Assignment 2 5.a

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

# PID parameters Kp, Ki, Kd
Kp = 4.9
Ki = 5.1
Kd = 2.5

##################################################################################
Ts = 0.01

Tf = 15
t = np.arange(0, Tf, Ts)
sG = cn.tf([1,1,0], [1,2,3,2])
controller = cn.tf([Kd, Kp, Ki], [1,0,0])  # GC is system in series with controller
clsys = cn.feedback(cn.series(sG,controller),1)        # GC/(1+GC) you can use this expression instead of cn.feedback()
y, T = cn.step(clsys, t)
info = cn.stepinfo(clsys,t)
# Algorithms for computing Rise time, Settling time, Maximum Overshoot and steady state Error
ess = 1-info["SteadyStateValue"]
tr = info["RiseTime"]
ts = info["SettlingTime"]
mp = info["Overshoot"]/100
tp = info["PeakTime"]

plt.plot(T,y, label=f'Steady state error: {np.absolute(ess):.2f}')
plt.scatter(tp,1+mp,label=f'Peak time = {tp} sec and Maximum overshoot = {mp:.3f}')
plt.scatter(ts,1,label=f'Settling time = {ts:.3f} sec')
plt.scatter(tr,info["SettlingMin"],label=f'Rising time = {tr:.3f} sec')
plt.plot(T, np.ones(T.size), "--", label = "Reference")
plt.xlabel("t")
plt.ylabel("c(t)")
plt.tight_layout()

plt.legend()
plt.show()