def nqstplot(num,den):
G = control.tf(num,den)
w = numpy.logspace(-3,3,5000)
control.nyquist(G,w)
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]+')'
plt.grid(True)
plt.title('Nyquist Diagram of G(s)H(s) = '+(s1)+'/'+(s2))
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
if not os.path.isdir('static'):
os.mkdir('static')
else:
# Remove old plot files
for filename in glob.glob(os.path.join('static', 'NyquistPlot','Plot3.png')):
os.remove(filename)
nqst=os.path.join('static','NyquistPlot', 'Plot3.png')
plt.savefig(nqst)
plt.clf()
plt.cla()
plt.close()
return nqst
def plot(self, type, entry1, entry2):
transfer_function = self.get_TF(entry1, entry2)
if type == "bode":
co.bode_plot(transfer_function)
elif type == "nyquist":
co.nyquist(transfer_function)
elif type == "rootlocus":
co.root_locus(transfer_function)
else:
[t1, y1] = self.plot_type(type, transfer_function)
plt.plot(t1, y1)
plt.xlabel('Time(s)')
plt.ylabel('Amplitude')
plt.grid()
plt.show()
def plot(self):
G = control.TransferFunction((1), (1, 1))
real, imag, freq = control.nyquist(G)
plt.title('Nyquist Plot')
plt.gcf().canvas.set_window_title('Nyquist Plot')
plt.xlabel('Real')
plt.ylabel('Imaginary')
plt.grid()
plt.show()
def nyq(self):
"""
Display Nyquist plot for the system.
Uses nyquist plotting functionality of the module control.
"""
plt.clf()
plt.figure(1)
real, imag, freq = control.nyquist(self.sys, Plot=True)
plt.title("Nyquist Plot")
plt.xlabel("Re($\omega$)")
plt.ylabel("Im($\omega$)")
plt.grid()
plt.show()
def loop_analysis(name, sys, zeta, wd, k, t_vect, k_vect, omega_vect):
sysc = control.feedback(sys * k, 1)
closed_loop_poles = control.pole(sysc)
plt.figure(figsize=(10, 5))
rlocus(name, sys, k_vect, k)
plt.axis([-16, 0, -8, 8])
theta = np.arccos(zeta)
plt.plot([0, -10], [0, 10 * np.tan(theta)], 'r--')
plt.vlines(-wd, -8, 8, linestyle='--', color='r')
plt.figure(figsize=(10, 5))
bode(name, sys, omega_vect, margins=True)
plt.figure(figsize=(10, 5))
control.nyquist(sys, omega=omega_vect)
plt.title(name + ' nyquist')
plt.axis([-10, 10, -10, 10])
plt.figure(figsize=(10, 5))
step_reponse(name, sysc, t_vect)
plt.figure(figsize=(10, 5))
bode(name + ' closed loop ', sysc, np.logspace(-2, 2))
def plot_nyquist(self, fig):
tf = self.tf if self.loop_type == 'ol' else self.tf_plant * self.tf_comp
w = np.logspace(-100, 100, 50000)
x, y, _ = control.nyquist(tf, omega=w)
fig.clf()
ax = fig.add_subplot(1, 1, 1)
ax.plot(x, y)
ax.plot(x, -y, '--')
ax.plot([-1], [0], color='r', marker='x', markersize=10)
ax.set_xlabel('Real axis')
ax.set_ylabel('Imaginary axis')
if not self.settings.is_nyquist_default():
xmin = self.settings.get_nyquist_xmin()
