def plotPolesAndZeros(tf):
num = [tf[0], tf[1], tf[2]]
den = [tf[3], tf[4], tf[5]]
sistema = cl.TransferFunction(num, den)
cl.pzmap(sistema, Plot=True)
plt.show()
return
def plot_zpk_from_H(H, title=None, w0=1):
control.pzmap(H, Plot=True, title=title)
theta = np.linspace(0, 2*np.pi, 100)
r = w0
x1 = r*np.cos(theta)
x2 = r*np.sin(theta)
plt.plot(x1, x2, 'r', label=r'$\Omega _0$ = {}'.format(w0))
plt.legend(fancybox=True, framealpha=1, shadow=True, borderpad=1, fontsize='x-large', bbox_to_anchor=(1, 1))
plt.grid()
plt.tight_layout()
def locate_poles():
"""
Finds location of a system's zeros and poles
"""
n1 = np.array([1, 1])
n2 = np.array([1, 2])
d1 = np.array([1, 2j])
d2 = np.array([1, -2j])
d3 = np.array([1, 3])
numerator_g, denominator_g = np.array([6, 0, 1]), np.array([1, 3, 3, 1])
sys_g = ct.tf(numerator_g, denominator_g)
zeros_g = ct.zero(sys_g)
pole_g = ct.pole(sys_g)
numerator_h = np.convolve(n1, n2)
denominator_h = np.convolve(d1, np.convolve(d2, d3))
sys_h = ct.tf(numerator_h, denominator_h)
sys_tf = sys_g / sys_h
pzmap_sys = ct.pzmap(sys_tf)
print(AsciiTable([['Poles and Zeros']]).table)
data = [['Function', 'Result Ouput'], ['G(s)', sys_g],
['Zeros(g)', zeros_g], ['Pole(g)', pole_g], ['H(s)', sys_h],
['T(s)', sys_tf], ['Pzmap(s)', pzmap_sys]]
print(AsciiTable(data).table)
def pzmap(W):
f = con.pzmap(W)
plt.title("Расположение полюсов на комплексной плоскости")
plt.grid(True)
plt.show()
g = f[0] # возвращает список всех полюсов - корней знаменателя
D = True
j = 0
G = False
while D and j < len(g):
r = g[j].real
if float(r) <= 0.000000:
# print("Левый корень = " + str(r))
D = True
if float(r) == 0.0:
G = True
else:
D = False
print("Первый правый корень = " + str(r))
j = j + 1
if D and G:
print("Система на границе устойчивости, есть нулевые корни")
elif D:
print("Система устойчива, все корни левые")
else:
print("Cистема не устойчива, есть хотя бы один правый корень")
def TranformadaZ(titutlo,num,den):
h1 = control.TransferFunction(num,den)
[zeros,poles,gain] = signal.tf2zpk(num,den)
print(titutlo)
print("zeros")
print(zeros)
print("polos ")
print(poles)
print("\n")
control.pzmap(h1, Plot=True, grid=False, title=titutlo)
[t,y] = signal.impulse( (num,den) )
plt.figure()
plt.suptitle(titutlo)
plt.plot(t, y)
plt.title('Respuesta al impulso')
def dpzmap(sys, title):
"""Plot poles and zeroes of discrete system.
Keyword arguments:
sys -- the system to plot
title -- the title of the plot
"""
cnt.pzmap(sys, title=title)
circle = plt.Circle((0, 0), radius=1, fill=False)
ax = plt.gca()
ax.add_artist(circle)
plt.xlim([-1, 1])
plt.ylim([-1, 1])
x0, x1 = ax.get_xlim()
y0, y1 = ax.get_ylim()
ax.set_aspect(abs(x1 - x0) / abs(y1 - y0))
def test_pzmap(kwargs, setdefaults, dt, editsdefaults, mplcleanup):
"""Test pzmap"""
# T from from pvtol-nested example
T = TransferFunction([
-9.0250000e-01, -4.7200750e+01, -8.6812900e+02, +5.6261850e+03,
+2.1258472e+05, +8.4724600e+05, +1.0192000e+06, +2.3520000e+05
], [
9.02500000e-03, 9.92862812e-01, 4.96974094e+01, 1.35705659e+03,
2.09294163e+04, 1.64898435e+05, 6.54572220e+05, 1.25274600e+06,
1.02420000e+06, 2.35200000e+05
], dt)
Pref = [
-23.8877 + 19.3837j, -23.8877 - 19.3837j, -23.8349 + 15.7846j,
-23.8349 - 15.7846j, -5.2320 + 0.4117j, -5.2320 - 0.4117j,
-2.2246 + 0.0000j, -1.5160 + 0.0000j, -0.3627 + 0.0000j
]
Zref = [
-23.8877 + 19.3837j, -23.8877 - 19.3837j, +14.3637 + 0.0000j,
-14.3637 + 0.0000j, -2.2246 + 0.0000j, -2.0000 + 0.0000j,
-0.3000 + 0.0000j
]
pzkwargs = kwargs.copy()
if setdefaults:
for k in ['plot', 'grid']:
if k in pzkwargs:
v = pzkwargs.pop(k)
config.set_defaults('pzmap', **{k: v})
P, Z = pzmap(T, **pzkwargs)
np.testing.assert_allclose(P, Pref, rtol=1e-3)
np.testing.assert_allclose(Z, Zref, rtol=1e-3)
if kwargs.get('plot', True):
ax = plt.gca()
assert ax.get_title() == kwargs.get('title', 'Pole Zero Map')
# FIXME: This won't work when zgrid and sgrid are unified
children = ax.get_children()
has_zgrid = False
for c in children:
if isinstance(c, matplotlib.text.Annotation):
if r'\pi' in c.get_text():
has_zgrid = True
has_sgrid = isinstance(ax, mpltAxes)
if kwargs.get('grid', False):
assert dt == has_zgrid
assert dt != has_sgrid
else:
assert not has_zgrid
assert not has_sgrid
else:
assert not plt.get_fignums()
def question1(Gpr, plot=True):
print(spacer + "Question 1" + spacer)
# 1. POLES AND ZEROS
poles = ct.pole(Gpr)
zeros = ct.zero(Gpr)
print("\t Poles of the system are {}, and zeroes are {}".format(
poles, zeros))
# 2. PZ MAP
H = 1
OLTF = Gpr * H
plt.figure("Q1 - PZ map")
ct.pzmap(OLTF)
if plot: plt.show
# 3. STABILITY
stable = True
for pole in poles:
if (pole > 0): stable = False
temp = "unstable"
if (stable): temp = "stable"
print("\t Since {} are the poles, the system is {}".format(poles, temp))
# 4. STEP RESPONSE
t, c = ct.step_response(OLTF)
end_value = c[c.size - 1]
print("\t The end value of the OL step_response is {}".format(end_value))
plt.figure("Q1 - Step response")
plt.plot(t, c)
# plot asymptote
x_coordinates = [t[0], t[t.size - 1]]
y_coordinates = [end_value, end_value]
plt.plot(x_coordinates, y_coordinates)
if plot: plt.show()
return OLTF
def grafic_pol(f, name):
# x = cm.pole(f).real
# y = cm.pole(f).imag
# plt.plot(x, y)
# plt.plot(cm.pole(f))
ctr.pzmap(f, Plot=True, title='Pole Zero Map {}'.format(name))
[p, z] = ctr.pzmap(f)
# x = ctr.pzmap(f).real
# y = ctr.pzmap(f).imag
print("Полюса {}: \n".format(name))
print("p = {}".format(p))
print("z = {}".format(z))
# print("x ={} \n".format(x))
# print("y = {} \n".format(y))
# plt.title("График полюсов функции {}".format(name))
# plt.ylabel("Мниманя ось")
# plt.xlabel("Действительная часть")
# plt.grid(True)
plt.show()
