In [25]:

    

import numpy as np
import sympy as sy
import control.matlab as cm


    

In [18]:

    

s,z = sy.symbols('s,z', real=False)
h,t = sy.symbols('h,t', real=True, positive=True)


    

In [9]:

    

G = (s+1)/(s+2)
Ya = sy.apart(G/s**2)


    

In [15]:

    

ya = sy.inverse_laplace_transform(Ya, s, t)
print sy.pretty_print(ya)
print sy.latex(ya)


    

    




         -2⋅t
t   1   ℯ    
─ + ─ - ─────
2   4     4  
None
\frac{t}{2} + \frac{1}{4} - \frac{1}{4 e^{2 t}}

In [19]:

    

num= 2*h*(z-sy.exp(-2*h)) + (z-1)*(z-sy.exp(-2*h)) - (z-1)**2


    

In [24]:

    

print sy.latex(sy.collect(sy.simplify(num), z))
print sy.pretty_print(sy.collect(sy.simplify(num), z))


    

    




- \frac{2 h}{e^{2 h}} + z \left(2 h + 1 - e^{- 2 h}\right) - 1 + e^{- 2 h}
       -2⋅h     ⎛           -2⋅h⎞        -2⋅h
- 2⋅h⋅ℯ     + z⋅⎝2⋅h + 1 - ℯ    ⎠ - 1 + ℯ    
None

In [26]:

    

cm.c2d??


    

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