def plotgraphs(kc,ti,x,num,entries,t,tfinal,dt,SP,kcst,tist):
import numpy as np
import matplotlib.pyplot as plt
from operator import itemgetter
import pareto
# calulates the overshoot ratio
def overshoot(x,num,SP,entries,t):
tpr = np.zeros(num)
por = np.zeros(num)
for u in range(0,num):
if (x[:][u]== None):
por[u]= None
tpr[u] = None
else:
por[u] = ((np.max(x[:][u]))- SP)/SP
for g in range(0,entries):
if x[u][g] ==np.max(x[:][u]):
tpr[u] = t[g]
if por[u] < 0:
por[u] = np.NINF
tpr[u] = np.NINF
return {'por':por ,'tpr':tpr}
por2 = overshoot(x,num,SP,entries,t)
por = por2['por']
tpr = por2['tpr']
# calculates the risetime
def risetime(x,num,entries,SP,t):
tr = np.zeros(num)
for j in range(0,num):
if (np.isnan(x[j][:])).all()== True:
tr[j] = None
else:
for k in range(0, entries-1):
if np.sign(SP - x[j][k])!=np.sign(SP - x[j][k+1]):
if np.sign(SP - x[j][k])==0:
tr[j] = t[k]
else :
tr[j] = np.interp(SP,[x[j][k],x[j][k+1]],[t[k],t[k+1]])
break
return tr
tr= risetime(x,num,entries,SP,t)
SSoffset = ~np.isneginf(por)
UNSTABLE =~np.isnan(por)
# plots the graphs
goodpoints = ~(np.isnan(tr)| np.isnan(por)|np.isneginf(por))
idx = np.arange(0,num)
tr = tr[goodpoints]
por = por[goodpoints]
tpr = tpr[goodpoints]
idx = idx[goodpoints]
x = x[goodpoints]
zns = len(por)
p = pareto.domset([itemgetter(1), itemgetter(2)], zip(idx, por, tr))
front = p.data
idx, xd, yd = map(np.array, zip(*front))
sortidx = np.argsort(xd)
xd = xd[sortidx]
yd = yd[sortidx]
fig = plt.figure()
fig.set_facecolor('white')
font = {'family' : 'cambria',
'weight' : 'normal',
'size' : 14}
plt.matplotlib.rc('font', **font)
ax1 = fig.add_subplot(2,2,1)
linea = ax1.plot(kc[~UNSTABLE],ti[~UNSTABLE], 'w.')
lineb = ax1.plot(kcst,tist,'k-')
linee = ax1.plot(kc[~SSoffset],ti[~SSoffset],'g+')
line1, = ax1.plot(kc[goodpoints], ti[goodpoints], 'wo',picker = 5,)
linec = ax1.plot(kc[idx], ti[idx],'ro')
lined = ax1.plot(kc[num-2],ti[num-2],'ks') # Ziegler Nichos settings
lineco = ax1.plot(kc[num-1],ti[num-1],'gs') # Cohen coon settings
linetl = ax1.plot(kc[num-3],ti[num-3],'ms') # tyreas n Luyben settings
plt.xlabel(r'$K_C$',fontsize = 'large')
plt.ylabel(r'$\tau_I$',fontsize = 'large')
ax2= fig.add_subplot(2,2,2)
line2, =ax2.plot(por, tr, 'wo',picker = 5,)
line222=ax2.plot(xd, yd, 'ro-')
line22 = ax2.plot(por[zns-2],tr[zns-2],'ks')
linecc2 = ax2.plot(por[zns-1],tr[zns-1],'gs') # cohen coon settings
plt.setp((linea,lineb,linee,line1),linewidth = 2.0)
plt.figlegend((linea,lineb,linec,lined,lineco,linetl,linee,line1),('Unstable','Stabilty limit','Pareto points','Z&N settings','Cohen Coon','Tyreus & Luyben','S/S offset','Stable'),'upper right',borderaxespad=0.)
