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

# %% Generating a z-transfer function of a time delay:

Ts = 0.1
Td = 5
nd = int(Td/Ts)
denom_tf = np.append([1], np.zeros(nd))
H_delay = control.tf([1], denom_tf, Ts)

# %% Displaying the z-transfer function:

print('H_delay(z) =', H_delay)

# %% Sim of step response of time delay transfer function:

t = np.arange(0, 10+Ts, Ts)
(t, y) = control.step_response(H_delay, t)
y = y[0,:] # Turning 2D array into 1D array for plotting
plt.plot(t, y)
plt.xlabel('t [s]')
plt.grid()

# %% Generating pdf file of the plotting figure:

plt.savefig('step_response_hz_time_delay.pdf')