def multi_loop():
"""
Gives the transfer funtion of multi-loop system
Feedback[ R(s) -> (G1 - H2) -> G2 -> feedback(G3G4, H1) , H3]-> C(s)
"""
g1 = np.array([
[1], [1, 10]])
g2 = np.array([
[1],
[1, 1]]
)
g3 = np.array([
[1, 0, 1],
[1, 4, 4]
])
g4 = np.array([
[1, 1],
[1, 6]
])
h1 = np.array([
[1, 1],
[1, 2]
])
h2 = np.array([[2], 1])
h3 = np.array([[1], 1])
sys_g1 = get_sys(g1, sys_name='tf')
sys_g2 = get_sys(g2, 'tf')
sys_g3 = get_sys(g3, 'tf')
sys_g4 = get_sys(g4, 'tf')
sysh1 = get_sys(h1, 'tf')
sysh2 = get_sys(h2, 'tf')
sysh3 = get_sys(h3, 'tf')
td.ouput(title='Exercise One',
keys=['G1', 'G2', 'G3', 'G4', 'H1', 'H2', 'H3'],
values=[sys_g1, sys_g2, sys_g3, sys_g4, sysh1, sysh2, sysh3])
sys_t = ct.series(sys_g1 - sysh2, sys_g2)
sys_t = ct.series(sys_t,
ct.feedback(
ct.series(sys_g3, sys_g4), sysh1, sign=1))
tS = ct.feedback(sys_t, sysh3)
zeros, poles = ct.pzmap(tS, Plot=True, grid=True)
show_plot(zeros, poles)
import control as co
import matplotlib.pyplot as plt
s = co.tf('s')
g = (s + 1) / (s**3 + 6 * s - 5)
plt.figure(1)
siso = co.sisotool(g)
plt.figure(2)
co.pzmap(g)
# control function
k = 11
z = -1
cs = k * (s - z)
"""Δοκιμάζοντας τιμές για μηδενικά, προσθέτω μόνο ένα πραγματικό μηδενικό, άρα το cs θα έχει
πολυώνυμο στο αριθμητή και 1 στον παρονομαστή"""
# the controlled system
g_feedback = co.feedback(co.series(g, cs), 1, sign=-1)
print(g_feedback)
# pole zero plot of the closed controlled system
plt.figure(3)
co.pzmap(g_feedback)
plt.show()
plt.subplot(2, 1, 2)
plt.semilogx(w / (2 * np.pi),
np.unwrap(phasec) * 180 / np.pi,
label='Continous')
plt.semilogx(w / (2 * np.pi),
np.unwrap(phased) * 180 / np.pi,
'--',
label='Discrete')
plt.grid(which='major', linestyle='-', linewidth='0.5', color='gray')
plt.grid(which='minor', linestyle=':', linewidth='0.5', color='gray')
plt.xlabel('Frequency [Hz]')
plt.ylabel('Phase [Deg]')
# plt.title('Frequency Response - Comparison')
plt.legend()
con.pzmap(sysc, title='Cont System Laplace plane')
con.pzmap(sysd, title='Discrete System Z plane')
if sysd.isdtime():
cir_phase = np.linspace(0, 2 * np.pi, 500)
plt.plot(np.real(np.exp(1j * cir_phase)), np.imag(np.exp(1j * cir_phase)),
'r--')
plt.axis('equal')
plt.figure()
real, imag, freq = con.nyquist_plot(sysc)
scale = K / 2 + 1
plt.axis([-scale, scale, -scale, scale])
plt.title('Nyquist plot discrete')
# plt.figure()
# plot unit circle
def Circle(x,y):
return (x*x+y*y)
plt.figure(1)
xx=numpy.linspace(-2,2,400)
yy=numpy.linspace(-2,2,400)
[X,Y]=numpy.meshgrid(xx,yy)
Z=Circle(X,Y)
plt.contour(X,Y,Z,[1])
# zero / pole plot
tf_bw = control.TransferFunction(b_bw, a_bw)
control.pzmap(tf_bw)
plt.show()
# plot frequency response
w, h = scipy.signal.freqz(b_bw, a_bw)
plt.figure(2)
plt.title('Butterworth Frequency Response')
plt.plot(w, 20 * numpy.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.ylim(-450, 100)
plt.xlabel('Frequency [rad/sample]')
plt.show()
label='Freq response from z-plane')
else:
plt.plot(w / (2 * np.pi),
freq_resp_dB[int(freq_resp_dB.size / 2):],
label='Freq response from s-plane')
plt.plot(w / (2 * np.pi),
hf.db(mag),
'r--',
label='Freq response from con.freqresp')
plt.xlabel('Frequency [Hz]')
