Merge branch 'austin/claw' into claw
diff --git a/frc971/control_loops/python/claw.py b/frc971/control_loops/python/claw.py
index 09718e5..b0767fb 100755
--- a/frc971/control_loops/python/claw.py
+++ b/frc971/control_loops/python/claw.py
@@ -13,15 +13,16 @@
     self.stall_torque = 2.42
     # Stall Current in Amps
     self.stall_current = 133
-    # Free Speed in RPM, pulled from drivetrain
-    self.free_speed = 4650.0
+    # Free Speed in RPM
+    self.free_speed = 5500.0
     # Free Current in Amps
     self.free_current = 2.7
     # Moment of inertia of the claw in kg m^2
-    # approzimately 0.76 (without ball) in CAD
-    self.J = 0.76
+    # measured from CAD
+    self.J_top = 0.3
+    self.J_bottom = 0.9
     # Resistance of the motor
-    self.R = 12.0 / self.stall_current + 0.024 + .003
+    self.R = 12.0 / self.stall_current
     # Motor velocity constant
     self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) /
                (13.5 - self.R * self.free_current))
@@ -32,25 +33,58 @@
     # Control loop time step
     self.dt = 0.01
 
-    # State is [bottom position, top - bottom position,
-    #           bottom velocity, top - bottom velocity]
-    # Input is [bottom power, top power]
-    # Motor time constant.
-    self.motor_timeconstant = self.Kt / self.Kv / (self.J * self.G * self.G * self.R)
+    # State is [bottom position, bottom velocity, top - bottom position,
+    #           top - bottom velocity]
+    # Input is [bottom power, top power - bottom power * J_top / J_bottom]
+    # Motor time constants. difference_bottom refers to the constant for how the
+    # bottom velocity affects the difference of the top and bottom velocities.
+    self.common_motor_constant = -self.Kt / self.Kv / (self.G * self.G * self.R)
+    self.bottom_bottom = self.common_motor_constant / self.J_bottom
+    self.difference_bottom = -self.common_motor_constant * (1 / self.J_bottom
+                                                        - 1 / self.J_top)
+    self.difference_difference = self.common_motor_constant / self.J_top
     # State feedback matrices
+
     self.A_continuous = numpy.matrix(
         [[0, 0, 1, 0],
          [0, 0, 0, 1],
-         [0, 0, -self.motor_timeconstant, 0],
-         [0, 0, 0, -self.motor_timeconstant]])
+         [0, 0, self.bottom_bottom, 0],
+         [0, 0, self.difference_bottom, self.difference_difference]])
 
-    self.motor_feedforward = self.Kt / (self.J * self.G * self.R)
+    self.A_bottom_cont = numpy.matrix(
+        [[0, 1],
+         [0, self.bottom_bottom]])
 
+    self.A_diff_cont = numpy.matrix(
+        [[0, 1],
+         [0, self.difference_difference]])
+
+  # self.A_continuous[0:2, 0:2] = self.A_bottom_cont
+  # self.A_continuous[2:4, 2:4] = self.A_diff_cont
+  # self.A_continuous[3, 1] = self.difference_bottom
+
+    self.motor_feedforward = self.Kt / (self.G * self.R)
+    self.motor_feedforward_bottom = self.motor_feedforward / self.J_bottom
+    self.motor_feedforward_difference = self.motor_feedforward / self.J_top
+    self.motor_feedforward_difference_bottom = (
+        self.motor_feedforward * (1 / self.J_bottom - 1 / self.J_top))
     self.B_continuous = numpy.matrix(
         [[0, 0],
          [0, 0],
-         [self.motor_feedforward, 0],
-         [0.0, self.motor_feedforward]])
+         [self.motor_feedforward_bottom, 0],
+         [-self.motor_feedforward_bottom,
+          self.motor_feedforward_difference]])
+
+    print "Cont X_ss", self.motor_feedforward / -self.common_motor_constant
+
+    self.B_bottom_cont = numpy.matrix(
+        [[0],
+         [self.motor_feedforward_bottom]])
+
+    self.B_diff_cont = numpy.matrix(
+        [[0],
+         [self.motor_feedforward_difference]])
+
     self.C = numpy.matrix([[1, 0, 0, 0],
                            [1, 1, 0, 0]])
     self.D = numpy.matrix([[0, 0],
@@ -59,28 +93,78 @@
     self.A, self.B = self.ContinuousToDiscrete(
         self.A_continuous, self.B_continuous, self.dt)
 
