139 lines
3.7 KiB
Python
Executable File
139 lines
3.7 KiB
Python
Executable File
#!/usr/bin/env python
|
|
# *-----------------------------------------------------------------------*
|
|
# | |
|
|
# | Copyright (c) 2019 by Paul Scherrer Institute (http://www.psi.ch) |
|
|
# | |
|
|
# | Author Thierry Zamofing (thierry.zamofing@psi.ch) |
|
|
# *-----------------------------------------------------------------------*
|
|
'''
|
|
Trajectory comparison:
|
|
pvt: position velocity time
|
|
p0t: position velocity=0 time
|
|
ift: inverse fourier transformation
|
|
|
|
-> look at trajectory and frequency components
|
|
'''
|
|
import numpy as np
|
|
import matplotlib as mpl
|
|
import matplotlib.pyplot as plt
|
|
|
|
def gen_pvt(p,v,t,ts):
|
|
'''generates a pvt motion
|
|
p: position array
|
|
v: velocity array
|
|
t: time array
|
|
ts: servo cycle time
|
|
!!! it is assumed, that the time intervals are constant !!!
|
|
'''
|
|
return
|
|
pvt=np.ndarray(len(tt))*0
|
|
t[-1]/ts
|
|
|
|
tt1=np.arange(0,t[1]-t[0],ts)
|
|
for i in range(len(t)-1):
|
|
d=p[i]
|
|
c=v[i]
|
|
a=(-2*(p[i+1]-p[i]-v[i]*w)+w*(v[i+1]-v[i]))/w**3
|
|
b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
|
|
pvt[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d
|
|
|
|
return pvt
|
|
|
|
w=40. # ms step between samples
|
|
ts=.2 # sampling time
|
|
n=int(w/ts)# servo cycle between samples
|
|
k=8 #number of unique samples
|
|
|
|
t = np.arange(0, w*(k+1), w) #time array of trajectory
|
|
|
|
#p=3.*np.cos(t)+4. #position array of trajectory
|
|
np.random.seed(10)
|
|
p=np.random.random(k+1)*4. #position array of trajectory
|
|
#p=3.*np.sin(1.3+2.*t/(w*k)*2.*np.pi)+10. #position array of trajectory
|
|
#p+=np.cos(1.5*t/(w*k)*2.*np.pi) #position array of trajectory
|
|
|
|
|
|
p[-1]=p[0] # put the first position at the end
|
|
|
|
tt = np.arange(t[0],t[-1], ts) #time array of servo cycles
|
|
ax=plt.gca()
|
|
ax.xaxis.set_ticks(t)
|
|
markerline, stemlines, baseline = ax.stem(t, p, '-')
|
|
|
|
|
|
#best trajectory with lowest frequency
|
|
p_iftf=np.fft.fft(p[:-1])
|
|
ft=np.hstack((p_iftf[:k/2],np.zeros((n-1)*k),p_iftf[k/2:]))
|
|
pp_ift=np.fft.ifft(ft)*n
|
|
|
|
ax.plot(tt,pp_ift,'-b',label='ift')
|
|
|
|
#plt.figure()
|
|
#ax=plt.gca()
|
|
#ax.xaxis.set_ticks(x)
|
|
#markerline, stemlines, baseline = ax.stem(x, y, '-')
|
|
|
|
#PVT move
|
|
p2=np.hstack((p[-2],p,p[1]))
|
|
|
|
v=(p2[2:]-p2[:-2])/(w*2)
|
|
|
|
gen_pvt(p,v,t,ts)
|
|
|
|
|
|
pp_pvt=np.ndarray(len(tt))*0
|
|
tt1=tt[:n]
|
|
for i in range(len(t)-1):
|
|
d=p[i]
|
|
c=v[i]
|
|
a=( -2*(p[i+1]-p[i]-v[i]*w)+ w*(v[i+1]-v[i]))/w**3
|
|
b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
|
|
pp_pvt[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d
|
|
|
|
ax.plot(tt,pp_pvt,'-g',label='pvt')
|
|
|
|
#PVT move with stop
|
|
v*=0
|
|
pp_p0t=np.ndarray(len(tt))*0
|
|
for i in range(len(t)-1):
|
|
d=p[i]
|
|
c=v[i]
|
|
a=( -2*(p[i+1]-p[i]-v[i]*w)+ w*(v[i+1]-v[i]))/w**3
|
|
b=(3*w*(p[i+1]-p[i]-v[i]*w)-w**2*(v[i+1]-v[i]))/w**3
|
|
pp_p0t[i*n:(i+1)*n]=a*tt1**3+b*tt1**2+c*tt1+d
|
|
|
|
ax.plot(tt,pp_p0t,'-r',label='p0t')
|
|
|
|
ax.legend(loc='best')
|
|
plt.show(block=False)
|
|
|
|
|
|
fig=plt.figure()
|
|
ax=fig.add_subplot(1,1,1)#ax=plt.gca()
|
|
|
|
#normalize with l -> value of k means amplitude of k at a given frequency
|
|
pp_iftf=np.fft.rfft(pp_ift)/(2*n)
|
|
pp_pvtf=np.fft.rfft(pp_pvt)/(2*n)
|
|
pp_p0tf=np.fft.rfft(pp_p0t)/(2*n)
|
|
|
|
f=np.fft.rfftfreq(pp_ift.shape[0], d=ts*1E-3)
|
|
f=f[1:] #remove dc value frequency
|
|
|
|
mag=abs(pp_iftf[1:])#; mag=20*np.log10(abs(mag))
|
|
ax.semilogx(f,mag,'-b',label='ift') # Bode magnitude plot
|
|
mag=abs(pp_pvtf[1:])#; mag=20*np.log10(abs(mag))
|
|
ax.semilogx(f,mag,'-g',label='pvt') # Bode magnitude plot
|
|
mag=abs(pp_p0tf[1:])#; mag=20*np.log10(abs(mag))
|
|
ax.semilogx(f,mag,'-r',label='p0t') # Bode magnitude plot
|
|
#ax.yaxis.set_label_text('dB ampl')
|
|
ax.yaxis.set_label_text('ampl')
|
|
ax.xaxis.set_label_text('frequency [Hz]')
|
|
plt.grid(True)
|
|
|
|
ax.legend(loc='best')
|
|
plt.show(block=False)
|
|
plt.show()
|
|
|
|
|
|
|