plt.ylabel('Mag [dB]')
plt.title('Comparing freq response from s/z plane to con.freqresp')
plt.legend()
# pole zero plot
poles, zeros = con.pzmap(sys_und_tst)
plt.axis('equal')
print(f'ploes are {poles}')
print(f'zeros are {zeros}')
# plt.figure()
# plt.grid()
# plt.axis('equal')
# if len(poles) > 0:
# plt.plot(poles.real, poles.imag, 'bx')
# if len(zeros) > 0:
# plt.plot(zeros.real, zeros.imag, 'bo')
if sys_und_tst.isdtime():
cir_phase = np.linspace(0, 2 * np.pi, nsamp_single)
#Encontrar la fucnion de transferencia
#Usar signal.tf2zpk para encontrar polos y zeros de cada función
#A
num = [1, -3]
den = [1, 4, 4]
h1 = control.TransferFunction(num, den)
[zeros, poles, gain] = signal.tf2zpk(num, den)
print("h1")
print("zeros")
print(zeros)
print("polos ")
print(poles)
print("\n")
control.pzmap(h1, Plot=True, grid=False, title='H1')
[t, y] = signal.impulse(([1, -3], [1, 4, 4]))
plt.figure()
plt.suptitle("H1")
plt.subplot(211)
plt.plot(t, y)
plt.title('Respuesta al impulso')
[t, y] = signal.step(([1, -3], [1, 4, 4]))
plt.subplot(212)
plt.plot(t, y)
plt.title('Respuesta al escalon')
#B
num = [1]
den = [1, 4, 4]
h2 = control.TransferFunction(num, den)
den = np.array([1, 0, 0])
z, p, k = sig.tf2zpk(num, den)
ww, hh = sig.freqz(num, den)
print("Z =", z, "\n", "P =", p, "\n", "K =", k, "\n")
ww, hh = sig.freqz(num, den)
ww = ww / np.pi
eps = np.finfo(float).eps
plt.figure("Filtro FIR")
ax1 = plt.subplot(2, 1, 1)
ax1.set_title('Módulo')
ax1.plot(ww, 20 * np.log10(abs(hh + eps)))
ax1.set_xlabel('Frequencia normalizada')
ax1.set_ylabel('Modulo [dB]')
plt.grid()
ax2 = plt.subplot(2, 1, 2)
ax2.set_title('Fase')
ax2.plot(ww, np.angle(hh))
ax2.set_xlabel('Frequencia normalizada')
ax2.set_ylabel('[Rad]')
plt.grid()
plt.show()
plt.tight_layout()
tf = control.TransferFunction(num, den, 1)
print(tf)
control.pzmap(tf, Plot=True, title='Pole Zero Map', grid=True)
#if using termux
import subprocess
import shlex
#end if
p1 = 2 * np.pi * 1e4
p2 = 2 * np.pi * 1e5
H = 81 / (4 * 1e4)
num = [1000]
den = [(1 / (p1 * p2)), ((1 / p1) + (1 / p2)), (1000 * H + 1)]
#den=[(1e-9), (11*1e-5), 3.025]
sys = control.tf(num, den)
pole, zero = control.pzmap(sys, Plot=False)
print("Poles are :", pole)
x = (pole.real)
y = (pole.imag)
plt.plot(x[0], y[0], marker="X")
plt.plot(x[1], y[1], marker="X")
plt.grid()
plt.axhline(y=0, color='k')
plt.axvline(x=0, color='k')
plt.savefig('./figs/ee18btech11036/ee18btech11036_1.pdf')
plt.savefig('./figs/ee18btech11036/ee18btech11036_1.eps')
subprocess.run(
shlex.split("termux-open ./figs/ee18btech11036/ee18btech11036_1.pdf"))
#else
#plt.show()
h1 = co.feedback(g1, 2, -1)
h2 = co.feedback(g1, 3, -1)
h3 = co.feedback(g1, 5, -1)
print("poles (k=2)")
for elem in co.pole(h1):
print(f'{elem: .2f}')
print("poles (k=3)")
for elem in co.pole(h2):
print(f'{elem: .2f}')
print("poles (k=5)")
for elem in co.pole(h3):
print(f'{elem: .2f}')
plt.figure(1)
h1_map = co.pzmap(h1, plot=True, title='pzmap (k=2)')
plt.figure(2)
h2_map = co.pzmap(h2, plot=True, title='pzmap (k=3)')
plt.figure(3)
h3_map = co.pzmap(h3, plot=True, title='pzmap (k=5)')
t = np.linspace(0, 10, 1000)
t1, imp1 = co.impulse_response(h1, t)
t2, imp2 = co.impulse_response(h2, t)
t3, imp3 = co.impulse_response(h3, t)
