import numpy as np
from gekko import GEKKO
import matplotlib.pyplot as plt

m = GEKKO()
m.time = np.linspace(0,20,41)

#constants
mass = 500

#Parameters
b = m.Param(value=50)
K = m.Param(value=0.8)

#Manipulated variable
p = m.MV(value=0, lb=0, ub=100)

#Controlled Variable
v = m.CV(value=0)

m.Equation(mass*v.dt() == -v*b + K*b*p)

m.options.IMODE = 6 #control

#MV tuning
p.STATUS = 1 #allow optimizer to change
p.DCOST = 0.1 #smooth out gas pedal movement
p.DMAX = 20 #slow down change of gas pedal

#CV tuning
#setpoint
v.STATUS = 1 #add the SP to the objective
m.options.CV_TYPE = 2 #L2 norm
v.SP = 40 #set point
v.TR_INIT = 1 #setpoint trajectory
v.TAU = 5 #time constant of setpoint trajectory

#%% Solve

m.solve()

#%% Plot solution
plt.figure()
plt.subplot(2,1,1)
plt.plot(m.time,p.value,'b-',lw=2)
plt.ylabel('gas')
plt.subplot(2,1,2)
plt.plot(m.time,v.value,'r--',lw=2)
plt.ylabel('velocity')
plt.xlabel('time')
plt.show()