import scipy.signal as sig
import matplotlib.pyplot as plt
import numpy as np

# simple first order step response simulation
# www.halvorsen.blog/documents/programming/python/resources/powerpoints/State Space Models with Python.pdf

# simulation Parameters

x0 = [0, 0]
start = 0
stop = 30
step = 1

t = np.arange(start,stop,step)
K = 3
T = 4

# state-space Model
A = [[-1/T, 0], [0, 0]]
B = [[K/T], [0]]
C = [[1, 0]]
D = 0
sys = sig.StateSpace(A, B, C, D)

# step Response
t, y = sig.step(sys, x0, t)

# plotting
plt.plot(t, y)
plt.title("Step Response")
plt.xlabel("t")
plt.ylabel("y")
plt.grid()
plt.show()