+    self.A_bottom, self.B_bottom = controls.c2d(
+        self.A_bottom_cont, self.B_bottom_cont, self.dt)
+    self.A_diff, self.B_diff = controls.c2d(
+        self.A_diff_cont, self.B_diff_cont, self.dt)
+
+    print "A"
+    print self.A
+    print "B"
+    print self.B
+
+    X_ss = numpy.matrix([[0], [0], [0.0], [0]])
+    
+    U = numpy.matrix([[1.0],[1.0]])
+    A = self.A
+    B = self.B
+   #X_ss[2, 0] = X_ss[2, 0] * A[2, 2] + B[2, 0] * U[0, 0]
+    X_ss[2, 0] = 1 / (1 - A[2, 2]) * B[2, 0] * U[0, 0]
+   #X_ss[3, 0] = X_ss[3, 0] * A[3, 3] + X_ss[2, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+   #X_ss[3, 0] * (1 - A[3, 3]) = X_ss[2, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+    X_ss[3, 0] = 1 / (1 - A[3, 3]) * (X_ss[2, 0] * A[3, 2] + B[3, 1] * U[1, 0] + B[3, 0] * U[0, 0])
+   #X_ss[3, 0] = 1 / (1 - A[3, 3]) / (1 - A[2, 2]) * B[2, 0] * U[0, 0] * A[3, 2] + B[3, 0] * U[0, 0] + B[3, 1] * U[1, 0]
+    X_ss[0, 0] = A[0, 2] * X_ss[2, 0] + B[0, 0] * U[0, 0]
+    X_ss[1, 0] = A[1, 2] * X_ss[2, 0] + A[1, 3] * X_ss[3, 0] + B[1, 0] * U[0, 0] + B[1, 1] * U[1, 0]
+
+    print "X_ss", X_ss
+    
     #controlability = controls.ctrb(self.A, self.B);
     #print "Rank of controlability matrix.", numpy.linalg.matrix_rank(controlability)
 
-    self.Q = numpy.matrix([[(1.0 / (0.10 ** 2.0)), 0.0, 0.0, 0.0],
-                           [0.0, (1.0 / (0.03 ** 2.0)), 0.0, 0.0],
+    self.Q = numpy.matrix([[(1.0 / (0.40 ** 2.0)), 0.0, 0.0, 0.0],
+                           [0.0, (1.0 / (0.007 ** 2.0)), 0.0, 0.0],
                            [0.0, 0.0, 0.2, 0.0],
                            [0.0, 0.0, 0.0, 2.00]])
 
-    self.R = numpy.matrix([[(1.0 / (20.0 ** 2.0)), 0.0],
-                           [0.0, (1.0 / (20.0 ** 2.0))]])
-    self.K = controls.dlqr(self.A, self.B, self.Q, self.R)
+    self.R = numpy.matrix([[(1.0 / (40.0 ** 2.0)), 0.0],
+                           [0.0, (1.0 / (5.0 ** 2.0))]])
+   #self.K = controls.dlqr(self.A, self.B, self.Q, self.R)
+
+    self.K = numpy.matrix([[50, 0.0, 1, 0.0],
+                           [0.0, 300, 0.0, 1.1]])
+    lstsq_A = numpy.identity(2)
+    lstsq_A[0] = self.B[1]
+    lstsq_A[1] = self.B[3]
+    print "System of Equations coefficients:"
+    print  lstsq_A
+    print "det", numpy.linalg.det(lstsq_A)
+    self.K[1, 0] = -lstsq_A[0, 0] * self.K[0, 0] / lstsq_A[0, 1]
+   #self.K[0:2, 0] = numpy.linalg.lstsq(lstsq_A, numpy.matrix([[0.0], [0.0]]))[0]
+    out_x = numpy.linalg.lstsq(
+                         lstsq_A,
+                         numpy.matrix([[self.A[1, 2]], [self.A[3, 2]]]))[0]
+    self.K[1, 2] = -lstsq_A[0, 0] * (self.K[0, 2] - out_x[0]) / lstsq_A[0, 1] + out_x[1]
 
