Add 2 example. 2nd Order system

Author: rssalessio

examples/1_example.py

@@ -34,7 +34,7 @@ def generateNoise(t):
 
 #PI Controller
 base = [ctl.tf([1], [1],t_step),
-		ctl.tf([1, 0], [1, -1],t_step)]
+	ctl.tf([1, 0], [1, -1],t_step)]
 
 #Experiment filter
 omega = 2*np.pi*0.1
@@ -49,23 +49,32 @@ def generateNoise(t):
 L = C*sys
 L = L/(1+L)
 
+L = L.minreal()
+#this is due to a bug in the control library
+L = ctl.tf(L.num, L.den, t_step)
+
 print "Theta:", theta
 
 #Analysis
 yr,t = ctl.step(refModel, t)
 yc,t = ctl.step(L, t)
+ys,t = ctl.step(sys, t)
+
 
-fig, ax = plt.subplots(3, sharex=True)
+fig, ax = plt.subplots(4, sharex=True)
 ax[0].plot(t,yr[0],label='Ref System')
 ax[0].plot(t,yc[0], label='CL System')
 ax[0].set_title('Systems response')
 ax[0].grid(True)
-ax[1].plot(t,y[0])
+ax[1].plot(t,ys[0], label='OL System')
+ax[1].set_title('OL Systems response')
 ax[1].grid(True)
-ax[1].set_title('Experiment data')
-ax[2].plot(t,r)
+ax[2].plot(t,y[0])
 ax[2].grid(True)
-ax[2].set_title('Virtual Reference')
+ax[2].set_title('Experiment data')
+ax[3].plot(t,r)
+ax[3].grid(True)
+ax[3].set_title('Virtual Reference')
 
 # Now add the legend with some customizations.
 legend = ax[0].legend(loc='lower right', shadow=True)

examples/2_example.png

@@ -0,0 +1,93 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import control as ctl
+from vrft import *
+
+def generateNoise(t):
+	omega = 2*np.pi*100
+	xi = 0.9
+	noise =  np.random.normal(0,0.1,t.size)
+	# Second order system
+	yn,t,x = ctl.lsim(ctl.tf([omega**2], [1, 2*xi*omega, omega**2]), \
+		noise, t)
+	return yn
+
+#Generate time and u(t) signals
+t_start = 0
+t_end = 10
+t_step = 1e-2
+t = np.arange(t_start, t_end, t_step)
+u = np.ones(len(t)).tolist()
+u[200:400] = np.zeros(200)
+u[600:800] = np.zeros(200)
+
+#Experiment
+num = [0.5]
+den = [1, -1.6, 0.8]
+sys = ctl.tf(num, den, t_step)
+y,t,x= ctl.lsim(sys, u, t)
+y += generateNoise(t)
+data = vrft.iddata(y[0],u,t_step,[0])
+
+#Reference Model
+refModel = ctl.tf([0.2], [1, -0.8], t_step)
+
+#PI Controller
+base = [ctl.tf([1], [1],t_step),
+	ctl.tf([1, 0], [1, -1],t_step),
+	ctl.tf([1, -1], [1, 0],t_step)]
+
+#Experiment filter
+omega = 2*np.pi*1
+L =  ctl.tf([1], [1/omega, 1])
+L =  ctl.sample_system(L, 0.01)
+
+#VRFT
+C, theta, r = vrft.vrftAlgorithm(data, refModel, base, L)
+
+#Obtained controller
+print "Controller:", C
+L = C*sys
+L = L/(1+L)
+
+L = L.minreal()
+#this is due to a bug in the control library
+L = ctl.tf(L.num, L.den, t_step)
+
+print "Theta:", theta
+
+#Analysis
+yr,t = ctl.step(refModel, t)
+yc,t = ctl.step(L, t)
+ys,t = ctl.step(sys, t)
+
+
+fig, ax = plt.subplots(4, sharex=True)
+ax[0].plot(t,yr[0],label='Ref System')
+ax[0].plot(t,yc[0], label='CL System')
+ax[0].set_title('Systems response')
+ax[0].grid(True)
+ax[1].plot(t,ys[0], label='OL System')
+ax[1].set_title('OL Systems response')
+ax[1].grid(True)
+ax[2].plot(t,y[0])
+ax[2].grid(True)
+ax[2].set_title('Experiment data')
+ax[3].plot(t,r)
+ax[3].grid(True)
+ax[3].set_title('Virtual Reference')
+
+# Now add the legend with some customizations.
+legend = ax[0].legend(loc='lower right', shadow=True)
+
+# The frame is matplotlib.patches.Rectangle instance surrounding the legend.
+frame = legend.get_frame()
+frame.set_facecolor('0.90')
+
+# Set the fontsize
+for label in legend.get_texts():
+    label.set_fontsize('large')
+
+for label in legend.get_lines():
+    label.set_linewidth(1.5)  # the legend line width
+plt.show()