t4, stp1 = co.step_response(h1, t)
t5, stp2 = co.step_response(h2, t)
t6, stp3 = co.step_response(h3, t)
t = Symbol('t')
K = Symbol('K')
#Some hard-coded values
num = [1]
den = [1, 3, 2]
H = 1
#Transfer Function
G = control.tf(num, den)
G_feedbacked = control.feedback(G, H)
control.sisotool(G_feedbacked)
print("OPEN LOOP TRANSFER FUNCTION")
print(G)
print("CLOSE LOOP TRANSFER FUNCTION")
print(G_feedbacked)
poles, zeros = control.pzmap(G, True, True)
all_points = np.concatenate([[-np.Infinity], zeros, poles])
all_points.sort()
all_real_points = np.real(all_points[np.isreal(all_points)])
print("Range in real axis :")
range_of_real_axis = []
for i in range(len(all_real_points) - 1, 0, -2):
print("From " + str(all_real_points[i - 1]) + " to " +
str(all_real_points[i]))
range_of_real_axis += [all_real_points[i - 1], all_real_points[i]]
print("The starting points are:" + str(poles))
print("The ending points are:" + str(zeros))
print("The total number of branches is: " + str(len(poles)))
sum_of_inverse_zeros = 0
sum_of_inverse_poles = 0
for zero in zeros:
plt.clf()
# plt.setp(plt.gca(), autoscale_on=False)
# tellme('click to begin')
# plt.waitforbuttonpress()
plt.ion()
plt.show(block=False)
# the output can be collected by this variable result
for i in range(-80, 80):
den = [1, 6, 11, 6, i * 0.25]
# result = checkStability(den)
# confirmation by plotting pole-zero graph on s-plane
p, z = ctrl.pzmap(ctrl.TransferFunction(num, den),
Plot=False,
title="when k=10.1")
if i == -80:
t1 = plt.plot(p[0].real, p[0].imag, 'k*')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
t1 = plt.plot(p[1].real, p[1].imag, 'k*')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
t1 = plt.plot(p[2].real, p[2].imag, 'k*')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
t1 = plt.plot(p[3].real, p[3].imag, 'k*')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
if i == 79:
t1 = plt.plot(p[0].real, p[0].imag, 'kx')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
t1 = plt.plot(p[1].real, p[1].imag, 'kx')
plt.setp(t1, markersize=24.0, markeredgewidth=2.0)
color = 'b'
# Add arrows to the plot
# H1 = L.evalfr(0.4); H2 = L.evalfr(0.41);
# arrow([real(H1), imag(H1)], [real(H2), imag(H2)], AM_normal_arrowsize, \
# 'EdgeColor', color, 'FaceColor', color);
# H1 = freqresp(L, 0.35); H2 = freqresp(L, 0.36);
# arrow([real(H2), -imag(H2)], [real(H1), -imag(H1)], AM_normal_arrowsize, \
# 'EdgeColor', color, 'FaceColor', color);
plt.figure(9)
Tvec, Yvec = ct.step_response(T, np.linspace(0, 20))
plt.plot(Tvec.T, Yvec.T)
Tvec, Yvec = ct.step_response(Co * S, np.linspace(0, 20))
plt.plot(Tvec.T, Yvec.T)
plt.figure(10)
plt.clf()
P, Z = ct.pzmap(T, plot=True, grid=True)
print("Closed loop poles and zeros: ", P, Z)
# Gang of Four
plt.figure(11)
plt.clf()
ct.gangof4_plot(Hi * Po, Co)
if 'PYCONTROL_TEST_EXAMPLES' not in os.environ:
plt.show()
import scipy.signal as signal
from base.impseq import *
from base.stepseg import *
b = np.array([0, 0.866, 0.0306, -2.486, 3.2094, -1.62, 0.84])
a = np.array([1, -2.9, 4.8, -4.7, 2.8, -0.9])
R, p, c = signal.residuez(b, a)
# print(R)
print("poles:")
print(p)
# print(c)
print("roots:")
roots = np.roots(b)