plt.axis([-0.2,1, 0,40])
plt.ylabel('risetime (s)',fontsize = 'large')
plt.xlabel('overshoot ratio',fontsize = 'large')
ax3 = fig.add_subplot(2,1,2)
plt.ylabel('x',fontsize = 12)
plt.xlabel('time (s)',fontsize = 12)
plt.axis([0,tfinal, 0,2])
ax3.text(0.02,0.5,'Click on the overshoot vs risetime plot to obtain the time response',fontsize = 13,color = 'red')
# graphical interaction
class timeresponse:
def __init__(self):
self.lastind = 0
self.selected, = ax2.plot([por[0]], [tr[0]], 'o', ms=12, alpha=0.4,
color='yellow', visible=False)
self.correspond, = ax1.plot([(kc[goodpoints])[0]],[(ti[goodpoints])[0]],'o',ms = 13,alpha = 0.5,color = 'yellow',visible= False)
def onpick(self,event):
if event.artist!=line2:
self.correspond.set_visible(False)
self.selected.set_visible(False)
return True
NW = len(event.ind)
if not NW: return True
x = event.mouseevent.xdata
y = event.mouseevent.ydata
radius = np.hypot(x-por[event.ind], y-tr[event.ind])
minind = radius.argmin()
pstn = event.ind[minind]
self.lastind = pstn
self.update()
def update(self):
if self.lastind is None: return
pstn = self.lastind
self.selected.set_visible(True)
self.selected.set_data(por[pstn], tr[pstn])
self.correspond.set_visible(True)
self.correspond.set_data([(kc[goodpoints])[pstn]],[(ti[goodpoints])[pstn]])
t = np.arange(0, tfinal, dt)
yt = x[pstn]
ax3.cla()
plt.ylabel('x',fontsize = 12)
plt.xlabel('time (s)',fontsize = 12)
plt.axis([0,tfinal, 0,2])
ax3.plot(t,yt,tpr[pstn],((por[pstn] + 1)*SP),'ro')
ax3.axhline(y=SP,color ='black',linestyle ='--')
rr = np.linspace(0,SP)
yy = [tr[pstn]]*len(rr)
ax3.plot(yy,rr,'k--')
fig.canvas.draw()
return True
time = timeresponse()
fig.canvas.mpl_connect('pick_event', time.onpick)
class kctiinteract(timeresponse):
def __init__(self):
self.l2 = 0
self.selectedtc, = ax1.plot([(kc[goodpoints])[0]],[(ti[goodpoints])[0]],'o',ms = 13,alpha = 0.5,color = 'orange',visible= False)
self.correspondtc,=ax2.plot([por[0]], [tr[0]], 'o', ms=12, alpha=0.4,
color='orange', visible=False)
def onpick(self,event):
if event.artist!=line1:
self.correspondtc.set_visible(False)
self.selectedtc.set_visible(False)
return True
NW2 = len(event.ind)
if not NW2: return True
x = event.mouseevent.xdata
y = event.mouseevent.ydata
r2 = np.hypot(x-(kc[goodpoints])[event.ind], y-(ti[goodpoints])[event.ind])
m2 = r2.argmin()
p2 = event.ind[m2]
self.l2 = p2
self.update()
def update(self):
if self.l2 is None: return
p2 = self.l2
self.selectedtc.set_visible(True)
self.selectedtc.set_data([(kc[goodpoints])[p2]],[(ti[goodpoints])[p2]])
self.correspondtc.set_visible(True)
self.correspondtc.set_data(por[p2], tr[p2])
t = np.arange(0, tfinal, dt)
yt = x[p2]
ax3.cla()
plt.ylabel('x')
plt.xlabel('time (s)')
plt.axis([0,tfinal, 0,2])
ax3.plot(t,yt,tpr[p2],((por[p2] + 1)*SP),'ro',linewidth = 2.0)
ax3.axhline(y=SP,color ='black',linestyle ='--')
rr = np.linspace(0,SP)
yy = [tr[p2]]*len(rr)
