| #!/usr/bin/python |
| |
| import control_loop |
| import controls |
| import numpy |
| import sys |
| from matplotlib import pylab |
| |
| class Claw(control_loop.ControlLoop): |
| def __init__(self, name="RawClaw"): |
| super(Claw, self).__init__(name) |
| # Stall Torque in N m |
| self.stall_torque = 2.42 |
| # Stall Current in Amps |
| self.stall_current = 133 |
| # 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 |
| # measured from CAD |
| self.J_top = 0.3 |
| self.J_bottom = 0.9 |
| # Resistance of the motor |
| 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)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| # Gear ratio |
| self.G = 14.0 / 48.0 * 18.0 / 32.0 * 18.0 / 66.0 * 12.0 / 60.0 |
| # Control loop time step |
| self.dt = 0.01 |
| |
| # 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, 0, 0], |
| [0, 0, 0, 0], |
| [0, 0, self.bottom_bottom, 0], |
| [0, 0, self.difference_bottom, self.difference_difference]]) |
| |
| 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], |
| [self.motor_feedforward_bottom, 0], |
| [0, 0], |
| [0,#self.motor_feedforward_difference_bottom, |
| self.motor_feedforward_difference]]) |
| |
| 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, 0, 1, 0]]) |
| self.D = numpy.matrix([[0, 0], |
| [0, 0]]) |
| |
| 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, A_bot, A_diff:" |
| print self.A, self.A_bottom, self.A_diff |
| print "B, B_bot, B_diff:" |
| print self.B, self.B_bottom, self.B_diff |
| |
| # If B should equal [[B_bot, 0],[0, B_diff]], then the B |
| # generated by ContinuousToDiscrete adds in a couple extra |
| # numbers which make it impossible to control 4 values in K. |
| # Here, I make B equal what I had thought it should, thereby |
| # allowing us to control 4 values in K. |
| self.B_actual = numpy.matrix(self.B) |
| self.B[2, 0] = 0.0 |
| self.B[3, 0] = 0.0 |
| # If we do the above, with setting values of B to zero, |
| # then we can no longer make all the necessary values of A - B * K |
| # zero, because the discrete transform added a term affecting position |
| # over the timestep and that term can no longer be cancelled out if we |
| # are to also cancel out the term where the velocity of the bottom |
| # affects the velocity of the separation. |
| self.A_actual = numpy.matrix(self.A) |
| self.A[2, 1] = self.A[3, 1] * self.B[2, 1] / self.B[3, 1] |
| |
| #controlability = controls.ctrb(self.A, self.B); |
| #print "Rank of controlability matrix.", numpy.linalg.matrix_rank(controlability) |
| |
| 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 / (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) |
| |
| # TODO(james): Fix this for discrete time domain. |
| self.K = numpy.matrix([[0, 0, 0.0, 0.0], |
| [0.0, self.A[3, 1] / self.B[3, 1], 0, 0]]) |
| self.K_bottom = controls.dplace(self.A_bottom, self.B_bottom, [0.6, 0.7]) |
| self.K_diff = controls.dplace(self.A_diff, self.B_diff, [0.3, 0.5]) |
| self.K[0, 0:2] = self.K_bottom |
| self.K[1, 2:4] = self.K_diff |
| #lstsq_A = numpy.identity(2) |
| #lstsq_A[0] = self.B[1] |
| #lstsq_A[1] = self.B[3] |
| #self.K[0:2, 0] = numpy.linalg.lstsq(lstsq_A, numpy.matrix([[0.0], [0.0]]))[0] |
| #self.K[0:2, 2] = numpy.linalg.lstsq( |
| # lstsq_A, |
| # numpy.matrix([[self.A[1, 2]], [self.A[3, 2]]]))[0] |
| |
| 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]) |