xmax = self.settings.get_nyquist_xmax()
ymin = self.settings.get_nyquist_ymin()
ymax = self.settings.get_nyquist_ymax()
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
return fig
m = np.arange(0, 3, 0.2)
for num in m:
if num != 1:
p = M_circle(num)
plt.plot(p[0], p[1])
if (num >= 0.6 and num <= 1):
plt.text(0.8 * (p[3] + p[2]), 0.8 * (p[4] + p[2]),
np.around(num, decimals=2))
elif (num >= 1.4 and num <= 1.6):
plt.text(0.8 * (p[3] - p[2]), 0.8 * (p[4] - p[2]),
np.around(num, decimals=2))
plt.axvline(x=-0.5, label='M=1')
w = np.logspace(-100, 100, 10000)
control.nyquist(G, w, label='nyquistplot')
plt.grid(True)
plt.title('M Circles and Nyquist plot')
plt.axis('equal')
plt.xlim(-4, 4)
plt.xlabel('Real')
plt.ylim(-3, 3)
plt.ylabel('Imaginary')
plt.legend(loc='best', prop={'size': 11})
#N circles plot
subplot(2, 1, 2)
n = np.arange(-2, 2, 0.2)
for num in n:
def M_circle(m):
theta = np.linspace(0, 2*np.pi, 100)
x0 = np.around(m**2/(1-m**2),decimals=2)
y0 = np.around(0,decimals=2)
r = abs(m/(1-m**2))
x = x0 + r*np.cos(theta)
y = y0 + r*np.sin(theta)
return np.around(x,decimals=2),np.around(y,decimals=2)
#Creating a transfer function G = num/den
nume = 1000
deno = [1,18,119,342,360]
G = control.tf(nume,deno)
niq = np.around(control.nyquist(G,Plot=0),decimals=2)
#finding the point of intersection
mag=np.empty(0)
freq=np.empty(0)
m=np.arange(0,8,0.02)
for num in m:
if num != 1:
for i in range (len(niq[0])):
for j in range (len(M_circle(num)[0])):
if niq[0][i] == M_circle(num)[0][j] and niq[1][i] == M_circle(num)[1][j]:
mag=np.append(mag,num)
freq=np.append(freq,niq[2][i])
print(mag)
print(len(mag))
B = matrix([[0.0], [1 / m]]) C = matrix([[1.0, 0.0]]) D = matrix([[0.0]]) G = ss(A, B, C, D) P = ss2tf(G) #------ W = matrix([[1.0]]) V = 1e8 * matrix([[1.0, 0.0], [0.0, 1.0]]) Y = linalg.solve_continuous_are(A.transpose(), C.transpose(), V, W) L = Y * C.transpose() * inv(W) #------------------- R = matrix([[1.0]]) Q = matrix([[1e2, 0.0], [0.0, 1.]]) X = linalg.solve_continuous_are(A, B, Q, R) K = inv(R) * B.transpose() * X # synthesis, controller in state space Ac = A - B * K Bc = matrix([[0.0], [0.0]]) Cc = K Dc = D H = ss(Ac, Bc, Cc, Dc) F = ss2tf(H) # show open loop controller and plant plt.figure() bode(F * P) plt.figure() nyquist(F * P) plt.figure() T, yout = step_response(F * P / (1 + F * P), T=np.linspace(0, 50, 10000)) plt.plot(T, yout)
def Lab2(numZ, denZ, numR, denR, n):
w1 = tf(numZ, denZ) # Передаточная и переходная функции
y1, x1 = step(w1)
print("\nПередаточная функция замкнутой САУ - ", w1)
w2 = tf(numR, denR)
y2, x2 = step(w2)
print("\nПередаточная функция разомкнутой САУ - ", w2)
plt.plot(x1, y1, "r", label="Название")
