昨天我在这里发布了一个问题:使用Integrate.odeint()的ValueError和odepack.error我认为已经成功回答了。然而我后来注意到了一些事情。
该程序旨在对集成控制系统(特别是巡航控制)进行建模。当前它从速度 v0 开始,以该速度运行一段时间,然后启用巡航控制。此时,我们应该看到速度的变化(我们确实看到了),最终稳定在所需的速度 vr 上。事实并非如此。由于未知的原因,它达到了一些其他值,并且该值根据骑行的坡度而不同。无论初始速度如何,它仍然无法达到所需的速度
我尝试过不同的参数和变量,但无济于事。我认为问题在于控制器没有传递正确的当前速度,但是我不确定如何解决该问题。
如果您需要更多信息,请告诉我。如果我应该编辑上一个问题,请告诉我,我会这样做,提前抱歉。
这是我的代码:
import matplotlib.pylab as plt
import numpy as np
import scipy.integrate as integrate
##Parameters
kp = .5 #proportional gain
ki = .1 #integral gain
vr = 25 #desired velocity in m/s
Tm = 190 #Max Torque in Nm
wm = 420 #engine speed
B = 0.4 #Beta
an = 12 #at gear 4
p = 1.3 #air density
Cd = 0.32 #Drag coefficient
Cr = .01 #Coefficient of rolling friction
A = 2.4 #frontal area
##Variables
m = 18000.0 #weight
v0 = 20. #starting velocity
t = np.linspace(61, 500, 5000) #time
theta = np.radians(4) #Theta
def torque(v):
return Tm * (1 - B*(an*v/wm - 1)**2)
def vderivs(v, t):
v1 = an * controller(v, t) * torque(v)
v2 = m*Cr*np.sign(v)
v3 = 0.5*p*Cd*A*v**2
v4 = m*np.sin(theta)
vtot = v1-v2-v3-v4*(t>=200)
return vtot/m
def uderivs(v, t):
return vr - v
def controller(currentV, time):
z = integrate.odeint(uderivs, currentV, time)
return kp*(vr-currentV) + ki*z.squeeze()
def velocity(desired, theta, time):
return integrate.odeint(vderivs, desired, time)
t0l = [i for i in range(61)]
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
tf=t0l+[time for time in t]
plt.plot(tf, vf, 'k-', label=('V(0) = '+str(v0)))
v0=35.
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
plt.plot(tf, vf, 'b-', label=('V(0) = '+str(v0)))
v0=vr
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
plt.plot(tf, vf, 'g-', label=('V(0) = Vr'))
plt.axhline(y=vr, xmin=0, xmax=1000, color='r', label='Desired Velocity')
plt.legend(loc = "upper right")
plt.axis([0,500,18,36])
plt.show()
速度的第一次急剧变化是巡航控制启动时,第二次是骑行坡度发生变化时
你的猜测是正确的。目标系统和PI控制器是集成的,你不能把它分成两个odeint。我修改了你的代码,系统有两个状态变量:一个用于系统的速度,一个用于控制误差的积分:
import matplotlib.pylab as plt
import numpy as np
import scipy.integrate as integrate
##Parameters
kp = .5 #proportional gain
ki = .1 #integral gain
vr = 25 #desired velocity in m/s
Tm = 190 #Max Torque in Nm
wm = 420 #engine speed
B = 0.4 #Beta
an = 12 #at gear 4
p = 1.3 #air density
Cd = 0.32 #Drag coefficient
Cr = .01 #Coefficient of rolling friction
A = 2.4 #frontal area
##Variables
m = 18000.0 #weight
v0 = 20. #starting velocity
t = np.linspace(61, 500, 5000) #time
theta = np.radians(4) #Theta
def torque(v):
return Tm * (1 - B*(an*v/wm - 1)**2)
def vderivs(status, t):
v, int_err = status
err = vr - v
control = kp * err + ki * int_err
v1 = an * control * torque(v)
v2 = m*Cr*np.sign(v)
v3 = 0.5*p*Cd*A*v**2
v4 = m*np.sin(theta)
vtot = v1-v2-v3-v4*(t>=200)
return vtot/m, err
def velocity(desired, theta, time):
return integrate.odeint(vderivs, [desired, 0], time)[:, 0]
t0l = [i for i in range(61)]
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
tf=t0l+[time for time in t]
plt.plot(tf, vf, 'k-', label=('V(0) = '+str(v0)))
v0=35.
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
plt.plot(tf, vf, 'b-', label=('V(0) = '+str(v0)))
v0=vr
vf=[v0 for i in range(61)]+[v for v in velocity(v0,theta,t)]
plt.plot(tf, vf, 'g-', label=('V(0) = Vr'))
plt.axhline(y=vr, xmin=0, xmax=1000, color='r', label='Desired Velocity')
plt.legend(loc = "upper right")
plt.axis([0,500,18,36])
plt.show()
输出: