| #!/usr/bin/python |
| |
| import control_loop |
| import controls |
| import numpy |
| import sys |
| import matplotlib |
| from matplotlib import pylab |
| |
| class Elevator(control_loop.ControlLoop): |
| def __init__(self, name="Elevator", mass=None): |
| super(Elevator, self).__init__(name) |
| # Stall Torque in N m |
| self.stall_torque = 2.402 |
| # Stall Current in Amps |
| self.stall_current = 126.145 |
| # Free Speed in RPM |
| self.free_speed = 5015.562 |
| # Free Current in Amps |
| self.free_current = 1.170 |
| # Mass of the Elevator |
| if mass is None: |
| self.mass = 5.0 |
| else: |
| self.mass = mass |
| |
| # Number of motors |
| self.num_motors = 2.0 |
| # Resistance of the motor |
| self.resistance = 12.0 / self.stall_current |
| # Motor velocity constant |
| self.Kv = ((self.free_speed / 60.0 * 2.0 * numpy.pi) / |
| (12.0 - self.resistance * self.free_current)) |
| # Torque constant |
| self.Kt = (self.num_motors * self.stall_torque) / self.stall_current |
| # Gear ratio |
| self.G = 8 |
| # Radius of pulley |
| self.r = 0.0254 |
| |
| # Control loop time step |
| self.dt = 0.005 |
| |
| # State is [position, velocity] |
| # Input is [Voltage] |
| |
| C1 = self.Kt * self.G * self.G / (self.Kv * self.resistance * self.r * self.r * self.mass) |
| C2 = self.G * self.Kt / (self.resistance * self.r * self.mass) |
| |
| self.A_continuous = numpy.matrix( |
| [[0, 1], |
| [0, -C1]]) |
| |
| # Start with the unmodified input |
| self.B_continuous = numpy.matrix( |
| [[0], |
| [C2]]) |
| |
| 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) |
| |
| controlability = controls.ctrb(self.A, self.B); |
| |
| q_pos = 0.015 |
| q_vel = 0.5 |
| self.Q = numpy.matrix([[(1.0 / (q_pos ** 2.0)), 0.0], |
| [0.0, (1.0 / (q_vel ** 2.0))]]) |
| |
| self.R = numpy.matrix([[(1.0 / (12.0 ** 2.0))]]) |
| self.K = controls.dlqr(self.A, self.B, self.Q, self.R) |
| |
| print 'K', self.K |
| print 'Poles are', numpy.linalg.eig(self.A - self.B * self.K)[0] |
| |
| self.rpl = 0.30 |
| self.ipl = 0.10 |
| self.PlaceObserverPoles([self.rpl + 1j * self.ipl, |
| self.rpl - 1j * self.ipl]) |
| |
| # print 'L is', self.L |
| |
| q_pos = 0.05 |
| q_vel = 2.65 |
| self.Q = numpy.matrix([[(q_pos ** 2.0), 0.0], |
| [0.0, (q_vel ** 2.0)]]) |
| |
| r_volts = 0.025 |
| self.R = numpy.matrix([[(r_volts ** 2.0)]]) |
| |
| self.KalmanGain, self.Q_steady = controls.kalman( |
| A=self.A, B=self.B, C=self.C, Q=self.Q, R=self.R) |
| |
| # print 'Kal', self.KalmanGain |
| self.L = self.A * self.KalmanGain |
| print 'KalL is', self.L |
| |
| # 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]]) |
| self.U_min = numpy.matrix([[-12.0]]) |
| |
| self.InitializeState() |
| |
| class IntegralElevator(Elevator): |
| def __init__(self, name="IntegralElevator", mass=None): |
| super(IntegralElevator, self).__init__(name=name, mass=mass) |
| |
| self.A_continuous_unaugmented = self.A_continuous |
| self.B_continuous_unaugmented = self.B_continuous |
| |
| self.A_continuous = numpy.matrix(numpy.zeros((3, 3))) |
| self.A_continuous[0:2, 0:2] = self.A_continuous_unaugmented |
| self.A_continuous[0:2, 2] = self.B_continuous_unaugmented |
| |
| self.B_continuous = numpy.matrix(numpy.zeros((3, 1))) |
| self.B_continuous[0:2, 0] = self.B_continuous_unaugmented |
| |
| self.C_unaugmented = self.C |
| self.C = numpy.matrix(numpy.zeros((1, 3))) |
| self.C[0:1, 0:2] = self.C_unaugmented |
| |
| self.A, self.B = self.ContinuousToDiscrete(self.A_continuous, self.B_continuous, self.dt) |
| |
| q_pos = 0.08 |
| q_vel = 4.00 |
| q_voltage = 6.0 |
| self.Q = numpy.matrix([[(q_pos ** 2.0), 0.0, 0.0], |
| [0.0, (q_vel ** 2.0), 0.0], |
| [0.0, 0.0, (q_voltage ** 2.0)]]) |
| |
| r_pos = 0.05 |
| self.R = numpy.matrix([[(r_pos ** 2.0)]]) |
| |
| self.KalmanGain, self.Q_steady = controls.kalman( |
| A=self.A, B=self.B, C=self.C, Q=self.Q, R=self.R) |
| self.L = self.A * self.KalmanGain |
| |
| self.K_unaugmented = self.K |
| self.K = numpy.matrix(numpy.zeros((1, 3))) |
| self.K[0, 0:2] = self.K_unaugmented |
| self.K[0, 2] = 1 |
| |
| self.InitializeState() |
| |
| |
| class ScenarioPlotter(object): |
| def __init__(self): |
| # Various lists for graphing things. |
| self.t = [] |
