| #!/usr/bin/python |
| |
| import control_loop |
| import controls |
| import polytope |
| import polydrivetrain |
| 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 = 0.476 |
| # Stall Current in Amps |
| self.stall_current = 80.730 |
| # Free Speed in RPM |
| self.free_speed = 13906.0 |
| # Free Current in Amps |
| self.free_current = 5.820 |
| # Mass of the elevator |
| if mass is None: |
| self.mass = 13.0 |
| else: |
| self.mass = mass |
| |
| # 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) / |
| (12.0 - self.R * self.free_current)) |
| # Torque constant |
| self.Kt = self.stall_torque / self.stall_current |
| # Gear ratio |
| self.G = (56.0 / 12.0) * (84.0 / 14.0) |
| # Pulley diameter |
| self.r = 32 * 0.005 / numpy.pi / 2.0 |
| # Control loop time step |
| self.dt = 0.005 |
| |
| # Elevator left/right spring constant (N/m) |
| self.spring = 800.0 |
| |
| # State is [average position, average velocity, |
| # position difference/2, velocity difference/2] |
| # Input is [V_left, V_right] |
| |
| C1 = self.spring / (self.mass * 0.5) |
| C2 = self.Kt * self.G / (self.mass * 0.5 * self.r * self.R) |
| C3 = self.G * self.G * self.Kt / ( |
| self.R * self.r * self.r * self.mass * 0.5 * self.Kv) |
| |
| self.A_continuous = numpy.matrix( |
| [[0, 1, 0, 0], |
| [0, -C3, 0, 0], |
| [0, 0, 0, 1], |
| [0, 0, -C1 * 2.0, -C3]]) |
| |
| print "Full speed is", C2 / C3 * 12.0 |
| |
| # Start with the unmodified input |
| self.B_continuous = numpy.matrix( |
| [[0, 0], |
| [C2 / 2.0, C2 / 2.0], |
| [0, 0], |
| [C2 / 2.0, -C2 / 2.0]]) |
| |
| self.C = numpy.matrix([[1, 0, 1, 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) |
| |
| print self.A |
| |
| controlability = controls.ctrb(self.A, self.B); |
| print "Rank of augmented controlability matrix.", numpy.linalg.matrix_rank( |
| controlability) |
| |
| q_pos = 0.02 |
| q_vel = 0.400 |
| q_pos_diff = 0.01 |
| q_vel_diff = 0.45 |
| self.Q = numpy.matrix([[(1.0 / (q_pos ** 2.0)), 0.0, 0.0, 0.0], |
| [0.0, (1.0 / (q_vel ** 2.0)), 0.0, 0.0], |
| [0.0, 0.0, (1.0 / (q_pos_diff ** 2.0)), 0.0], |
| [0.0, 0.0, 0.0, (1.0 / (q_vel_diff ** 2.0))]]) |
| |
| self.R = numpy.matrix([[(1.0 / (12.0 ** 2.0)), 0.0], |
| [0.0, 1.0 / (12.0 ** 2.0)]]) |
| self.K = controls.dlqr(self.A, self.B, self.Q, self.R) |
| print self.K |
| |
| print numpy.linalg.eig(self.A - self.B * self.K)[0] |
| |
| self.rpl = 0.20 |
| self.ipl = 0.05 |
| 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], [12.0]]) |
| self.U_min = numpy.matrix([[-12.0], [-12.0]]) |
| |
| self.InitializeState() |
| |
| |
| def CapU(U): |
| if U[0, 0] - U[1, 0] > 24: |
| return numpy.matrix([[12], [-12]]) |
| elif U[0, 0] - U[1, 0] < -24: |
| return numpy.matrix([[-12], [12]]) |
| else: |
| max_u = max(U[0, 0], U[1, 0]) |
| min_u = min(U[0, 0], U[1, 0]) |
| if max_u > 12: |
| return U - (max_u - 12) |
| if min_u < -12: |
| return U - (min_u + 12) |
| return U |
| |
| |
| def run_test(elevator, initial_X, goal, max_separation_error=0.01, |
| show_graph=True, iterations=200, controller_elevator=None, |
| observer_elevator=None): |
| """Runs the elevator plant with an initial condition and goal. |
| |
| The tests themselves are not terribly sophisticated; I just test for |
| whether the goal has been reached and whether the separation goes |