ax3.plot(yy,rr,'k--')
fig.canvas.draw()
return True
tim = kctiinteract()
fig.canvas.mpl_connect('pick_event', tim.onpick)
plt.show()
def plotgraphs(kc,ti,x,num,entries,t,tfinal,dt,SP):
por,tpr = obj.overshoot(t,x,num,entries,SP)
# calculates the risetime
tr= obj.risetime(t,x,num,entries,SP)
SSoffset = np.isneginf(por)
UNSTABLE = np.isnan(por)
ISE = obj.ISE(t,x,num,entries,SP)
goodpoints = ~(np.isnan(tr)| np.isnan(por)|np.isneginf(por))
idx = np.arange(0,num)
tr = tr[goodpoints]
por = por[goodpoints]
tpr = tpr[goodpoints]
ISE = ISE[goodpoints]
idx = idx[goodpoints]
x = x[goodpoints]
zns = len(por)
p = pareto.domset([itemgetter(1), itemgetter(2)], zip(idx, por, tr))
front = p.data
idx, xd, yd = map(np.array, zip(*front))
sortidx = np.argsort(xd)
xd = xd[sortidx]
yd = yd[sortidx]
fig = plt.figure()
fig.set_facecolor('white')
font = {'family' : 'cambria',
'weight' : 'normal',
'size' : 14}
plt.matplotlib.rc('font', **font)
#ax1
ax1 = fig.add_subplot(2,2,1)
linea = ax1.plot(kc[UNSTABLE],ti[UNSTABLE], 'r+') # adds ustables points
linee = ax1.plot(kc[SSoffset],ti[SSoffset],'g+')
line1, = ax1.plot(kc[goodpoints], ti[goodpoints], 'wo',picker = 5,) # adds good points
linec = ax1.plot(kc[idx], ti[idx],'bo') # from pareto.data
lined = ax1.plot(kc[num-2],ti[num-2],'ks') # Ziegler Nichos settings
lineco = ax1.plot(kc[num-1],ti[num-1],'gs') # Cohen coon settings
linetl = ax1.plot(kc[num-3],ti[num-3],'ms') # tyreas n Luyben settings
plt.xlabel(r'$K_C$',fontsize = 'large')
plt.ylabel(r'$\tau_I$',fontsize = 'large')
#ax2
ax2= fig.add_subplot(2,2,2)
line2, =ax2.plot(por, tr, 'wo',picker = 5,)
line222=ax2.plot(xd, yd, 'bo-')
line22 = ax2.plot(por[zns-2],tr[zns-2],'ks')
linecc2 = ax2.plot(por[zns-1],tr[zns-1],'gs') # cohen coon settings
plt.setp((linea,linee,line1),linewidth = 2.0)
plt.figlegend((linea,linec,lined,lineco,linetl,linee,line1),('Unstable''Pareto points','Z&N settings','Cohen Coon','Tyreus & Luyben','S/S offset','Stable'),'upper right',borderaxespad=0.)
plt.axis([-0.2,1, 0,40])
plt.ylabel('risetime (s)',fontsize = 'large')
plt.xlabel('overshoot ratio',fontsize = 'large')
#ax3
ax3 = fig.add_subplot(2,1,2)
plt.ylabel('x',fontsize = 12)
plt.xlabel('time (s)',fontsize = 12)
plt.axis([0,tfinal, 0,SP*2]) ###
ax3.text(0.02,SP,'Click on the overshoot vs risetime plot to obtain the time response',fontsize = 13,color = 'red')
# graphical interaction
class timeresponse:
def __init__(self):
self.lastind = 0
self.selected, = ax2.plot(None, None, 'o', ms=12, alpha=0.4,
color='yellow', visible=False)
self.correspond, = ax1.plot(None,None,'o',ms = 13,alpha = 0.5,color = 'yellow',visible= False)
def onpick(self,event):
if event.artist!=line2:
self.correspond.set_visible(False)
self.selected.set_visible(False)
return True
NW = len(event.ind)
if not NW: return True
x = event.mouseevent.xdata
y = event.mouseevent.ydata
radius = np.hypot(x-por[event.ind], y-tr[event.ind])
