| #!/usr/bin/python |
| |
| import control_loop |
| import numpy |
| import sys |
| from matplotlib import pylab |
| |
| class Shooter(control_loop.ControlLoop): |
| def __init__(self, name="RawShooter"): |
| super(Shooter, self).__init__(name) |
| # Stall Torque in N m |
| self.stall_torque = .4862 |
| # Stall Current in Amps |
| self.stall_current = 85 |
| # Free Speed in RPM |
| self.free_speed = 19300.0 |
| # Free Current in Amps |
| self.free_current = 1.4 |
| # Moment of inertia of the shooter in kg m^2 |
| # TODO(aschuh): Measure this in reality. It doesn't seem high enough. |
| # James measured 0.51, but that can't be right given what I am seeing. |
| self.J = 2.0 |
| # Resistance of the motor |
| self.R = 12.0 / self.stall_current + 0.024 + .003 #TODO comment on these constants |
| # 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 = 1.0 / ((84.0 / 20.0) * (50.0 / 14.0) * (40.0 / 14.0) * (40.0 / 12.0)) |
| # Control loop time step |
| self.dt = 0.01 |
| |
| # 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.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([0.85, 0.45]) |
| |
| self.rpl = .05 |
| self.ipl = 0.008 |
| self.PlaceObserverPoles([self.rpl + 1j * self.ipl, |
| self.rpl - 1j * self.ipl]) |
| |
| 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, 0.35, 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() |
| |
| |
| def ClipDeltaU(shooter, delta_u): |
| old_u = numpy.matrix([[shooter.X[2, 0]]]) |
| 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 step input. |
| shooter = ShooterDeltaU() |
| simulated_x = [] |
| for _ in xrange(100): |
| shooter.Update(numpy.matrix([[12.0]])) |
| simulated_x.append(shooter.X[0, 0]) |
| |
| pylab.plot(range(100), simulated_x) |
| pylab.show() |
| |
| # Simulate the closed loop response of the system to a step input. |
| shooter = ShooterDeltaU() |
| close_loop_x = [] |
| close_loop_u = [] |
| R = numpy.matrix([[1.0], [0.0], [0.0]]) |
| shooter.X[2, 0] = -5 |
| for _ in xrange(100): |
| U = numpy.clip(shooter.K * (R - shooter.X_hat), shooter.U_min, shooter.U_max) |
| U = ClipDeltaU(shooter, U) |
| shooter.UpdateObserver(U) |
| shooter.Update(U) |
| close_loop_x.append(shooter.X[0, 0] * 10) |
| close_loop_u.append(shooter.X[2, 0]) |
| |
| pylab.plot(range(100), close_loop_x) |
| pylab.plot(range(100), 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_shooter = Shooter("RawShooter") |
| unaug_loop_writer = control_loop.ControlLoopWriter("RawShooter", |
| [unaug_shooter]) |
| if argv[3][-3:] == '.cc': |
| unaug_loop_writer.Write(argv[4], argv[3]) |
| else: |
| unaug_loop_writer.Write(argv[3], argv[4]) |
| |
| loop_writer = control_loop.ControlLoopWriter("Shooter", [shooter]) |
| 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)) |