| outside of the initial and goal values by more than max_separation_error. |
| Prints out something for a failure of either condition and returns |
| False if tests fail. |
| Args: |
| elevator: elevator object to use. |
| initial_X: starting state. |
| goal: goal state. |
| show_graph: Whether or not to display a graph showing the changing |
| states and voltages. |
| 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. |
| """ |
| |
| elevator.X = initial_X |
| |
| if controller_elevator is None: |
| controller_elevator = elevator |
| |
| if observer_elevator is not None: |
| observer_elevator.X_hat = initial_X + 0.01 |
| observer_elevator.X_hat = initial_X |
| |
| # Various lists for graphing things. |
| t = [] |
| x_avg = [] |
| x_sep = [] |
| x_hat_avg = [] |
| x_hat_sep = [] |
| v_avg = [] |
| v_sep = [] |
| u_left = [] |
| u_right = [] |
| |
| sep_plot_gain = 100.0 |
| |
| for i in xrange(iterations): |
| X_hat = elevator.X |
| if observer_elevator is not None: |
| X_hat = observer_elevator.X_hat |
| x_hat_avg.append(observer_elevator.X_hat[0, 0]) |
| x_hat_sep.append(observer_elevator.X_hat[2, 0] * sep_plot_gain) |
| U = controller_elevator.K * (goal - X_hat) |
| U = CapU(U) |
| x_avg.append(elevator.X[0, 0]) |
| v_avg.append(elevator.X[1, 0]) |
| x_sep.append(elevator.X[2, 0] * sep_plot_gain) |
| v_sep.append(elevator.X[3, 0]) |
| if observer_elevator is not None: |
| observer_elevator.PredictObserver(U) |
| elevator.Update(U) |
| if observer_elevator is not None: |
| observer_elevator.Y = elevator.Y |
| observer_elevator.CorrectObserver(U) |
| |
| t.append(i * elevator.dt) |
| u_left.append(U[0, 0]) |
| u_right.append(U[1, 0]) |
| |
| print numpy.linalg.inv(elevator.A) |
| print "delta time is ", elevator.dt |
| print "Velocity at t=0 is ", x_avg[0], v_avg[0], x_sep[0], v_sep[0] |
| print "Velocity at t=1+dt is ", x_avg[1], v_avg[1], x_sep[1], v_sep[1] |
| |
| if show_graph: |
| pylab.subplot(2, 1, 1) |
| pylab.plot(t, x_avg, label='x avg') |
| pylab.plot(t, x_sep, label='x sep') |
| if observer_elevator is not None: |
| pylab.plot(t, x_hat_avg, label='x_hat avg') |
| pylab.plot(t, x_hat_sep, label='x_hat sep') |
| pylab.legend() |
| |
| pylab.subplot(2, 1, 2) |
| pylab.plot(t, u_left, label='u left') |
| pylab.plot(t, u_right, label='u right') |
| pylab.legend() |
| pylab.show() |
| |
| |
| def main(argv): |
| loaded_mass = 25 |
| #loaded_mass = 0 |
| elevator = Elevator(mass=13 + loaded_mass) |
| elevator_controller = Elevator(mass=13 + 15) |
| observer_elevator = Elevator(mass=13 + 15) |
| #observer_elevator = None |
| |
| # Test moving the elevator with constant separation. |
| initial_X = numpy.matrix([[0.0], [0.0], [0.01], [0.0]]) |
| #initial_X = numpy.matrix([[0.0], [0.0], [0.00], [0.0]]) |
| R = numpy.matrix([[1.0], [0.0], [0.0], [0.0]]) |
| run_test(elevator, initial_X, R, controller_elevator=elevator_controller, |
| observer_elevator=observer_elevator) |
| |
| # Write the generated constants out to a file. |
| if len(argv) != 3: |
| print "Expected .h file name and .cc file name for the elevator." |
| else: |
| elevator = Elevator("Elevator") |
| loop_writer = control_loop.ControlLoopWriter("Elevator", [elevator]) |
| 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)) |