num21, den21):
w11 = ctrl.tf(num11, den11)
w21 = ctrl.tf(num21, den21)
print('результат w11={} w21={}'.format(w11, w21))
TimeLine = []
for i in range(1, 3000):
TimeLine.append(i / 1000)
plt.figure(0, figsize=[7, 6])
[y11, x11] = ctrl.step(w11, TimeLine)
[y21, x21] = ctrl.step(w21, TimeLine)
plt.plot(x11, y11, "r", label='Исходная')
plt.plot(x21, y21, "b", label='Увеличенная k и уменшенная Т')
plt.title('Переходная функция звена')
plt.ylabel('Амплитуда')
plt.xlabel('Время(с)')
plt.grid(True)
plt.show()
[y11, x11] = ctrl.impulse(w11, TimeLine)
[y21, x21] = ctrl.impulse(w21, TimeLine)
plt.plot(x11, y11, "r", label='Исходная')
plt.plot(x21, y21, "b", label='Увеличенная k и уменшенная Т')
plt.title('Импульсная функция звена')
plt.ylabel('Амплитуда')
plt.xlabel('Время(с)')
plt.grid(True)
plt.show()
ctrl.mag, ctrl.phase, ctrl.omega = ctrl.bode(w11, w21, dB=False)
plt.plot()
plt.show()
return w11, w21
def test_impulse(self):
A, B, C, D = self.make_SISO_mats()
sys = ss(A, B, C, D)
figure()
#everything automatically
t, y = impulse(sys)
plot(t, y, label='Simple Case')
#supply time and X0
T = linspace(0, 2, 100)
X0 = [0.2, 0.2]
t, y = impulse(sys, T, X0)
plot(t, y, label='t=0..2, X0=[0.2, 0.2]')
#Test system with direct feed-though, the function should print a warning.
D = [[0.5]]
sys_ft = ss(A, B, C, D)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
t, y = impulse(sys_ft)
plot(t, y, label='Direct feedthrough D=[[0.5]]')
#Test MIMO system
A, B, C, D = self.make_MIMO_mats()
sys = ss(A, B, C, D)
t, y = impulse(sys)
plot(t, y, label='MIMO System')
legend(loc='best')
def testImpulse_mimo(self, mimo):
"""Test impulse() for MIMO system"""
t = np.linspace(0, 1, 10)
youttrue = np.array([86., 70.1808, 57.3753, 46.9975, 38.5766, 31.7344,
26.1668, 21.6292, 17.9245, 14.8945])
sys = mimo.ss1
with pytest.warns(UserWarning, match="System has direct feedthrough"):
y_00, _t = impulse(sys, T=t, input=0, output=0)
y_11, _t = impulse(sys, T=t, input=1, output=1)
np.testing.assert_array_almost_equal(y_00, youttrue, decimal=4)
np.testing.assert_array_almost_equal(y_11, youttrue, decimal=4)
def BAGUVIX(GG1, name_gg1, GG2, name_gg2,
t): # функция для построения графиков характеристик
topic = {
'G1': 'безынерционного звена',
'G2': 'апериодического звена',
'G3': 'интегрирующего звена',
'G4': 'реального диф. звена',
'G5': 'идеального диф. звена',
} # словарь для графика
if name_gg1 in topic: # определяем какой именно строим, для графика
k1 = topic[name_gg1]
plt.figure(1) # Вывод графиков в отдельном окне
y1, t1 = con.step(GG1, t)
y2, t2 = con.step(GG2, t)
lines = [y1, y2]
# plt.subplot(1, 1, 1) # 1цифра - количество строк в графике, 2 -тьиьтиколичество графиков в строке, 3 -номер графика
lines[0], lines[1] = plt.plot(t, y1, "r", t, y2, "b")
plt.legend(lines, ['h(t) для 1', 'h(t) для 2'],
loc='best',
ncol=2,
fontsize=10)
plt.title('Переходная характеристика' + '\n для ' + k1, fontsize=10)
plt.ylabel('h')
plt.xlabel('t, c')
plt.grid()
plt.figure(2)
y2, t2 = con.impulse(GG2, t)
y1, t1 = con.impulse(GG1, t)
lines[0], lines[1] = plt.plot(t, y1, "r", t, y2, "b")
plt.legend(lines, ['w(t) для 1', 'w(t) для 2'],
loc='best',
ncol=2,
fontsize=10)
plt.title('Импульсная характеристика' + '\n для ' + k1, fontsize=10)
plt.ylabel('w')
plt.xlabel('t, c')
plt.grid()
plt.figure(3)
mag1, phase1, omega1 = con.bode(GG1, dB=False)
# plt.plot()
plt.title('Частотные характеристики' + "\n для " + k1,
fontsize=10,
y=2.2)
mag1, phase1, omega1 = con.bode(GG2, dB=False)
plt.plot()
plt.title('Частотные характеристики' + "\n для " + k1,