| self.x = [] |
| self.v = [] |
| self.a = [] |
| self.x_hat = [] |
| self.u = [] |
| |
| def run_test(self, elevator, goal, |
| iterations=200, controller_elevator=None, |
| observer_elevator=None): |
| """Runs the Elevator plant with an initial condition and goal. |
| |
| Args: |
| Elevator: elevator object to use. |
| initial_X: starting state. |
| goal: goal state. |
| iterations: Number of timesteps to run the model for. |
| controller_Elevator: elevator object to get K from, or None if we should |
| use Elevator. |
| observer_Elevator: elevator object to use for the observer, or None if we should |
| use the actual state. |
| """ |
| |
| if controller_elevator is None: |
| controller_elevator = elevator |
| |
| vbat = 10.0 |
| if self.t: |
| initial_t = self.t[-1] + elevator.dt |
| else: |
| initial_t = 0 |
| for i in xrange(iterations): |
| X_hat = elevator.X |
| if observer_elevator is not None: |
| X_hat = observer_elevator.X_hat |
| self.x_hat.append(observer_elevator.X_hat[0, 0]) |
| gravity_compensation = 9.8 * elevator.mass * elevator.r / elevator.G / elevator.Kt * elevator.resistance |
| |
| U = controller_elevator.K * (goal - X_hat) |
| U[0, 0] = numpy.clip(U[0, 0], -vbat , vbat ) |
| self.x.append(elevator.X[0, 0]) |
| if self.v: |
| last_v = self.v[-1] |
| else: |
| last_v = 0 |
| self.v.append(elevator.X[1, 0]) |
| self.a.append((self.v[-1] - last_v) / elevator.dt) |
| |
| if observer_elevator is not None: |
| observer_elevator.Y = elevator.Y |
| observer_elevator.CorrectObserver(U) |
| |
| elevator.Update(U - gravity_compensation) |
| |
| if observer_elevator is not None: |
| observer_elevator.PredictObserver(U) |
| |
| self.t.append(initial_t + i * elevator.dt) |
| self.u.append(U[0, 0]) |
| # if numpy.abs((goal - X_hat)[0:2, 0]).sum() < .025: |
| # print "Time: ", self.t[-1] |
| # break |
| |
| print "Time: ", self.t[-1] |
| |
| |
| def Plot(self): |
| pylab.subplot(3, 1, 1) |
| pylab.plot(self.t, self.x, label='x') |
| pylab.plot(self.t, self.x_hat, label='x_hat') |
| pylab.legend() |
| |
| pylab.subplot(3, 1, 2) |
| pylab.plot(self.t, self.u, label='u') |
| |
| pylab.subplot(3, 1, 3) |
| pylab.plot(self.t, self.a, label='a') |
| |
| pylab.legend() |
| pylab.show() |
| |
| |
| def main(argv): |
| loaded_mass = 7+4.0 |
| #loaded_mass = 0 |
| #observer_elevator = None |
| |
| # Test moving the Elevator |
| initial_X = numpy.matrix([[0.0], [0.0]]) |
| up_R = numpy.matrix([[0.4572], [0.0], [0.0]]) |
| down_R = numpy.matrix([[0.0], [0.0], [0.0]]) |
| totemass = 3.54 |
| scenario_plotter = ScenarioPlotter() |
| |
| elevator_controller = IntegralElevator(mass=4*totemass + loaded_mass) |
| observer_elevator = IntegralElevator(mass=4*totemass + loaded_mass) |
| |
| for i in xrange(0, 7): |
| elevator = Elevator(mass=i*totemass + loaded_mass) |
| print 'Actual poles are', numpy.linalg.eig(elevator.A - elevator.B * elevator_controller.K[0, 0:2])[0] |
| |
| elevator.X = initial_X |
| scenario_plotter.run_test(elevator, goal=up_R, controller_elevator=elevator_controller, |
| observer_elevator=observer_elevator, iterations=200) |
| scenario_plotter.run_test(elevator, goal=down_R, controller_elevator=elevator_controller, |
| observer_elevator=observer_elevator, iterations=200) |
| |
| scenario_plotter.Plot() |
| |
| # Write the generated constants out to a file. |
| if len(argv) != 5: |
| print "Expected .h file name and .cc file name for the Elevator and integral elevator." |
| else: |
| design_mass = 4*totemass + loaded_mass |
| elevator = Elevator("Elevator", mass=design_mass) |
| loop_writer = control_loop.ControlLoopWriter("Elevator", [elevator], |
| namespaces=['bot3', 'control_loops']) |
| if argv[1][-3:] == '.cc': |
| loop_writer.Write(argv[2], argv[1]) |
| else: |
| loop_writer.Write(argv[1], argv[2]) |
| |
| integral_elevator = IntegralElevator("IntegralElevator", mass=design_mass) |
| integral_loop_writer = control_loop.ControlLoopWriter("IntegralElevator", [integral_elevator], |
| namespaces=['bot3', 'control_loops']) |
| if argv[3][-3:] == '.cc': |
| integral_loop_writer.Write(argv[4], argv[3]) |
| else: |
| integral_loop_writer.Write(argv[3], argv[4]) |
| |
| if __name__ == '__main__': |
| sys.exit(main(sys.argv)) |