In [1]:

    

import numpy as np
import sympy as sy
import matplotlib.pyplot as plt
import control.matlab as cm
%matplotlib inline


    

In [2]:

    

np.log(2)/2.0


    

    
Out[2]:





0.34657359027997264

In [10]:

    

Hc = cm.tf([1],[1, 0], np.log(2)/2.0)
Hc


    

    
Out[10]:





1
-
z

dt = 0.34657359028

In [9]:

    

Td = np.log(2)/2*np.arange(20)
(yd,td) = cm.step(Hc, Td)
plt.plot(td,yd[0], '*')
plt.xlim([0,8])
plt.ylim([0,1.4])
plt.savefig("step-dead-beat.pdf")


    

In [13]:

    

b = (2-np.sqrt(2))/2.0
a1 = -(3*np.sqrt(2)-2)/2.0
a2 = (2*np.sqrt(2)-2)/2.0
Hc2 = cm.tf([2*b, -b], [1, a1, a2], np.log(2)/4.0)
Td2 = np.log(2)/4*np.arange(40)
(yd2,td2) = cm.step(Hc2, Td2)
plt.plot(td,yd[0], '*')
plt.plot(td2,yd2[0], 'r*')
plt.xlim([-0.2,8])
plt.ylim([-0.2,1.4])
plt.savefig("step-half-sampling-time.pdf")


    

In [19]:

    

cm.feedback?


    

In [41]:

    

H = cm.tf([0.5],[1, -0.5], np.log(2)/2.0)
F = 1.05*cm.tf([2, -1],[1, -1], np.log(2)/2.0)
FH = F*H
Hcl = cm.feedback(FH)
print Hcl
Hcu = cm.feedback(F, H)
print Hcu


    

    




   1.05 z - 0.525
--------------------
z^2 - 0.45 z - 0.025

dt = 0.34657359028


2.1 z^2 - 2.1 z + 0.525
-----------------------
  z^2 - 0.45 z - 0.025

dt = 0.34657359028

In [42]:

    

Td = np.log(2)/2*np.arange(20)
(yd,td) = cm.step(Hcl, Td)
(ud,td) = cm.step(Hcu, Td)
plt.plot(td,yd[0], '*')
plt.plot(td,ud[0], 'r*')
plt.xlim([-0.2,8])
plt.ylim([-0.2,3.1])
plt.savefig("step-dead-beat.pdf")


    

In [22]:

    

ud


    

    
Out[22]:





array([[ 2.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,
         1.,  1.,  1.,  1.,  1.,  1.,  1.]])

In [ ]: