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

gain=2
tc=20
dt=5
bias=13.5

Kp = 1
Ki = 0.05
Kd = 1.5

# First-order plus deadtime system
num=np.array([gain])
den=np.array([tc,1])
#Add dead time
n_pade = 10
(num_pade,den_pade) = control.pade(dt,n_pade)
H_pade=control.tf(num_pade,den_pade)
H_noDelay = control.tf(num,den)
H = control.series(H_pade,H_noDelay)
# PID controller
C = control.tf([Kd, Kp, Ki], [1, 0])
# First-order plus deadtime system and PID Controller
G = control.feedback(H*C, 1)
t = np.linspace(0, 100, 100)
t, pv = control.step_response(G, t)

sp=np.ones(len(pv))

# Plot the results
plt.plot(t, sp, label='SP')
plt.plot(t, pv, label='PV')
plt.legend()
plt.show()