| #!/usr/bin/python |
| |
| import control_loop |
| import controls |
| import polytope |
| import polydrivetrain |
| import numpy |
| import math |
| import sys |
| import matplotlib |
| from matplotlib import pylab |
| |
| |
| class Arm(control_loop.ControlLoop): |
| def __init__(self, name="Arm", mass=None): |
| super(Arm, 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 arm |
| 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 = (44.0 / 12.0) * (54.0 / 14.0) * (54.0 / 14.0) * (44.0 / 20.0) * (72.0 / 16.0) |
| # Fridge arm length |
| self.r = 32 * 0.0254 |
| # Control loop time step |
| self.dt = 0.005 |
| |
| # Arm moment of inertia |
| self.J = self.r * self.mass |
| |
| # Arm left/right spring constant (N*m / radian) |
| self.spring = 100.0 |
| |
| # State is [average position, average velocity, |
| # position difference/2, velocity difference/2] |
| # Position difference is 1 - 2 |
| # Input is [Voltage 1, Voltage 2] |
| |
| self.C1 = self.spring / (self.J * 0.5) |
| self.C2 = self.Kt * self.G / (self.J * 0.5 * self.R) |
| self.C3 = self.G * self.G * self.Kt / (self.R * self.J * 0.5 * self.Kv) |
| |
| self.A_continuous = numpy.matrix( |
| [[0, 1, 0, 0], |
| [0, -self.C3, 0, 0], |
| [0, 0, 0, 1], |
| [0, 0, -self.C1 * 2.0, -self.C3]]) |
| |
| print 'Full speed is', self.C2 / self.C3 * 12.0 |
| |
| print 'Stall arm difference is', 12.0 * self.C2 / self.C1 |
| print 'Stall arm difference first principles is', self.stall_torque * self.G / self.spring |
| |
| print '5 degrees of arm error is', self.spring / self.r * (math.pi * 5.0 / 180.0) |
| |
| # Start with the unmodified input |
| self.B_continuous = numpy.matrix( |
| [[0, 0], |
| [self.C2 / 2.0, self.C2 / 2.0], |
| [0, 0], |
| [self.C2 / 2.0, -self.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) |
| |
| controlability = controls.ctrb(self.A, self.B) |
| print 'Rank of augmented controlability matrix.', numpy.linalg.matrix_rank( |
| controlability) |
| |
| q_pos = 0.02 |
| q_vel = 0.300 |
| q_pos_diff = 0.005 |
| q_vel_diff = 0.13 |
| 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 'Controller' |
| print self.K |
| |
| print 'Controller Poles' |
| 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]]) |
| |
| print 'Observer (Converted to a KF)', numpy.linalg.inv(self.A) * self.L |
| |
| self.InitializeState() |
| |
| |
| class IntegralArm(Arm): |
| def __init__(self, name="IntegralArm", mass=None): |
| super(IntegralArm, self).__init__(name=name, mass=mass) |
| |
| self.A_continuous_unaugmented = self.A_continuous |
| self.A_continuous = numpy.matrix(numpy.zeros((5, 5))) |
| self.A_continuous[0:4, 0:4] = self.A_continuous_unaugmented |
| self.A_continuous[1, 4] = self.C2 |
| |
| # Start with the unmodified input |
| self.B_continuous_unaugmented = self.B_continuous |
| self.B_continuous = numpy.matrix(numpy.zeros((5, 2))) |
| self.B_continuous[0:4, 0:2] = self.B_continuous_unaugmented |
| |
| self.C_unaugmented = self.C |
| self.C = numpy.matrix(numpy.zeros((2, 5))) |
| self.C[0:2, 0:4] = self.C_unaugmented |
| |
| self.A, self.B = self.ContinuousToDiscrete( |
| self.A_continuous, self.B_continuous, self.dt) |
| print 'A cont', self.A_continuous |
| print 'B cont', self.B_continuous |
| print 'A discrete', self.A |
| |
| q_pos = 0.08 |
| q_vel = 0.40 |
| |
| q_pos_diff = 0.08 |
| q_vel_diff = 0.40 |
| q_voltage = 6.0 |
| self.Q = numpy.matrix([[(q_pos ** 2.0), 0.0, 0.0, 0.0, 0.0], |
| [0.0, (q_vel ** 2.0), 0.0, 0.0, 0.0], |
| [0.0, 0.0, (q_pos_diff ** 2.0), 0.0, 0.0], |
| [0.0, 0.0, 0.0, (q_vel_diff ** 2.0), 0.0], |
| [0.0, 0.0, 0.0, 0.0, (q_voltage ** 2.0)]]) |
| |
| r_volts = 0.05 |
| self.R = numpy.matrix([[(r_volts ** 2.0), 0.0], |
| [0.0, (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) |
| |
| self.U_max = numpy.matrix([[12.0], [12.0]]) |
| self.U_min = numpy.matrix([[-12.0], [-12.0]]) |
| |
| self.K_unaugmented = self.K |
| self.K = numpy.matrix(numpy.zeros((2, 5))) |
| self.K[0:2, 0:4] = self.K_unaugmented |
| self.K[0, 4] = 1 |
| self.K[1, 4] = 1 |
| print 'Kal', self.KalmanGain |
| self.L = self.A * self.KalmanGain |
| |
| 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(arm, initial_X, goal, max_separation_error=0.01, |
| show_graph=True, iterations=200, controller_arm=None, |
| observer_arm=None): |
| """Runs the arm 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: |
