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


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


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


```python
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}}



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


```python
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



```python
cm.c2d??
```


```python

```

4d6cbf22ea907aef6be191d827e2414a09cfbfd6
ipynb
Jupyter Notebook
approximating-cont-controller/notebooks/L8-spring16-ramp-invariance.ipynb
kjartan-at-tec/mr2007-computerized-control
16e35f5007f53870eaf344eea1165507505ab4aa
MIT
2020-11-07T05:20:37.000Z
2020-12-22T09:46:13.000Z
approximating-cont-controller/notebooks/L8-spring16-ramp-invariance.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2020-06-12T20:44:41.000Z
2020-06-12T20:49:00.000Z
approximating-cont-controller/notebooks/L8-spring16-ramp-invariance.ipynb
alfkjartan/control-computarizado
5b9a3ae67602d131adf0b306f3ffce7a4914bf8e
MIT
2019-09-25T20:02:23.000Z
2019-09-25T20:02:23.000Z
Qwen/Qwen-72B
1. YES
2. YES