| |
| # 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]]) |
| |
| self.InitializeState() |
| |
| |
| class ClawDeltaU(Claw): |
| def __init__(self, name="Claw"): |
| super(ClawDeltaU, self).__init__(name) |
| A_unaugmented = self.A |
| B_unaugmented = self.B |
| C_unaugmented = self.C |
| |
| self.A = numpy.matrix([[0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.0, 1.0]]) |
| self.A[0:4, 0:4] = A_unaugmented |
| self.A[0:4, 4] = B_unaugmented[0:4, 0] |
| |
| self.B = numpy.matrix([[0.0, 0.0], |
| [0.0, 0.0], |
| [0.0, 0.0], |
| [0.0, 0.0], |
| [1.0, 0.0]]) |
| self.B[0:4, 1] = B_unaugmented[0:4, 1] |
| |
| self.C = numpy.concatenate((C_unaugmented, numpy.matrix([[0.0], [0.0]])), |
| axis=1) |
| self.D = numpy.matrix([[0.0, 0.0], |
| [0.0, 0.0]]) |
| |
| #self.PlaceControllerPoles([0.55, 0.35, 0.55, 0.35, 0.80]) |
| self.Q = numpy.matrix([[(1.0 / (0.04 ** 2.0)), 0.0, 0.0, 0.0, 0.0], |
| [0.0, (1.0 / (0.01 ** 2)), 0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.01, 0.0, 0.0], |
| [0.0, 0.0, 0.0, 0.08, 0.0], |
| [0.0, 0.0, 0.0, 0.0, (1.0 / (10.0 ** 2))]]) |
| |
| self.R = numpy.matrix([[0.000001, 0.0], |
| [0.0, 1.0 / (10.0 ** 2.0)]]) |
| self.K = controls.dlqr(self.A, self.B, self.Q, self.R) |
| |
| self.K = numpy.matrix([[50.0, 0.0, 10.0, 0.0, 1.0], |
| [50.0, 0.0, 10.0, 0.0, 1.0]]) |
| #self.K = numpy.matrix([[50.0, -100.0, 0, -10, 0], |
| # [50.0, 100.0, 0, 10, 0]]) |
| |
| controlability = controls.ctrb(self.A, self.B); |
| print "Rank of augmented controlability matrix.", numpy.linalg.matrix_rank(controlability) |
| |
| print "K" |
| print self.K |
| print "Placed controller poles are" |
| print numpy.linalg.eig(self.A - self.B * self.K)[0] |
| print [numpy.abs(x) for x in numpy.linalg.eig(self.A - self.B * self.K)[0]] |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl + 1j * self.ipl, 0.10, 0.09, |
| self.rpl - 1j * self.ipl, 0.90]) |
| #print "A is" |
| #print self.A |
| #print "L is" |
| #print self.L |
| #print "C is" |
| #print self.C |
| #print "A - LC is" |
| #print self.A - self.L * self.C |
| |
| #print "Placed observer poles are" |
| #print numpy.linalg.eig(self.A - self.L * self.C)[0] |
| |
| self.U_max = numpy.matrix([[12.0], [12.0]]) |
| self.U_min = numpy.matrix([[-12.0], [-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| def FullSeparationPriority(claw, U): |
| bottom_u = U[0, 0] |
| top_u = U[1, 0] + bottom_u |
| |
| #print "Bottom is", new_unclipped_bottom_u, "Top is", top_u |
| if bottom_u > claw.U_max[0, 0]: |
| #print "Bottom is too big. Was", new_unclipped_bottom_u, "changing top by", new_unclipped_bottom_u - claw.U_max[0, 0] |
| top_u -= bottom_u - claw.U_max[0, 0] |
| if top_u < claw.U_min[1, 0]: |
| top_u = claw.U_min[1, 0] |
| |
| bottom_u = claw.U_max[0, 0] |
| if top_u > claw.U_max[1, 0]: |
| bottom_u -= top_u - claw.U_max[1, 0] |
| if bottom_u < claw.U_min[0, 0]: |
| bottom_u = claw.U_min[0, 0] |
| |
| top_u = claw.U_max[1, 0] |
| if top_u < claw.U_min[1, 0]: |
| bottom_u -= top_u - claw.U_min[1, 0] |
| if bottom_u > claw.U_max[0, 0]: |
| bottom_u = claw.U_max[0, 0] |
| |
| top_u = claw.U_min[1, 0] |
| if bottom_u < claw.U_min[0, 0]: |
| top_u -= bottom_u - claw.U_min[0, 0] |
| if top_u > claw.U_max[1, 0]: |
| top_u = claw.U_max[1, 0] |
| |
| bottom_u = claw.U_min[0, 0] |
| |
| return numpy.matrix([[bottom_u], [top_u - bottom_u]]) |