plt.title("Переходная функция замкнутой системы")
plt.xlabel("Время, с")
plt.ylabel("Амплитуда")
plt.grid(True)
plt.show()
plt.plot(x2, y2, "r", label="Название")
plt.title("Переходная функция разомкнутой системы")
plt.xlabel("Время, с")
plt.ylabel("Амплитуда")
plt.grid(True)
plt.show()
G = control.tf(numR, denR) # Найквист
GG = num.logspace(-3, 3, 10000)
real, imag, freq = control.nyquist(G, GG)
real = list(real)
imag = list(imag)
y = []
x = []
for i in range(-1, 2, 1):
y.append(i)
for i in range(-1, 2, 1):
x.append(-1)
plt.plot(x, y, "r")
for i in range(0, len(real)):
z = abs(complex(real[i], imag[i]))
if 0.999 < z < 1.001 and real[i] < 0 and imag[i] < 0:
fi = atan(imag[i] / real[i]) * 180 / math.pi
print("Запас по фазе - ", real[i], imag[i])
plt.plot(real[i], imag[i], '-x')
print("Угол - ", fi)
plt.plot()
xx, yy = [0, real[i]], [0, imag[i]]
plt.plot(xx, yy)
break
for i in range(0, len(real)):
z = abs(complex(real[i], imag[i]))
if -0.0001 < imag[i] < 0.0001 and abs(real[i]) > 0.05:
print("Запас по амплитуде - ", real[i], imag[i])
plt.plot(real[i], imag[i], '-o')
xx1, yy1 = [-1, -1], [0, -1.1]
xx2, yy2 = [real[i], real[i]], [0, -1.1]
plt.plot(xx1, yy1, "r", xx2, yy2, "r")
break
phi = num.linspace(0, 2 * num.pi, 100)
r = num.sqrt(1.0)
x1 = r * num.cos(phi)
x2 = r * num.sin(phi)
plt.plot(x1, x2)
plt.title("Диаграмма Найквиста")
plt.plot(label="Название")
plt.xlabel("+1")
plt.ylabel("+j")
plt.grid(True)
plt.show()
mag, phase, omega = bode(w1, dB=True) # ЛАЧХ и ЛФЧХ
plt.title("ЛАЧХ и ЛФЧХ")
plt.grid(True)
plt.show()
print("Полюса - %s" % pole(w1))
pzmap(w1)
plt.title("Расположение полюсов на комплексной плоскости")
plt.grid(True)
plt.show()
plt.figure()
w = symbols("w", real=True) # Годограф Михайлова
if n == 1:
z = factor(160 * (I * w) ** 3 + 89 * (I * w) ** 2 + 16.4 * I * w + 2)
elif n == 2:
z = factor(160 * (I * w) ** 3 + 89 * (I * w) ** 2 + 16.4 * I * w + 9.1225)
elif n == 3:
z = factor(160 * (I * w) ** 3 + 89 * (I * w) ** 2 + 16.4 * I * w + 10)
zR = re(z)
zIm = im(z)
x = [zR.subs({w: q}) for q in arange(0, 100, 0.1)]
y = [zIm.subs({w: q}) for q in arange(0, 100, 0.1)]
print(z)
plt.title("Годограф Михайлова")
plt.axis([-150, 10, -45, 5])
plt.plot(x, y)
plt.grid(True)
plt.show()
if n == 1:
Matrix = num.matrix([[89, 2], [160, 16.4]])
elif n == 2:
Matrix = num.matrix([[89, 9.1225], [160, 16.4]])
elif n == 3:
Matrix = num.matrix([[89, 10], [160, 16.4]])
Det = num.linalg.det(Matrix)
print("Уравнение - ", denZ, "\nМатрица - \n", Matrix)
print(" Определитель - ", Det)
import numpy as np
import matplotlib.pyplot as plt
H = 1121.
m = 200
kp = 0.091
T = 1
Td = 2
num = H * kp * np.array([Td, 1.])
