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