minind = radius.argmin()
pstn = event.ind[minind]
self.lastind = pstn
self.update()
def update(self):
if self.lastind is None: return
pstn = self.lastind
self.selected.set_visible(True)
self.selected.set_data(por[pstn], tr[pstn])
print self.correspond.set_visible(False)
print self.correspond.set_data([(kc[goodpoints])[pstn]],[(ti[goodpoints])[pstn]])
t = np.arange(0, tfinal, dt)
yt = x[pstn]
ax3.cla()
plt.ylabel('y',fontsize = 12)
plt.xlabel('time (s)',fontsize = 12)
# plt.axis([0,tfinal, 0,SP*2]) #####Change of response graph y-axis
ax3.plot(t,yt,tpr[pstn],((por[pstn] + 1)*SP),'bo')
ax3.axhline(y=SP,color ='black',linestyle ='--')
rr = np.linspace(0,SP)
yy = [tr[pstn]]*len(rr)
ax3.plot(yy,rr,'k--')
fig.canvas.draw()
return True
time = timeresponse()
fig.canvas.mpl_connect('pick_event', time.onpick)
class kctiinteract():
def __init__(self):
self.l2 = 0
self.selectedtc, = ax1.plot(None,None,'o',ms = 13,alpha = 0.5,color = 'orange',visible= False)
self.correspondtc,=ax2.plot(None, None, 'o', ms=12, alpha=0.4,
color='orange', visible=False)
def onpick(self,event):
if event.artist!=line1:
self.correspondtc.set_visible(False)
self.selectedtc.set_visible(False)
return True
NW2 = len(event.ind)
if not NW2: return True
x = event.mouseevent.xdata
y = event.mouseevent.ydata
r2 = np.hypot(x-(kc[goodpoints])[event.ind], y-(ti[goodpoints])[event.ind])
m2 = r2.argmin()
p2 = event.ind[m2]
self.l2 = p2
self.update()
def update(self):
if self.l2 is None: return
p2 = self.l2
self.selectedtc.set_visible(True)
self.selectedtc.set_data([(kc[goodpoints])[p2]],[(ti[goodpoints])[p2]])
print self.correspondtc.set_visible(True)
print self.correspondtc.set_data(por[p2], tr[p2])
t = np.arange(0, tfinal, dt)
yt = x[p2]
ax3.cla()
plt.ylabel('x')
plt.xlabel('time (s)')
# plt.axis([0,tfinal, 0,SP*2]) #######
ax3.plot(t,yt,tpr[p2],((por[p2] + 1)*SP),'bo',linewidth = 2.0)
ax3.axhline(y=SP,color ='black',linestyle ='--')
rr = np.linspace(0,SP) ##########
yy = [tr[p2]]*len(rr)
ax3.plot(yy,rr,'k--')
fig.canvas.draw()
return True
tim = kctiinteract()
fig.canvas.mpl_connect('pick_event', tim.onpick)
plt.show()
tr = np.zeros(N)
aa = np.random.rand(N,2)
kc = 10*aa[:, 0]
ti = 10*aa[:, 1]
for i in range (0, N):
x[i,:], tr[i], por[i] = outp(kc[i], ti[i])
goodpoints = ~(np.isnan(tr) | np.isnan(por))
idx = np.arange(0, N)
tr = tr[goodpoints]
por = por[goodpoints]
idx = idx[goodpoints]
x = x[goodpoints]
p = pareto.domset([itemgetter(1), itemgetter(2)], zip(idx, por, tr))
front = p.data
idx, xd, yd = map(np.array, zip(*front))
sortidx = np.argsort(xd)
xd = xd[sortidx]
yd = yd[sortidx]
fig = plt.figure()
#plt.hold(True)
ax1 = fig.add_subplot(2,2,1)
line = ax1.plot(kc[~goodpoints], ti[~goodpoints], 'y.',
kc[idx], ti[idx], 'ro')
line1, = ax1.plot(kc[goodpoints], ti[goodpoints], 'b.')
kcst = np.linspace(1.3,10)
tauist = 4*kp*kcst/((1 + kp*kcst)**2/tau)
ax1.plot(kcst,tauist)