# b = np.array([3])
# a = np.array([1,-1])
delta, n1 = impseg(0, 0, 10)
delta = delta.astype('float64')
xb1 = signal.lfilter(b, a, delta)
step, n2 = stepseg(0, 0, 10)
step_minus_2, _ = stepseg(2, 0, 10)
xb2 = n2 * np.sin(np.pi / 3 * n2) * step + np.power(0.9, n2) * step_minus_2
err = xb1 - xb2
print(err)
tfx = control.tf(b, a)
control.pzmap(tfx)
plt.show()
# C = np.array([[0, 1, 0, 0]])
D = np.array([[0]])
S = ctl.ss(A, B, C, D)
print('S =', S)
#########################################################
# Funcao de transferencia
#########################################################
G = ctl.ss2tf(S)
print('G =', G)
#########################################################
# Polos e zeros
#########################################################
(p, z) = ctl.pzmap(G)
print('polos =', p)
print('zeros =', z)
plt.show()
#########################################################
# Plot da resp no dominio do tempo ao impulso unitario
#########################################################
# T, yout = ctl.impulse_response(G)
# plt.plot(T, yout)
# plt.show()
#########################################################
# Plot da resp no dominio do tempo ao degrau unitario
#########################################################
T, yout = ctl.step_response(G)
den = den.subs({f0: 77500, r3: 100000, r4: 47000})
poles = []
zeros = []
max_r_jfet = 10000
for i in range(0, max_r_jfet + 1000, 100):
new_den = sympy.Poly(den.subs(r_jfet, i), s)
new_num = sympy.Poly(num.subs(r_jfet, i), s)
num_coeffs = list(new_num.coeffs())
den_coeffs = list(new_den.coeffs())
num_coeffs = [float(e) for e in num_coeffs]
den_coeffs = [float(e) for e in den_coeffs]
sys = control.tf(num_coeffs, den_coeffs)
new_poles, new_zeros = control.pzmap(sys, Plot=False)
poles.extend(new_poles)
zeros.extend(new_zeros)
x_poles = [pole.real for pole in poles]
y_poles = [pole.imag for pole in poles]
x_zeros = [zero.real for zero in zeros]
y_zeros = [zero.imag for zero in zeros]
fig, (poles_plot, zeros_plot) = plt.subplots(1, 2)
fig.suptitle('Diagrama de polos y ceros')
poles_plot.scatter(x_poles, y_poles, marker='x', c='red')
zeros_plot.scatter(x_zeros, y_zeros, marker='o', c='blue')
poles_plot.set_xlabel('Parte real σ (Hz)')
poles_plot.set_ylabel('Parte imaginaria jω (Hz)')
# ---------------- Initiate Plant ------------------ num = 2 * gamma * v_bar / (r_bar**2) p1 = 2 * gamma * v_bar**2 / r_bar**3 den = [1, 0, p1] Gsys = control.TransferFunction(num, den) # ------------- Initiate Controller --------------- Kgain = 100 tau = .025 # 1/intended zero placement numC = np.array([tau, 1]) * Kgain Csys = control.TransferFunction(numC, 1) # ---------------- Multiply the transfer functions ------------- CGsys = control.series(Csys, Gsys) control.pzmap(CGsys, Plot=True, title='Pole Zero Map of Plant') print(Csys) print(Gsys) print(CGsys) plt.figure() tout, y, x = control.forced_response(CGsys, t, step, R_hat_0) plt.plot(t, y) plt.show() # tout,y,x = signal.lsim(CG, step, t, R_hat_0) # print(y) # plt.plot(t,y) # #plt.legend(loc='best') # plt.show()
for i in range(len(rowArray) - 1):
if rowArray[i][0] * rowArray[i + 1][0] < 0:
flag = 1
if flag == 0:
print('Stable System! CoolControlEngineer!')
return True
else:
print('System Unstable! Get back to work!')
return False
# numerator and denominator may be given as input here
num = [30, 150, -900]
# den = [1, 12, 49, 78, 40]
#example1
# den = [1, 1, 10, 72, 152, 240]
#example2
# den = [1, 1, 2, 2, 5]
#example3
den = [1, 2, 11, 18, 18]
# the output can be collected by this variable result
result = checkStability(den)
# confirmation by plotting pole-zero graph on s-plane
p, z = ctrl.pzmap(ctrl.TransferFunction(num, den),
Plot=True,
title="pole zero plot")
plt.show()
import subprocess
import shlex
#end if
p1 = 2 * np.pi * 1e4
p2 = 2 * np.pi * 1e5
H = ((p1 - p2)**2) / (4000 * p1 * p2)
num = [1000]
den = [(1 / (p1 * p2)), ((1 / p1) + (1 / p2)), (1000 * H + 1)]
#den=[(1e-9), (11*1e-5), 3.025]
sys = control.tf(num, den)
s = signal.lti(num, den)
w, mag, phase = signal.bode(s)
pole, zero = control.pzmap(sys, Plot=True, title='Pole Zero Map')
print("Poles are :", pole)
gain_y = np.full((len(w)), 44.3866)
x_val = abs(pole[0])
y_val = 44.3866
plt.figure()
plt.plot(w, mag)
plt.plot(w, gain_y)
plt.plot(x_val, y_val, 'ro')
plt.text(x_val, y_val, "(345575, 44.3866)")
plt.grid()
print("Low frequency Gain ", mag[0])
print("Gain at crossover frequency dB ", 44.3866)
b_el, a_el = scipy.signal.ellip(N_el, Rp * -1, Rs * -1, wp1_el, output='ba')
# plot unit circle
def Circle(x, y):
return (x * x + y * y)
plt.figure(1)
xx = numpy.linspace(-2, 2, 400)
yy = numpy.linspace(-2, 2, 400)
[X, Y] = numpy.meshgrid(xx, yy)
Z = Circle(X, Y)
plt.contour(X, Y, Z, [1])
# zero / pole plot
tf_el = control.TransferFunction(b_el, a_el)
control.pzmap(tf_el)
plt.show()
# plot frequency response
w, h = scipy.signal.freqz(b_el, a_el)
plt.figure(2)
plt.title('Chebyshev Type II Frequency Response')
plt.plot(w, 20 * numpy.log10(abs(h)), 'b')
plt.ylabel('Amplitude [dB]', color='b')
plt.ylim(-120, 10)
plt.xlabel('Frequency [rad/sample]')
plt.show()
acbas = co.series(acp, bap)
acbaef = co.feedback(acbas, e, +1)
print(acbaef)
g_poles = co.pole(acbaef)
print("G poles")
for elem in g_poles:
print(f'{elem: .2f}')
g_zeros = co.zero(acbaef)
print("G zeros")
for elem in g_zeros:
print(f'{elem: .2f}')
g1_map = co.pzmap(acbaef, plot=True)
t = np.linspace(0, 25, 100)
t1, stp = co.step_response(acbaef, t)
t2, imp = co.impulse_response(acbaef, t) # Warning for infinite impulse at t=0
plt.figure(2)
plt.plot(t1, stp)
plt.title("Step Response")
plt.ylabel("Amplitude")
plt.xlabel("Time")
plt.grid()
plt.figure(3)
plt.plot(t2, imp)
plt.title("Impulse Response")
# Hitung eigenvalue dari sistem pegas massa tersebut
poles = mySys.pole()
print('Poles sistem adalah: \n', poles, '\n')
# Nyatakan apakah sistem stabil atau tidak. Apabila nilai poles nya bukan bilangan complex
# sistem tidak stabil
if str(type(poles[1])) == "<class 'numpy.float64'>":
print('===> sistem tidak stabil \n')
else:
print('===> sistem stabil \n')
# Visualisasikan pula lokasi poles dengan memetakannya di ruang kompleks C.
# Seluruh poles dari sistem yang stabil berada di sebelah kanan sumbu
# imajiner
pzmap(mySys)
#fig = plt.figure()
# Berikutnya dilakukan perhitungan dinamika sistem pegas-massa
# Membuat array selang waktu dari 0 sampai 20 dengan time frame 0.05
dt = 0.05
t = np.arange(0.0, 20, dt)
yt = []
for i in range(len(t)):
yt.append(-0.5)
# Mendefinisikan kondisis awal masing-masing state
vInit = 1.0 # kecepatan awal
sInit = 0.0 # posisi/simpangan awal
# Kondisi awal state