     print "K unaugmented"
     print self.K
+    print "B * K unaugmented"
+    print self.B * self.K
+    F = self.A - self.B * self.K
+    print "A - B * K unaugmented"
+    print F
+    print "eigenvalues"
+    print numpy.linalg.eig(F)[0]
 
     self.rpl = .05
     self.ipl = 0.008
     self.PlaceObserverPoles([self.rpl + 1j * self.ipl,
-                             self.rpl - 1j * self.ipl,
                              self.rpl + 1j * self.ipl,
+                             self.rpl - 1j * self.ipl,
                              self.rpl - 1j * self.ipl])
 
+    # The box formed by U_min and U_max must encompass all possible values,
+    # or else Austin's code gets angry.
     self.U_max = numpy.matrix([[12.0], [24.0]])
     self.U_min = numpy.matrix([[-12.0], [-24.0]])
 
@@ -194,18 +278,47 @@
 
   return numpy.matrix([[bottom_u], [top_u - bottom_u]])
 
-def AverageUFix(claw, U):
-  bottom_u = U[0, 0]
-  top_u = U[1, 0] + bottom_u
+def AverageUFix(claw, U, preserve_v3=False):
+  """Clips U as necessary.
 
-  #print "Bottom is", new_unclipped_bottom_u, "Top is", top_u
-  if (bottom_u > claw.U_max[0, 0] or top_u > claw.U_max[1, 0] or
-      top_u < claw.U_min[1, 0] or bottom_u < claw.U_min[0, 0]):
-    scalar = 12.0 / max(numpy.abs(top_u), numpy.abs(bottom_u))
+    Args:
+      claw: claw object containing moments of inertia and U limits.
+      U: Input matrix to clip as necessary.
+      preserve_v3: There are two ways to attempt to clip the voltages:
+        -If you preserve the imaginary v3, then it will attempt to 
+          preserve the effect on the separation of the two claws.
+          If it is not able to do this, then it calls itself with preserve_v3
+          set to False.
+        -If you preserve the ratio of the voltage of the bottom and the top,
+          then it will attempt to preserve the ratio of those two. This is
+          equivalent to preserving the ratio of v3 and the bottom voltage.
+  """
+  bottom_u = U[0, 0]
+  top_u = U[1, 0]
+  seperation_u = top_u - bottom_u * claw.J_top / claw.J_bottom
+
+  top_big = top_u > claw.U_max[0, 0]
+  top_small = top_u < claw.U_min[0, 0]
+  bot_big = bottom_u > claw.U_max[0, 0]
+  bot_small = top_u < claw.U_min[0, 0]
+  bottom_bad = bot_big or bot_small
+  top_bad = top_big or top_small
+  scalar = claw.U_max[0, 0] / max(numpy.abs(top_u), numpy.abs(bottom_u))
+  if bottom_bad and preserve_v3:
+    bottom_u *= scalar
+    top_u = seperation_u + bottom_u * claw.J_top / claw.J_bottom
+    if abs(top_u) > claw.U_max[0, 0]:
+      return AverageUFix(claw, U, preserve_v3=False)
+  elif top_bad and preserve_v3:
+    top_u *= scalar
+    bottom_u = (top_u - seperation_u) * claw.J_bottom / claw.J_top
+    if abs(bottom_u) > claw.U_max[0, 0]:
+      return AverageUFix(claw, U, preserve_v3=False)
+  elif (bottom_bad or top_bad) and not preserve_v3:
     top_u *= scalar
     bottom_u *= scalar
 