fontsize=10,
y=2.2)
plt.show()
def analysis(self, w, block, which):
nume = [int(n) for n in block.nume_coef]
if block.deno_coef == []:
deno = [1]
else:
deno = [int(d) for d in block.deno_coef]
nume.reverse()
deno.reverse()
print(nume)
print(deno)
system = matlab.tf(nume, deno)
if which == 'bode':
matlab.bode(system)
plt.show()
elif which == 'rlocus':
matlab.rlocus(system)
plt.show()
elif which == 'nyquist':
matlab.nyquist(sys)
plt.show()
elif which == 'impulse':
t = np.linspace(0, 3, 1000)
yout, T = matlab.impulse(system, t)
plt.plot(T, yout)
plt.axhline(0, color="b", linestyle="--")
plt.xlim(0, 3)
plt.show()
elif which == 'step':
t = np.linspace(0, 3, 1000)
yout, T = matlab.step(system, t)
plt.plot(T, yout)
plt.axhline(1, color="b", linestyle="--")
plt.xlim(0, 3)
plt.show()
def create_Plot(var,name,num, den):
W=ml.tf(num,den)
if var!=5:
#Переходная функция
plt.figure().canvas.set_window_title(name)
y,x=ml.step(W,timeVector)
plt.plot(x,y,"b")
plt.title('Переходная функция')
plt.ylabel('Амплитуда, о.е.')
plt.xlabel('Время, с.')
plt.grid(True)
#TimeLine=[]
#for i in range(0;3000):
# TimeLine = [i/1000]
plt.show()
#Импульсная функция
plt.figure().canvas.set_window_title(name)
y,x=ml.impulse(W, timeVector)
plt.plot(x,y,"r")
plt.title('Импульсная функция')
plt.ylabel('Амплитуда, о.е.')
plt.xlabel('Время, с.')
plt.grid(True)
plt.show()
#Диаграмма Боде
plt.figure().canvas.set_window_title(name)
mag, phase, omega = ml.bode(W, dB=False)
plt.plot()
plt.xlabel('Частота, Гц')
plt.show()
return
def test_impulse_mimo(self, MIMO_mats, mplcleanup):
#Test MIMO system
A, B, C, D = MIMO_mats
sys = ss(A, B, C, D)
y, t = impulse(sys)
plot(t, y[:, :, 0], label='MIMO System')
legend(loc='best')
def testImpulse(self, siso):
"""Test impulse()"""
t = np.linspace(0, 1, 10)
# test transfer function
yout, tout = impulse(siso.tf1, T=t)
youttrue = np.array([
0., 0.0994, 0.1779, 0.2388, 0.2850, 0.3188, 0.3423, 0.3573, 0.3654,
0.3679
])
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
sys = siso.ss1
youttrue = np.array([
86., 70.1808, 57.3753, 46.9975, 38.5766, 31.7344, 26.1668, 21.6292,
17.9245, 14.8945
])
# produce a warning for a system with direct feedthrough
with pytest.warns(UserWarning, match="System has direct feedthrough"):
# Test SISO system
yout, tout = impulse(sys, T=t)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# produce a warning for a system with direct feedthrough
with pytest.warns(UserWarning, match="System has direct feedthrough"):
# Play with arguments
yout, tout = impulse(sys, T=t, X0=0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# produce a warning for a system with direct feedthrough
with pytest.warns(UserWarning, match="System has direct feedthrough"):
X0 = np.array([0, 0])
yout, tout = impulse(sys, T=t, X0=X0)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
# produce a warning for a system with direct feedthrough
with pytest.warns(UserWarning, match="System has direct feedthrough"):
yout, tout, xout = impulse(sys, T=t, X0=0, return_x=True)
np.testing.assert_array_almost_equal(yout, youttrue, decimal=4)
np.testing.assert_array_almost_equal(tout, t)
def test_impulse(self, SISO_mats, mplcleanup):
A, B, C, D = SISO_mats
sys = ss(A, B, C, D)
figure()
#everything automatically
t, y = impulse(sys)
plot(t, y, label='Simple Case')
#supply time and X0
T = linspace(0, 2, 100)
X0 = [0.2, 0.2]
t, y = impulse(sys, T, X0)
plot(t, y, label='t=0..2, X0=[0.2, 0.2]')
#Test system with direct feed-though, the function should print a warning.
