import numpy as np
from scipy.integrate import odeint
import matplotlib.pyplot as plt
# function that returns dz/dt
def model(z,t,u):
x = z[0]
y = z[1]
dxdt = (-x + u)/2.0
dydt = (-y + x)/5.0
dzdt = [dxdt,dydt]
return dzdt
# initial condition
z0 = [0,0]
# number of time points
n = 401
# time points
t = np.linspace(0,40,n)
# step input
u = np.zeros(n)
# change to 2.0 at time = 5.0
u[51:] = 2.0
# store solution
x = np.empty_like(t)
y = np.empty_like(t)
# record initial conditions
x[0] = z0[0]
y[0] = z0[1]
# solve ODE
for i in range(1,n):
# span for next time step
tspan = [t[i-1],t[i]]
# solve for next step
z = odeint(model,z0,tspan,args=(u[i],))
# store solution for plotting
x[i] = z[1][0]
y[i] = z[1][1]
# next initial condition
z0 = z[1]
# plot results
plt.plot(t,u,'g:',label='u(t)')
plt.plot(t,x,'b-',label='x(t)')
plt.plot(t,y,'r--',label='y(t)')
plt.ylabel('values')
plt.xlabel('time')
plt.legend(loc='best')
plt.show()