-  return numpy.matrix([[bottom_u], [top_u - bottom_u]])
+  return numpy.matrix([[bottom_u], [top_u]])
 
 def ClipDeltaU(claw, U):
   delta_u = U[0, 0]
@@ -246,33 +359,47 @@
   #pylab.plot(range(100), simulated_x)
   #pylab.show()
 
-  # Simulate the closed loop response of the system to a step input.
+  # Simulate the closed loop response of the system.
   claw = Claw("TopClaw")
   t = []
   close_loop_x_bottom = []
   close_loop_x_sep = []
+  actual_sep = []
+  actual_x_bottom = []
+  close_loop_x_top = []
   close_loop_u_bottom = []
   close_loop_u_top = []
-  R = numpy.matrix([[1.0], [1.0], [0.0], [0.0]])
-  claw.X[0, 0] = 0
+  R = numpy.matrix([[0.0], [0.00], [0.0], [0.0]])
+  claw.X[0, 0] = 1
+  claw.X[1, 0] = .0
+  claw.X_hat = claw.X
+ #X_actual = claw.X
   for i in xrange(100):
     #print "Error is", (R - claw.X_hat)
-    U = claw.K * (R - claw.X_hat)
+    U = claw.K * (R - claw.X)
     #U = numpy.clip(claw.K * (R - claw.X_hat), claw.U_min, claw.U_max)
     #U = FullSeparationPriority(claw, U)
-    U = AverageUFix(claw, U)
+   #U = AverageUFix(claw, U, preserve_v3=True)
     #U = claw.K * (R - claw.X_hat)
     #U = ClipDeltaU(claw, U)
     claw.UpdateObserver(U)
     claw.Update(U)
+   #X_actual = claw.A_actual * X_actual + claw.B_actual * U
+   #claw.Y = claw.C * X_actual
     close_loop_x_bottom.append(claw.X[0, 0] * 10)
     close_loop_u_bottom.append(U[0, 0])
-    close_loop_x_sep.append(claw.X[1, 0] * 10)
-    close_loop_u_top.append(U[1, 0] + U[0, 0])
+   #actual_sep.append(X_actual[2, 0] * 100)
+   #actual_x_bottom.append(X_actual[0, 0] * 10)
+    close_loop_x_sep.append(claw.X[1, 0] * 100)
+    close_loop_x_top.append((claw.X[1, 0] + claw.X[0, 0]) * 10)
+    close_loop_u_top.append(U[1, 0])
     t.append(0.01 * i)
 
   pylab.plot(t, close_loop_x_bottom, label='x bottom')
   pylab.plot(t, close_loop_x_sep, label='separation')
+ #pylab.plot(t, actual_x_bottom, label='true x bottom')
+ #pylab.plot(t, actual_sep, label='true separation')
+  pylab.plot(t, close_loop_x_top, label='x top')
   pylab.plot(t, close_loop_u_bottom, label='u bottom')
   pylab.plot(t, close_loop_u_top, label='u top')
   pylab.legend()
diff --git a/frc971/control_loops/python/control_loop.py b/frc971/control_loops/python/control_loop.py
index 4b63aec..0610225 100644
--- a/frc971/control_loops/python/control_loop.py
+++ b/frc971/control_loops/python/control_loop.py
@@ -183,7 +183,7 @@
 
   def Update(self, U):
     """Simulates one time step with the provided U."""
-    U = numpy.clip(U, self.U_min, self.U_max)
+   #U = numpy.clip(U, self.U_min, self.U_max)
     self.X = self.A * self.X + self.B * U
     self.Y = self.C * self.X + self.D * U