Graphics - PTN Encirclement-checkpoint



In [3]:
import numpy as np
import control as cn
import Algorithms as alg
import matplotlib.pyplot as plt
%matplotlib
from Algorithms import TUBScolorscale,cm2in

MSC = lambda MS, color: plt.Circle((-1 ,0),1/MS, color =color, alpha=0.4)
MTC = lambda MT, color: plt.Circle((-MT**2/(MT**2 - 1),0),MT/(MT**2 -1), color =color, alpha = 0.4)
MCC = lambda M : plt.Circle((-(2*M**2-2*M+1)/(2*M*(M-1)),0), (2*M-1)/(2*M*(M-1)), color = 'b', fill = None,linestyle = 'dashed', alpha = 0.4)
MC = lambda MS,MT,color: plt.Circle((-(MS*(2*MT-1)-MT+1)/(2*MS*(MT-1)),0),(MS+MT-1)/(2*MS*(MT-1)), color =color, alpha = 0.4)


Using matplotlib backend: Qt5Agg

In [9]:
# Matplotlib plot
plt.rcParams['svg.fonttype'] = 'none'
plt.style.use('seaborn-whitegrid')

# Make a system with TSum = 100 and T = TSum/order
TSum = 100.
plt.clf()
fig, ax = plt.subplots(3,3,figsize=(10,10))
fig2, ax2 = plt.subplots(1,figsize=(10,10))
ax2.cla()
row = 0
col = 0
for order in range(1,10):
    # Get the current time constant
    T = TSum/order
    print(T)
    # Make a transfer function
    G = cn.tf(1,[T,1])
    G = 5*G**order
    # Step experiment
    y,t = cn.step(G)
    u = np.ones_like(t)
    # FOTD identification
    k,t,l = alg.Integral_Identification(y,u,t)
    # Make a controller
    c, b = alg.AMIGO_Tune(k,t,l)
    KY = cn.tf(c[0],1)+cn.tf(c[1],[1,0])
    KR = cn.tf(c[0],1)+cn.tf(c[1],[1,0])
    # Open Loop
    OL = G*KR
    # Compute the sensitivity
    S = 1/(1+G*KY)
    # Complementary
    T = G*KR/(1+G*KY)
    # Compute the Open Loop Nyquist Plot
    real,imag, w = cn.nyquist(OL, np.logspace(-5,5,10000))
    ax[row,col].cla()
    ax[row,col].plot(real,imag)
    # Compute the maximum Sensitivity
    mag, phase, freq = cn.freqresp(S, np.logspace(-5,5,10000))
    MS = np.max(mag)
    # Compute the maximum Complementary Sensitivity
    mag, phase, freq = cn.freqresp(T,  np.logspace(-5,5,10000))
    MT = np.max(mag)
    print(order,MS,MT)
    # Compute the circles
    ax[row,col].add_artist(MC(MS,MT,TUBScolorscale[0]))
    ax[row,col].add_artist(MTC(MT, 'w'))
    ax[row,col].add_artist(MSC(MS, 'w'))
    ax[row,col].add_artist(MSC(MS, TUBScolorscale[1]))
    ax[row,col].add_artist(MTC(MT, TUBScolorscale[3]))
    ax[row,col].add_artist(MCC(1.4))
    ax[row,col].plot(-1,0,'r+')
    ax[row,col].set_xlim(-3,3)
    ax[row,col].set_ylim(-3,3)
    ax[row,col].set_title('Order '+str(order))
    # Second plot
    ax2.plot(-1,0,'r+')
    ax2.add_artist(MSC(1.4,'r'))
    ax2.plot(real,imag,color=TUBScolorscale[order])
    ax2.set_xlim(-3,3)
    ax2.set_ylim(-3,3)
    if order%3 != 0:
        row = row
        col = col+1
    else:
        row = row+1
        col = 0
plt.show()


10.0
(1, 0.99999999999987876, 0.9999999952484715)
5.0
(2, 1.1831182291247999, 0.99999999607340095)
3.33333333333
(3, 1.2390999905130877, 0.99999999332077605)
2.5
(4, 1.3276894201485749, 0.99999999617449231)
2.0
(5, 1.4901804877001028, 0.99999999978944931)
1.66666666667
(6, 1.8162137221596941, 1.1747089647633286)
1.42857142857
(7, 2.6567128355175318, 1.9455865730105666)
1.25
(8, 8.597201301871193, 7.8411264231910343)
1.11111111111
(9, 4.2280569556118461, 5.0151373866240485)

In [15]:
t,y = cn.step_response(T)
plt.clf()
plt.plot(t,y)
plt.show()



In [54]:
# Get the circles
MS = np.max(abs(re_S+1j*im_S))
MT = np.max(abs(re_T+1j*im_T))
M = 1.4
plt.clf
msc = plt.Circle((-1,0),1/MS, color = 'r', alpha = 0.4)
mtc = plt.Circle((-MT**2/(MT**2-1),0), MT/(MT**2-1), color = 'b', alpha = 0.4)
mc = plt.Circle((-(2*M**2-2*M+1)/(2*M*(M-1)),0),(2*M-1)/(2*M*(M-1)),color = 'g', alpha = 0.4)
mcc = plt.Circle((-(MS*(2*MT-1)-MT+1)/(2*MS*(MT-1)) ,0),(MS+MT-1)/(2*MS*(MT-1)), color = None, alpha=0.4)
fig, ax = plt.subplots(1,figsize = (10,10))
plt.scatter(-1,0)
plt.plot(re_CL,im_CL)
ax.add_artist(msc)
ax.add_artist(mtc)
#ax.add_artist(mc)
#ax.add_artist(mcc)
ax.set_xlim(-3,3)
ax.set_ylim(-3,3)
plt.show()



In [11]:
G = cn.tf(1,[1,1])
c, b = alg.AMIGO_Tune(1,1,0)
KY = cn.tf(c[0],1)+cn.tf(c[1],[1,0])
KR = cn.tf(c[0],1)+cn.tf(c[1],[1,0])
CL = G*KR/(1+G*KY)
y,t = cn.step(CL)

In [12]:
plt.plot(t,y)
plt.show()

In [ ]: