Merge branch 'simulation' into devel

analysis/Simulation/TranslationalMass.py

@@ -1,6 +1,8 @@
 import os
 import matplotlib.pyplot as plt
 from control.matlab import *
+import numpy as np
+
 
 # Input: Current (A)
 # Output: Torque (Nm)
@@ -26,10 +28,35 @@ def mass(m, b, k):
 def pulley(r):
     return tf(r, 1)
 
-sys = series(motor(2.5), pulley(0.015), mass(0.10, 0, 0))
+# Make s a transfer function s/1
+s = tf('s')
+print(s)
+
+# build a new transfer function using our variable s as a handy placeholder
+sys = 1 / (s*s + s + 1)
+print(sys)
+
+# Hit the system with a step command
+yout, T = step(sys)
+plt.plot(T, yout)
+
+# convert our continuous time model to discrete time via Tustin at 0.01s timestep
+sysd = c2d(tf(sys), 0.01, method='tustin')
+print(sysd)
+
+# Hit the discrete system with a step command, and sample it at 0.01 timestep from 0 to 14 seconds
+yout, T = step(sysd, np.arange(0, 14, 0.01))
+plt.plot(T, yout)
+plt.legend(['Continuous', 'Discrete'])
+
+# Build a system based on the series connection of the motor, pulley, and mass "blocks"
+sys = series(motor(2.5), pulley(0.015), mass(0.10, .1, .1))
+print(tf(sys))
+
+# Step our series system, returning y (outputs) and x (states)
 yout, T, xout = step(sys, return_x=True)
-print(yout)
-# plt.plot(T, yout)
+plt.figure()
+plt.plot(T, yout)
 plt.plot(T, xout)
-plt.legend(['Displacement', 'Velocity'])
+plt.legend(['Displacement', r'$x$', r'$\dot{x}$'])
 plt.show()