| #!/usr/bin/python |
| |
| import control_loop |
| import numpy |
| import sys |
| from matplotlib import pylab |
| |
| class SprungShooter(control_loop.ControlLoop): |
| def __init__(self, name="RawSprungShooter"): |
| super(SprungShooter, self).__init__(name) |
| # Stall Torque in N m |
| self.stall_torque = .4982 |
| # Stall Current in Amps |
| self.stall_current = 85 |
| # Free Speed in RPM |
| self.free_speed = 19300.0 |
| # Free Current in Amps |
| self.free_current = 1.2 |
| # Effective mass of the shooter in kg. |
| # This rough estimate should about include the effect of the masses |
| # of the gears. If this number is too low, the eigen values of self.A |
| # will start to become extremely small. |
| self.J = 200 |
| # Resistance of the motor, divided by the number of motors. |
| self.R = 12.0 / self.stall_current / 2.0 |
| # Motor velocity constant |
| self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) / |
| (12.0 - self.R * self.free_current)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| # Spring constant for the springs, N/m |
| self.Ks = 2800.0 |
| # Gear ratio multiplied by radius of final sprocket. |
| self.G = 10.0 / 40.0 * 20.0 / 54.0 * 24.0 / 54.0 * 20.0 / 84.0 * 16.0 * (3.0 / 8.0) / (2.0 * numpy.pi) * 0.0254 |
| |
| # Control loop time step |
| self.dt = 0.01 |
| |
| # State feedback matrices |
| self.A_continuous = numpy.matrix( |
| [[0, 1], |
| [-self.Ks / self.J, |
| -self.Kt / self.Kv / (self.J * self.G * self.G * self.R)]]) |
| self.B_continuous = numpy.matrix( |
| [[0], |
| [self.Kt / (self.J * self.G * self.R)]]) |
| self.C = numpy.matrix([[1, 0]]) |
| self.D = numpy.matrix([[0]]) |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| |
| self.PlaceControllerPoles([0.45, 0.45]) |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl, |
| self.rpl]) |
| |
| self.U_max = numpy.matrix([[12.0]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| class Shooter(SprungShooter): |
| def __init__(self, name="RawShooter"): |
| super(Shooter, self).__init__(name) |
| |
| # State feedback matrices |
| self.A_continuous = numpy.matrix( |
| [[0, 1], |
| [0, -self.Kt / self.Kv / (self.J * self.G * self.G * self.R)]]) |
| self.B_continuous = numpy.matrix( |
| [[0], |
| [self.Kt / (self.J * self.G * self.R)]]) |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| |
| self.PlaceControllerPoles([0.45, 0.45]) |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl, |
| self.rpl]) |
| |
| self.U_max = numpy.matrix([[12.0]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| class SprungShooterDeltaU(SprungShooter): |
| def __init__(self, name="SprungShooter"): |
| super(SprungShooterDeltaU, self).__init__(name) |
| A_unaugmented = self.A |
| B_unaugmented = self.B |
| |
| self.A = numpy.matrix([[0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0], |
| [0.0, 0.0, 1.0]]) |
| self.A[0:2, 0:2] = A_unaugmented |
| self.A[0:2, 2] = B_unaugmented |
| |
| self.B = numpy.matrix([[0.0], |
| [0.0], |
| [1.0]]) |
| |
| self.C = numpy.matrix([[1.0, 0.0, 0.0]]) |
| self.D = numpy.matrix([[0.0]]) |
| |
| self.PlaceControllerPoles([0.50, 0.35, 0.80]) |
| |
| print "K" |
| print self.K |
| print "Placed controller poles are" |
| print numpy.linalg.eig(self.A - self.B * self.K)[0] |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl + 1j * self.ipl, |
| self.rpl - 1j * self.ipl, 0.90]) |
| print "Placed observer poles are" |
| print numpy.linalg.eig(self.A - self.L * self.C)[0] |
| |
