Added the feed forwards constant to StateFeedbackLoop.

Change-Id: Ie222de1f302b0edcf5c8b1fdd7f2958e0de608c3
diff --git a/frc971/control_loops/python/control_loop.py b/frc971/control_loops/python/control_loop.py
index 586a375..951a114 100644
--- a/frc971/control_loops/python/control_loop.py
+++ b/frc971/control_loops/python/control_loop.py
@@ -38,7 +38,7 @@
 
     self._namespace_end = '\n'.join(
         ['}  // namespace %s' % name for name in reversed(self._namespaces)])
-    
+
     self._constant_list = []
 
   def AddConstant(self, constant):
@@ -330,10 +330,14 @@
 
     ans.append(self._DumpMatrix('L', self.L))
     ans.append(self._DumpMatrix('K', self.K))
+    if not hasattr(self, 'Kff'):
+      self.Kff = numpy.matrix(numpy.zeros(self.K.shape))
+
+    ans.append(self._DumpMatrix('Kff', self.Kff))
     ans.append(self._DumpMatrix('A_inv', numpy.linalg.inv(self.A)))
 
     ans.append('  return StateFeedbackController<%d, %d, %d>'
-               '(L, K, A_inv, Make%sPlantCoefficients());\n' % (
+               '(L, K, Kff, A_inv, Make%sPlantCoefficients());\n' % (
                    num_states, num_inputs, num_outputs, self._name))
     ans.append('}\n')
     return ''.join(ans)
diff --git a/frc971/control_loops/python/controls.py b/frc971/control_loops/python/controls.py
index e2c6c93..ed6a809 100644
--- a/frc971/control_loops/python/controls.py
+++ b/frc971/control_loops/python/controls.py
@@ -149,3 +149,25 @@
   P = (I - K * C) * P_prior
 
   return K, P
+
+def TwoStateFeedForwards(B, Q):
+  """Computes the feed forwards constant for a 2 state controller.
+
+  This will take the form U = Kff * (R(n + 1) - A * R(n)), where Kff is the
+  feed-forwards constant.  It is important that Kff is *only* computed off
+  the goal and not the feed back terms.
+
+  Args:
+    B: numpy.Matrix[num_states, num_inputs] The B matrix.
+    Q: numpy.Matrix[num_states, num_states] The Q (cost) matrix.
+
+  Returns:
+    numpy.Matrix[num_inputs, num_states]
+  """
+
+  # We want to find the optimal U such that we minimize the tracking cost.
+  # This means that we want to minimize
+  #   (B * U - (R(n+1) - A R(n)))^T * Q * (B * U - (R(n+1) - A R(n)))
+  # TODO(austin): This doesn't take into account the cost of U
+
+  return numpy.linalg.inv(B.T * Q * B) * B.T * Q.T