def plot_behavior(xset,kp,ki,kd,m,b,k,g=1,s=1, total_time=10, npoints=100):
dev = Device()
dev.m = m
dev.b = b
dev.k = k
dev.g = g
dev.s = s
cont = Controller()
cont.kp = kp
cont.ki = ki
cont.kd = kd
tt = np.linspace(0,total_time, npoints)
xx0 = np.zeros(tt.shape)
xx0[5:] = xset
xx = [0]
vv = [0]
aa = [0]
t0 = tt[0]
for t,x0 in zip(tt[1:],xx0[1:]):
cont.set_point = x0
a = cont(dev.x,t)
x,v = dev(a,t-t0)
aa.append(a)
xx.append(x)
vv.append(v)
t0 = t
fig,ax = pyplot.subplots(1,2,figsize=(10,3))
ptset, = ax[1].plot(tt, xx0, color='blue',label='set point')
ptcont, = ax[1].plot(tt, aa, color='red',label='control')
ptval, = ax[0].plot(tt, xx, color='green',label='actual')
ptvel, = ax[1].plot(tt, vv, color='magenta',label='velocity')
ax[0].margins(0,0.1)
ax[1].margins(0,0.1)
l = ax[1].legend((ptset,ptcont,ptval,ptvel), ('set point','control','actual','velocity'),
loc='best')
l.set_zorder(1)
return tt, xx0, aa, xx, vv
n = len(xx[len(xx)//2:]) # length of the signal
k = np.arange(n)
T = n/Fs
frq = k/T # two sides frequency range
frq = frq[range(n//2)] # one side frequency range
Y = np.fft.fft(xx[len(xx)//2:])/n # fft computing and normalization
Y = Y[range(n//2)]
fig, ax = plt.subplots()
ax.plot(frq,abs(Y),'r') # plotting the spectrum
ax.set_xlabel('Freq (Hz)')
ax.set_ylabel('|Y(freq)|')
ax.set_ylim(0,1.1*max(abs(Y[2:])))
cont = Controller(set_point=1)
cont.ziegler_nichols(ku=kp,tu=1/frq[2:][np.argmax(Y[2:])],control_type='no_overshoot')
print(cont.kp,cont.ki,cont.kd)
_=plot_behavior(xset=1, kp=cont.kp, ki=cont.ki, kd=cont.kd, m=1, b=10, k=20, g=1000, s=2, total_time=5, npoints=600)
# <codecell>
g,s = 300,1
x = np.linspace(-5*g,5*g,100)
fig,ax = pyplot.subplots(figsize=(10,10))
pt = ax.plot(x,g * (2/π) * np.arctan((s/g) * x))
ax.set_aspect('equal')
ax.grid(True)