| self.U_max = numpy.matrix([[12.0]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| class ShooterDeltaU(Shooter): |
| def __init__(self, name="Shooter"): |
| super(ShooterDeltaU, self).__init__(name) |
| A_unaugmented = self.A |
| B_unaugmented = self.B |
| |
| self.A = numpy.matrix([[0.0, 0.0, 0.0], |
| [0.0, 0.0, 0.0], |
| [0.0, 0.0, 1.0]]) |
| self.A[0:2, 0:2] = A_unaugmented |
| self.A[0:2, 2] = B_unaugmented |
| |
| self.B = numpy.matrix([[0.0], |
| [0.0], |
| [1.0]]) |
| |
| self.C = numpy.matrix([[1.0, 0.0, 0.0]]) |
| self.D = numpy.matrix([[0.0]]) |
| |
| self.PlaceControllerPoles([0.55, 0.45, 0.80]) |
| |
| print "K" |
| print self.K |
| print "Placed controller poles are" |
| print numpy.linalg.eig(self.A - self.B * self.K)[0] |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl + 1j * self.ipl, |
| self.rpl - 1j * self.ipl, 0.90]) |
| print "Placed observer poles are" |
| print numpy.linalg.eig(self.A - self.L * self.C)[0] |
| |
| self.U_max = numpy.matrix([[12.0]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| def ClipDeltaU(shooter, old_voltage, delta_u): |
| old_u = old_voltage |
| new_u = numpy.clip(old_u + delta_u, shooter.U_min, shooter.U_max) |
| return new_u - old_u |
| |
| def main(argv): |
| # Simulate the response of the system to a goal. |
| sprung_shooter = SprungShooterDeltaU() |
| raw_sprung_shooter = SprungShooter() |
| close_loop_x = [] |
| close_loop_u = [] |
| goal_position = -0.3 |
| R = numpy.matrix([[goal_position], [0.0], [-sprung_shooter.A[1, 0] / sprung_shooter.A[1, 2] * goal_position]]) |
| voltage = numpy.matrix([[0.0]]) |
| for _ in xrange(500): |
| U = sprung_shooter.K * (R - sprung_shooter.X_hat) |
| U = ClipDeltaU(sprung_shooter, voltage, U) |
| sprung_shooter.Y = raw_sprung_shooter.Y + 0.01 |
| sprung_shooter.UpdateObserver(U) |
| voltage += U; |
| raw_sprung_shooter.Update(voltage) |
| close_loop_x.append(raw_sprung_shooter.X[0, 0] * 10) |
| close_loop_u.append(voltage[0, 0]) |
| |
| pylab.plot(range(500), close_loop_x) |
| pylab.plot(range(500), close_loop_u) |
| pylab.show() |
| |
| shooter = ShooterDeltaU() |
| raw_shooter = Shooter() |
| close_loop_x = [] |
| close_loop_u = [] |
| goal_position = -0.3 |
| R = numpy.matrix([[goal_position], [0.0], [-shooter.A[1, 0] / shooter.A[1, 2] * goal_position]]) |
| voltage = numpy.matrix([[0.0]]) |
| for _ in xrange(500): |
| U = shooter.K * (R - shooter.X_hat) |
| U = ClipDeltaU(shooter, voltage, U) |
| shooter.Y = raw_shooter.Y + 0.01 |
| shooter.UpdateObserver(U) |
| voltage += U; |
| raw_shooter.Update(voltage) |
| close_loop_x.append(raw_shooter.X[0, 0] * 10) |
| close_loop_u.append(voltage[0, 0]) |
| |
| pylab.plot(range(500), close_loop_x) |
| pylab.plot(range(500), close_loop_u) |
| pylab.show() |
| |
| # Write the generated constants out to a file. |
| if len(argv) != 5: |
| print "Expected .h file name and .cc file name for" |
| print "both the plant and unaugmented plant" |
| else: |
| unaug_sprung_shooter = SprungShooter("RawSprungShooter") |
| unaug_shooter = Shooter("RawShooter") |
| unaug_loop_writer = control_loop.ControlLoopWriter("RawShooter", |
| [unaug_sprung_shooter, |
| unaug_shooter]) |
| if argv[3][-3:] == '.cc': |
| unaug_loop_writer.Write(argv[4], argv[3]) |
| else: |
| unaug_loop_writer.Write(argv[3], argv[4]) |
| |
| sprung_shooter = SprungShooterDeltaU() |
| shooter = ShooterDeltaU() |
| loop_writer = control_loop.ControlLoopWriter("Shooter", [sprung_shooter, |
| shooter], |
| write_constants=True) |
| 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)) |