D = [[0.5]]
sys_ft = ss(A, B, C, D)
with pytest.warns(UserWarning, match="has direct feedthrough"):
t, y = impulse(sys_ft)
plot(t, y, label='Direct feedthrough D=[[0.5]]')
def validation(SYS,u,y,Time, k = 1, centering = 'None'):
# check dimensions
y = 1. * np.atleast_2d(y)
u = 1. * np.atleast_2d(u)
[n1, n2] = y.shape
ydim = min(n1, n2)
ylength = max(n1, n2)
if ylength == n1:
y = y.T
[n1, n2] = u.shape
udim = min(n1, n2)
ulength = max(n1, n2)
if ulength == n1:
u = u.T
Yval = np.zeros((ydim,ylength))
# Data centering
#y_rif = np.zeros(ydim)
#u_rif = np.zeros(udim)
if centering == 'InitVal':
y_rif = 1. * y[:, 0]
u_rif = 1. * u[:, 0]
elif centering == 'MeanVal':
for i in range(ydim):
y_rif = np.mean(y,1)
#y_rif[i] = np.mean(y[i, :])
for i in range(udim):
u_rif = np.mean(u,1)
#u_rif[i] = np.mean(u[i, :])
elif centering == 'None':
y_rif = np.zeros(ydim)
u_rif = np.zeros(udim)
else:
# elif centering != 'None':
sys.stdout.write("\033[0;35m")
print("Warning! \'Centering\' argument is not valid, its value has been reset to \'None\'")
sys.stdout.write(" ")
# MISO approach
# centering inputs and outputs
for i in range(u.shape[0]):
u[i,:] = u[i,:] - u_rif[i]
for i in range(ydim):
# one-step ahead predictor
if k == 1:
Y_u, T, Xv = cnt.lsim((1/SYS.H[i,0])*SYS.G[i,:], u, Time)
Y_y, T, Xv = cnt.lsim(1 - (1/SYS.H[i,0]), y[i,:] - y_rif[i], Time)
Yval[i,:] = np.atleast_2d(Y_u + Y_y + y_rif[i])
else:
# k-step ahead predictor
# impulse response of disturbance model H
hout, T = cnt.impulse(SYS.H[i,0], Time)
# extract first k-1 coefficients
h_k_num = hout[0:k]
# set denumerator
h_k_den = np.hstack((np.ones((1,1)), np.zeros((1,k-1))))
# FdT of impulse response
Hk = cnt.tf(h_k_num,h_k_den[0],SYS.ts)
# plot impulse response
# plt.subplot(ydim,1,i+1)
# plt.plot(Time,hout)
# plt.grid()
# if i == 0:
# plt.title('Impulse Response')
# plt.ylabel("h_j ")
# plt.xlabel("Time [min]")
# k-step ahead prediction
Y_u, T, Xv = cnt.lsim(Hk*(1/SYS.H[i,0])*SYS.G[i,:], u, Time)
#Y_y, T, Xv = cnt.lsim(1 - Hk*(1/SYS.H[i,0]), y[i,:] - y[i,0], Time)
Y_y, T, Xv = cnt.lsim(1 - Hk*(1/SYS.H[i,0]), y[i,:] - y_rif[i], Time)
#Yval[i,:] = np.atleast_2d(Y_u + Y_y + y[i,0])
Yval[i,:] = np.atleast_2d(Y_u + Y_y + y_rif[i])
return Yval
)
k = 5
b = 2
m1 = 10
m2 = 80
t = np.linspace(0, 1000, 10001)
s = co.tf('s')
g1 = 1 / (m1 * s**2 + b * s + k)
g2 = 1 / (m2 * s**2 + b * s + k)
print(g1, g2)
imp1, t1 = cm.impulse(g1, t)
stp1, t2 = cm.step(g1, t)
imp2, t3 = cm.impulse(g2, t)
stp2, t4 = cm.step(g2, t)
# sample = co.step_info(stp1, t, SettlingTimeThreshold=0.01, RiseTimeLimits=(0.1, 0.9))
print("g1 impulse info")
signal_info(imp1, t1)
print("g1 step info")
signal_info(stp1, t2)
print("g2 impulse info")
signal_info(imp2, t3)
print("g2 step info")
signal_info(stp2, t4)
import numpy as np
import control.matlab as ctrl
import matplotlib.pyplot as plt
import matplotlib.patches as patches
m = 1 # 質量 [kg] 非負
c = 1 # 減衰係数 [N/m] 非負
k = 10 # バネ係数 [Ns/m] 非負
# 伝達関数
sys = ctrl.tf((1), (m, c, k))
print(sys)
t_range = (0, 10)
y, t = ctrl.impulse(sys, T=np.arange(*t_range, 0.01))
fig, ax = plt.subplots(2, 1)
ax[0].hlines(0, *t_range, colors='gray', ls=':')
ax[0].plot(t, y)
ax[0].grid()
ax[1].set_xlim((y.min() - 1, y.max() + 1))
ax[1].set_ylim((0, 0.5))
ax[1].grid()
ax[1].set_aspect("equal")
for i in range(len(t)):
r = patches.Rectangle(xy=(y[i] - 0.2, 0.1),
width=0.4,
B = np.array([[2.], [0.], [0.], [0.]])