| arm: arm 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_arm: arm object to get K from, or None if we should |
| use arm. |
| observer_arm: arm object to use for the observer, or None if we should |
| use the actual state. |
| """ |
| |
| arm.X = initial_X |
| |
| if controller_arm is None: |
| controller_arm = arm |
| |
| if observer_arm is not None: |
| observer_arm.X_hat = initial_X + 0.01 |
| observer_arm.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 = arm.X |
| if observer_arm is not None: |
| X_hat = observer_arm.X_hat |
| x_hat_avg.append(observer_arm.X_hat[0, 0]) |
| x_hat_sep.append(observer_arm.X_hat[2, 0] * sep_plot_gain) |
| U = controller_arm.K * (goal - X_hat) |
| U = CapU(U) |
| x_avg.append(arm.X[0, 0]) |
| v_avg.append(arm.X[1, 0]) |
| x_sep.append(arm.X[2, 0] * sep_plot_gain) |
| v_sep.append(arm.X[3, 0]) |
| if observer_arm is not None: |
| observer_arm.PredictObserver(U) |
| arm.Update(U) |
| if observer_arm is not None: |
| observer_arm.Y = arm.Y |
| observer_arm.CorrectObserver(U) |
| |
| t.append(i * arm.dt) |
| u_left.append(U[0, 0]) |
| u_right.append(U[1, 0]) |
| |
| print numpy.linalg.inv(arm.A) |
| print "delta time is ", arm.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_arm 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 run_integral_test(arm, initial_X, goal, observer_arm, disturbance, |
| max_separation_error=0.01, show_graph=True, |
| iterations=400): |
| """Runs the integral control arm 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: |
| arm: arm object to use. |
| initial_X: starting state. |
| goal: goal state. |
| observer_arm: arm object to use for the observer. |
| show_graph: Whether or not to display a graph showing the changing |
| states and voltages. |
| iterations: Number of timesteps to run the model for. |
| disturbance: Voltage missmatch between controller and model. |
| """ |
| |
| arm.X = 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 = [] |
| u_error = [] |
| |
| sep_plot_gain = 100.0 |
| |
| unaugmented_goal = goal |
| goal = numpy.matrix(numpy.zeros((5, 1))) |
| goal[0:4, 0] = unaugmented_goal |
| |
| for i in xrange(iterations): |
| X_hat = observer_arm.X_hat[0:4] |
| |
| x_hat_avg.append(observer_arm.X_hat[0, 0]) |
| x_hat_sep.append(observer_arm.X_hat[2, 0] * sep_plot_gain) |
| |
| U = observer_arm.K * (goal - observer_arm.X_hat) |
| u_error.append(observer_arm.X_hat[4,0]) |
| U = CapU(U) |
| x_avg.append(arm.X[0, 0]) |
| v_avg.append(arm.X[1, 0]) |
| x_sep.append(arm.X[2, 0] * sep_plot_gain) |
| v_sep.append(arm.X[3, 0]) |
| |
| observer_arm.PredictObserver(U) |
| |
| arm.Update(U + disturbance) |
| observer_arm.Y = arm.Y |
| observer_arm.CorrectObserver(U) |
| |
| t.append(i * arm.dt) |
| u_left.append(U[0, 0]) |
| u_right.append(U[1, 0]) |
| |
| print 'End is', observer_arm.X_hat[4, 0] |
| |
| 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_arm 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.plot(t, u_error, label='u error') |
| pylab.legend() |
| pylab.show() |
| |
| |
| def main(argv): |
| loaded_mass = 25 |
| #loaded_mass = 0 |
| arm = Arm(mass=13 + loaded_mass) |
| #arm_controller = Arm(mass=13 + 15) |
| #observer_arm = Arm(mass=13 + 15) |
| #observer_arm = None |
| |
| integral_arm = IntegralArm(mass=13 + loaded_mass) |
| integral_arm.X_hat[0, 0] += 0.02 |
| integral_arm.X_hat[2, 0] += 0.02 |
| integral_arm.X_hat[4] = 0 |
| |
| # Test moving the arm with constant separation. |
| initial_X = numpy.matrix([[0.0], [0.0], [0.0], [0.0]]) |
| R = numpy.matrix([[0.0], [0.0], [0.0], [0.0]]) |
| run_integral_test(arm, initial_X, R, integral_arm, disturbance=2) |
| |
| # Write the generated constants out to a file. |
| if len(argv) != 5: |
| print "Expected .h file name and .cc file name for the arm and augmented arm." |
| else: |
| arm = Arm("Arm", mass=13) |
| loop_writer = control_loop.ControlLoopWriter("Arm", [arm]) |
| if argv[1][-3:] == '.cc': |
| loop_writer.Write(argv[2], argv[1]) |
| else: |
| loop_writer.Write(argv[1], argv[2]) |
| |
| integral_arm = IntegralArm("IntegralArm", mass=13) |
| loop_writer = control_loop.ControlLoopWriter("IntegralArm", [integral_arm]) |
| if argv[3][-3:] == '.cc': |
| loop_writer.Write(argv[4], argv[3]) |
| else: |
| loop_writer.Write(argv[3], argv[4]) |
| |
| if __name__ == '__main__': |
| sys.exit(main(sys.argv)) |