Added integral control to the arm.
Change-Id: I866d2749837841f3f8d34e6ffe0e1a0b11c4120e
diff --git a/frc971/control_loops/python/arm.py b/frc971/control_loops/python/arm.py
index 812a0c3..e17990a 100755
--- a/frc971/control_loops/python/arm.py
+++ b/frc971/control_loops/python/arm.py
@@ -10,6 +10,7 @@
import matplotlib
from matplotlib import pylab
+
class Arm(control_loop.ControlLoop):
def __init__(self, name="Arm", mass=None):
super(Arm, self).__init__(name)
@@ -52,19 +53,19 @@
# Position difference is 1 - 2
# Input is [Voltage 1, Voltage 2]
- C1 = self.spring / (self.J * 0.5)
- C2 = self.Kt * self.G / (self.J * 0.5 * self.R)
- C3 = self.G * self.G * self.Kt / (self.R * self.J * 0.5 * self.Kv)
+ 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, -C3, 0, 0],
+ [0, -self.C3, 0, 0],
[0, 0, 0, 1],
- [0, 0, -C1 * 2.0, -C3]])
+ [0, 0, -self.C1 * 2.0, -self.C3]])
- print 'Full speed is', C2 / C3 * 12.0
+ print 'Full speed is', self.C2 / self.C3 * 12.0
- print 'Stall arm difference is', 12.0 * C2 / C1
+ 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)
@@ -72,9 +73,9 @@
# Start with the unmodified input
self.B_continuous = numpy.matrix(
[[0, 0],
- [C2 / 2.0, C2 / 2.0],
+ [self.C2 / 2.0, self.C2 / 2.0],
[0, 0],
- [C2 / 2.0, -C2 / 2.0]])
+ [self.C2 / 2.0, -self.C2 / 2.0]])
self.C = numpy.matrix([[1, 0, 1, 0],
[1, 0, -1, 0]])
@@ -118,6 +119,65 @@
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()
@@ -225,31 +285,125 @@
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)
+ #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], [0.01], [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(arm, initial_X, R, controller_arm=arm_controller,
- observer_arm=observer_arm)
+ 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) != 3:
- print "Expected .h file name and .cc file name for the arm."
+ if len(argv) != 5:
+ print "Expected .h file name and .cc file name for the arm and augmented arm."
else:
- arm = Arm("Arm", 2)
+ 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))