import numpy as np
import control
import matplotlib.pyplot as plt

# %% Generating transfer function of Pade approx:
T_delay = 5
n_pade = 10
(num_pade, den_pade) = control.pade(T_delay, n_pade)
H_pade = control.tf(num_pade, den_pade)

# %% Generating transfer function without time delay:
num = np.array([1])
den = np.array([10, 1])
H_without_delay = control.tf(num, den)

# %% Generating transfer function with time delay:
H_with_delay = control.series(H_pade, H_without_delay)

# %% Simulation of step response:
t = np.linspace(0, 40, 100)
(t, y) = control.step_response(H_with_delay, t)
plt.plot(t, y)
plt.xlabel('t [s]')
plt.grid()

# %% Generating pdf file of the plotting figure:
plt.savefig('pade_approx.pdf')