den = m * np.array([T, 1, 0, 0])
G = ctr.tf(num, den)
fig1, ax = plt.subplots()
mag, phase, omega = ctr.nyquist(G, [0.01, 1000])
t = np.linspace(0, 2 * np.pi, 100)
ax.plot(np.cos(t), np.sin(t))
fig2 = plt.figure()
ws = np.geomspace(0.01, 100, 50)
mag, phase, omega = ctr.bode(G, ws)
zero_db = np.argmin(abs(np.log10(mag)))
for ax in fig2.axes:
ax.axvline(ws[zero_db], color='tab:orange')
print(ws[zero_db])
print(phase[zero_db])
plt.show()
from control.matlab import *
import control
import matplotlib.pyplot as plt
import numpy as num
from sympy import *
from sympy import I
from numpy import arange
import math
G = control.tf([0, 2], [160, 89, 16.4, 1]) # Найквист
GG = num.logspace(-3, 3, 10000)
real, imag, freq = control.nyquist(G, GG)
real = list(real)
imag = list(imag)
y1 = []
x1 = []
y2 = []
x2 = []
for i in range(0, len(real)): # запас по фазе
z = abs(complex(real[i], imag[i]))
if 0.999 < z < 1.001 and real[i] < 0 and imag[i] < 0:
fi = atan(imag[i] / real[i]) * 180 / math.pi
print("Запас по фазе - ", real[i], imag[i])
plt.plot(real[i], imag[i], '-x')
print("Угол - ", fi)
plt.plot()
xx, yy = [0, real[i]], [0, imag[i]]
plt.plot(xx, yy)
break
#end if
#coefficents of open loop transfer function
den = [4,1,0,0]
num1 = [1]
num2 = [2]
#Creating a transfer function G = num/den
G1 = control.tf(num1,den)
G2 = control.tf(num2,den)
#plotting the nyquist plot for three different transfer functions for a variable K
control.nyquist(G1,label='K=1')
control.nyquist(G2,label='K=2')
plt.xlim(-4,0)
plt.ylim(-2,2)
plt.legend()
plt.annotate("-1+0j",(-1,0))
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
#if using termux
plt.savefig('./figs/ee18btech11034/ee18btech11034_2.pdf')
plt.savefig('./figs/ee18btech11034/ee18btech11034_2.eps')
subprocess.run(shlex.split("termux-open ./figs/ee18btech11034/ee18btech11034_2.pdf"))
#else
#plt.show()
plt.text(0.8 * (p[3] + p[2]), 0.8 * (p[4] + p[2]),
np.around(num, decimals=2))
elif (num >= 1.4 and num <= 1.6):
plt.text(0.8 * (p[3] - p[2]), 0.8 * (p[4] - p[2]),
np.around(num, decimals=2))
plt.xlim(-5, 5)
plt.ylim(-2, 2)
#Creating a transfer function G = num/den
nume = 1000
deno = [1, 18, 119, 342, 360]
G = control.tf(nume, deno)
w = np.logspace(-100, 100, 10000)
control.nyquist(G, w)
plt.text(2, 0, "niquest plot")
plt.grid(True)
plt.title('M circles and niquest plot')
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
plt.savefig("M_circles.eps")
plt.show()
#if using termux
#plt.savefig('M_circles.eps')
#subprocess.run(shlex.split("termux-open M_circles.pdf"))
#plt.show()
#N_circles plot
n = np.arange(-2, 2, 0.2)
Q = np.eye(4,4)
R = np.eye(2,2)
#S1 = sp.linalg.solve_continuous_are(A, B, Q, R)
#K1 = np.linalg.inv(R).dot(B.T).dot(S1)
#E1 = np.linalg.eigvals(A-B.dot(K1))
#print("S1 =\n", S1)
#print("K1 =\n", K1)
#print("E1 =\n", E1)
S2, E2, K2 = ct.care(Ap, Bp, Q, R)
#print("\nS2 =\n", S2)
#print("K2 =\n", K2)
#print("E2 =\n", E2)
print "ctrb = "+ str(np.linalg.matrix_rank(ct.ctrb(Ap,Bp)))
print "obsv = " + str(np.linalg.matrix_rank(ct.obsv(Ap,Cp)))
#K3, S3, E3 = ct.matlab.lqr(Ap, Bp, Q, R)
#print("\nS3 =\n", S3)
#print("K3 =\n", K3)
#print("E3 =\n", E3)
ss_P = ct.ss(Ap,Bp,Cp,Dp)
print ss_P
t = np.linspace(0, 3, 1000)
stepy = ct.step(ss_P,t)
#plt.plot(t,stepy)
#ct.impulse(ss_P)
ct.nyquist(ss_P)
#bode plot only implemented for SISO system.omg
#ct.bode(ss_P)
[n2,d2]=control.pade(0.5,10) #Creating delay of 0.5
[n3,d3]=control.pade(0.0005,10) #Creating delay of 0.0005
#Creating a transfer function G = num/den
G = control.tf(num,den)
G1=control.tf(n1,d1)
G2=control.tf(n2,d2)
G3=control.tf(n3,d3)
#assigning delay to system G
G4=G*G1
G5=G*G2
G6=G*G3
#plotting nyquist plot with variable tau
control.nyquist(G4,label='$t=0.1744$')
control.nyquist(G5,label='$t=0.5$')
control.nyquist(G6,label='$t=0.0005$')
plt.grid(True)
plt.xlim(-4,0)
plt.ylim(-2,2)
plt.legend()
plt.annotate("-1+0j",(-1,0))
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
#if using termux
plt.savefig('./figs/ee18btech11035/ee18btech11035_1.pdf')
plt.savefig('./figs/ee18btech11035/ee18btech11035_1.eps')
subprocess.run(shlex.split("termux-open ./figs/ee18btech11035/ee18btech11035_1.pdf"))
#else
#plt.show()
#if using termux
import subprocess
import shlex
#end if
import control
import matplotlib.pyplot as plt
import numpy as np
G1 = control.tf([1], [1, 2, 2, 2, 1])
G2 = control.tf([1], [1, 2, 0, 0, -1])
G3 = control.tf([1], [1, 2, 1, 1, 0])
w = np.linspace(-50, 50, 5000)
control.nyquist(G1, w, label='k=1')
control.nyquist(G2, w, label='k=-1')
control.nyquist(G3, w, label='k=0')
plt.legend()
#if using termux
plt.savefig('./figs/ee18btech11042/ee18btech11042_1.pdf')
plt.savefig('./figs/ee18btech11042/ee18btech11042_1.eps')
subprocess.run(
shlex.split("termux-open ./figs/ee18btech11042/ee18btech11042_1.pdf"))
#else
#plt.show()
plt.show()
#M circles plot
subplot(2,1,1)
m=np.arange(0,3,0.2)
for num in m:
if num != 1:
p=M_circle(num)
plt.plot(p[0],p[1] )
if (num >= 0.6 and num <= 1):
plt.text(0.8*(p[3]+p[2]),0.8*(p[4]+p[2]),np.around(num,decimals=2))
elif (num >=1.4 and num <= 1.6):
plt.text(0.8*(p[3]-p[2]),0.8*(p[4]-p[2]),np.around(num,decimals=2))
plt.axvline(x=-0.5,label='M=1')
w=np.logspace(-100,100,1000)
control.nyquist(G,w,label='Rect coord')
plt.grid(True)
plt.title('M Contors in rect coordinates')
plt.axis('equal')
plt.xlim(-4,4)
plt.xlabel('Real')
plt.ylim(-3,3)
plt.ylabel('Imaginary')
plt.legend(loc='best',prop={'size':11})
#N circles plot
subplot(2,1,2)
n=np.arange(-2,2,0.2)
nrows, ncols = A.shape
dtype = {
'names': ['f{}'.format(i) for i in range(ncols)],
'formats': ncols * [A.dtype]
}
return A.view(dtype)
#M circle intersection
num = [50, 150]
den = [1, 6, 8, 0]
G = control.tf(num, den)
w = np.logspace(-3, 3, 1000)
Real, Imag, Freq = np.around(control.nyquist(G, w), decimals=2) # Rounding Off
NyQ_Data = np.append(np.expand_dims(Real, axis=1),
np.expand_dims(Imag, axis=1),
axis=1)
M = list(np.arange(0.01, 5, 0.3))
#finds intersection points and return M and frequency
def Extract(M, NyQ_Data, Freq):
Output = []
for m in M:
Circle_Data = list(Intersection(Circle_M(m)))
ND = list(Intersection(NyQ_Data))
Int = np.intersect1d(Circle_Data, ND)
for p in Int:
#end if
num1 = [81]
den1 = [1, 18, 103, 198, 121]
num2 = [100]
den2 = [1, 18, 101, 180, 100]
num3 = [121]
den3 = [1, 18, 99, 162, 81]
#Creating a transfer function G = num/den
G1 = control.tf(num1, den1)
G2 = control.tf(num2, den2)
G3 = control.tf(num3, den3)
w = np.logspace(-3, 3, 5000)
#Plotting the Nyquist plot
control.nyquist(G1, w, label='k=-9')
control.nyquist(G2, w, label='k=-10')
control.nyquist(G3, w, label='k=-11')
plt.plot(1, 0, 'o')
plt.annotate("(1,0)", (1, 0))
plt.legend()
#if using termux
plt.savefig('./figs/ee18btech11029/ee18btech11029_1.pdf')
plt.savefig('./figs/ee18btech11029/ee18btech11029_1.eps')
subprocess.run(
shlex.split("termux-open ./figs/ee18btech11029/ee18btech11029_1.pdf"))
#else
#plt.show()
import control
import matplotlib.pyplot as plt
num = [0, 0, 1, 3]
den = [1, -3, 0, 0]
#Transfer function GH = num/den
G = control.tf(num, den)
control.nyquist(G)
plt.grid(True)
plt.scatter(-1, 0, s=40)
plt.annotate("-1+0j", (-1, 0))
plt.title('Nyquist Diagram of G(s)H(s)')
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
plt.show()
Q = np.eye(4, 4)
R = np.eye(2, 2)
#S1 = sp.linalg.solve_continuous_are(A, B, Q, R)
#K1 = np.linalg.inv(R).dot(B.T).dot(S1)
#E1 = np.linalg.eigvals(A-B.dot(K1))
#print("S1 =\n", S1)
#print("K1 =\n", K1)
#print("E1 =\n", E1)
S2, E2, K2 = ct.care(Ap, Bp, Q, R)
#print("\nS2 =\n", S2)
#print("K2 =\n", K2)
#print("E2 =\n", E2)
print "ctrb = " + str(np.linalg.matrix_rank(ct.ctrb(Ap, Bp)))
print "obsv = " + str(np.linalg.matrix_rank(ct.obsv(Ap, Cp)))
#K3, S3, E3 = ct.matlab.lqr(Ap, Bp, Q, R)
#print("\nS3 =\n", S3)
#print("K3 =\n", K3)
#print("E3 =\n", E3)
ss_P = ct.ss(Ap, Bp, Cp, Dp)
print ss_P
t = np.linspace(0, 3, 1000)
stepy = ct.step(ss_P, t)
#plt.plot(t,stepy)
#ct.impulse(ss_P)
ct.nyquist(ss_P)
#bode plot only implemented for SISO system.omg
#ct.bode(ss_P)
import control
import matplotlib.pyplot as plt
import sys
#if using termux
import subprocess
import shlex
#end if
s = control.TransferFunction.s
GH = 41 * (s + 4) / (s**2 * (s + 3)) #open looop transfer function G(s)H(s)
control.nyquist(GH)
plt.xlim(-2, 1)
plt.ylim(-0.5, 0.5)
plt.text(-1, 0, "(-1,0)")
plt.title('Zoomed in Nyquist Plot of G(s)H(s)')
plt.grid(True)
plt.xlabel('Re(s)')
plt.ylabel('Im(s)')
#if using termux
plt.savefig('./figs/ee18btech11041_1.pdf')
plt.savefig('ee18btech11041_1.eps')
subprocess.run(shlex.split("termux-open ./figs/ee18btech11041_1.pdf"))
#else
#plt.show()
from scipy import signal
from matplotlib import style
import control
from control import tf
# style.use('seaborn')
systems=[50,60,70,100]
plt.figure()
# mag=20*np.log(mag)
for i in systems:
sys=tf([i],[1,6,11,6])
gm,pm,wg,wp= control.margin(sys)
control.nyquist(sys, label=i)
plt.legend()
plt.show()
# plt.show()