C = np.array([[0.5, 0.6875, 0.7031, 0.5]])
D = np.array([[0.]])
# The full system
fsys = StateSpace(A, B, C, D)
# The reduced system, truncating the order by 1
n = 3
rsys = msimp.balred(fsys, n, method='truncate')
# Comparison of the step responses of the full and reduced systems
plt.figure(1)
y, t = mt.step(fsys)
yr, tr = mt.step(rsys)
plt.plot(t.T, y.T)
plt.plot(tr.T, yr.T)
# Repeat balanced reduction, now with 100-dimensional random state space
sysrand = mt.rss(100, 1, 1)
rsysrand = msimp.balred(sysrand, 10, method='truncate')
# Comparison of the impulse responses of the full and reduced random systems
plt.figure(2)
yrand, trand = mt.impulse(sysrand)
yrandr, trandr = mt.impulse(rsysrand)
plt.plot(trand.T, yrand.T, trandr.T, yrandr.T)
if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:
plt.show()
den = [J, C, 0] G = matlab.tf(num, den) # feedback loop sys = matlab.feedback(K * G, 1) # step response t = np.linspace(0, 3, 1000) yout, T = matlab.step(sys, t) plt.plot(T, yout) plt.axhline(1, color="b", linestyle="--") plt.xlim(0, 3) plt.show() # impulse response yout, T = matlab.impulse(sys, t) plt.plot(T, yout) plt.axhline(0, color="b", linestyle="--") plt.xlim(0, 3) #plt.show() # nyquist diagram matlab.nyquist(sys) #plt.show() # bode diagram matlab.bode(sys) #plt.show() # root locus matlab.rlocus(sys)
C = np.matrix('0.5, 0.6875, 0.7031, 0.5')
D = np.matrix('0.')
# The full system
fsys = StateSpace(A,B,C,D)
# The reduced system, truncating the order by 1
ord = 3
rsys = msimp.balred(fsys,ord, method = 'truncate')
# Comparison of the step responses of the full and reduced systems
plt.figure(1)
y, t = mt.step(fsys)
yr, tr = mt.step(rsys)
plt.plot(t.T, y.T)
plt.plot(tr.T, yr.T)
# Repeat balanced reduction, now with 100-dimensional random state space
sysrand = mt.rss(100, 1, 1)
rsysrand = msimp.balred(sysrand,10,method ='truncate')
# Comparison of the impulse responses of the full and reduced random systems
plt.figure(2)
yrand, trand = mt.impulse(sysrand)
yrandr, trandr = mt.impulse(rsysrand)
plt.plot(trand.T, yrand.T, trandr.T, yrandr.T)
if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:
plt.show()
c = 1 # 減衰係数 [N/m] 非負
k = 10 # バネ係数 [Ns/m] 非負
A = [[0, 1], [-k / m, -c / m]]
B = [[0], [1 / m]]
C = [[1, 0], [0, 1]]
D = 0
# 状態空間モデル
sys = ctrl.ss(A, B, C, D)
print(sys)
t_range = (0, 10)
# x1（=変位）の初期値を 0.1 に設定。x2（=速度）の初期値は 0 に設定
y, t = ctrl.impulse(sys, T=np.arange(*t_range, 0.05), X0=[0.1, 0.0])
fig, ax = plt.subplots(3, 1)
ax[0].hlines(0, *t_range, colors='gray', ls=':')
ax[0].plot(t, y[:, 0])
ax[0].grid()
ax[0].set_title("position")
ax[1].hlines(0, *t_range, colors='gray', ls=':')
ax[1].plot(t, y[:, 1])
ax[1].grid()
ax[1].set_title("velocity")
ax[2].set_xlim((y.min() - 1, y.max() + 1))
ax[2].set_ylim((0, 0.5))
ax[2].grid()