| |
| def AverageUFix(claw, U): |
| bottom_u = U[0, 0] |
| top_u = bottom_u + U[1, 0] |
| top_u = bottom_u * claw.J_top / claw.J_bottom + U[1, 0] |
| |
| #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[0, 0] or |
| top_u < claw.U_min[0, 0] or bottom_u < claw.U_min[0, 0]): |
| scalar = 12.0 / max(numpy.abs(top_u), numpy.abs(bottom_u)) |
| top_u *= scalar |
| bottom_u *= scalar |
| |
| #return numpy.matrix([[bottom_u], [top_u - bottom_u]]) |
| return numpy.matrix([[bottom_u], [top_u - bottom_u * claw.J_top / claw.J_bottom]]) |
| |
| def ClipDeltaU(claw, U): |
| delta_u = U[0, 0] |
| top_u = U[1, 0] |
| old_bottom_u = claw.X[4, 0] |
| |
| # TODO(austin): Preserve the difference between the top and bottom power. |
| new_unclipped_bottom_u = old_bottom_u + delta_u |
| |
| #print "Bottom is", new_unclipped_bottom_u, "Top is", top_u |
| if new_unclipped_bottom_u > claw.U_max[0, 0]: |
| #print "Bottom is too big. Was", new_unclipped_bottom_u, "changing top by", new_unclipped_bottom_u - claw.U_max[0, 0] |
| top_u -= new_unclipped_bottom_u - claw.U_max[0, 0] |
| new_unclipped_bottom_u = claw.U_max[0, 0] |
| if top_u > claw.U_max[1, 0]: |
| new_unclipped_bottom_u -= top_u - claw.U_max[1, 0] |
| top_u = claw.U_max[1, 0] |
| if top_u < claw.U_min[1, 0]: |
| new_unclipped_bottom_u -= top_u - claw.U_min[1, 0] |
| top_u = claw.U_min[1, 0] |
| if new_unclipped_bottom_u < claw.U_min[0, 0]: |
| top_u -= new_unclipped_bottom_u - claw.U_min[0, 0] |
| new_unclipped_bottom_u = claw.U_min[0, 0] |
| |
| new_bottom_u = numpy.clip(new_unclipped_bottom_u, claw.U_min[0, 0], claw.U_max[0, 0]) |
| new_top_u = numpy.clip(top_u, claw.U_min[1, 0], claw.U_max[1, 0]) |
| |
| return numpy.matrix([[new_bottom_u - old_bottom_u], [new_top_u]]) |
| |
| def main(argv): |
| # Simulate the response of the system to a step input. |
| #claw = ClawDeltaU() |
| #simulated_x = [] |
| #for _ in xrange(100): |
| # claw.Update(numpy.matrix([[12.0]])) |
| # simulated_x.append(claw.X[0, 0]) |
| |
| #pylab.plot(range(100), simulated_x) |
| #pylab.show() |
| |
| # 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([[0.0], [0.00], [0.0], [0.0]]) |
| claw.X[0, 0] = 1 |
| claw.X_hat[0, 0] = 1 |
| X_actual = claw.X |
| print "B actual" |
| print claw.B_actual |
| for i in xrange(100): |
| #print "Error is", (R - claw.X_hat) |
| U = claw.K * (R - claw.X_hat) |
| #U = numpy.clip(claw.K * (R - claw.X_hat), claw.U_min, claw.U_max) |
| #U = FullSeparationPriority(claw, U) |
| #U = AverageUFix(claw, U) |
| #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_hat[0, 0] * 10) |
| close_loop_u_bottom.append(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_hat[2, 0] * 100) |
| close_loop_x_top.append((claw.X_hat[2, 0] + claw.X_hat[0, 0]) * 10) |
| close_loop_u_top.append(U[1, 0] + U[0, 0] * claw.J_top / claw.J_bottom) |
| 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() |
| pylab.show() |
| |
| # Write the generated constants out to a file. |
| if len(argv) != 3: |
| print "Expected .h file name and .cc file name for the claw." |
| else: |
| claw = Claw("Claw") |
| loop_writer = control_loop.ControlLoopWriter("Claw", [claw]) |
| if argv[1][-3:] == '.cc': |
| loop_writer.Write(argv[2], argv[1]) |
| else: |
| loop_writer.Write(argv[1], argv[2]) |
| |
| if __name__ == '__main__': |
| sys.exit(main(sys.argv)) |