Unpredictable learning of neural network based controller for dc motor

Specific Domains Machine Learning
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1

Hello,

I am new to the Julia language. I am trying to make neural network based position controller using Julia libraries. My code is given below.

J = 0.1999
Ke = 2.1918
Kt = 38.185
L = 0.020453
R = 3.9694
Tq = 0.20142
b = 0.37219

function dc_motor(du, u, h, p, t)
    
    i, w, pos, pd, pdd, vin = u

    #vin = p(t)

    hd1 = h(p, t - 0.01)[2]
    hd2 = h(p, t - 0.02)[2]

    du[1] = (vin - R*i - Ke*w)/L

    du[2] = (Kt*i - b*w - Tq)/J

    du[3] = w

    du[4] = hd1

    du[5] = hd2

end

function dc_motor_controller(du, u, h, p, t)
    voltage = 0
    dc_motor(du, u[1:6], h, t->voltage, t)
end

controller = FastChain((x, p) -> x, FastDense(4, 32, tanh), FastDense(32, 16, tanh), FastDense(16, 1))
weights = initial_params(controller)

h(p, t) = zeros(6)
lags = [0.02]

u0 = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
params  = weights
tspan = (0.0, 0.5)
N = 50
tsteps = range(tspan[1], length = N, tspan[2])
dt = (tspan[2] - tspan[1]) / N

prob = DDEProblem(dc_motor_controller, u0, h, tspan, params; constant_lags=lags)

function control_loop_new!(integrator)

    voltage = controller([integrator.u[3], integrator.u[4], integrator.u[5], integrator.p[end]], integrator.p[1:end-1])[1]

    if abs(voltage) >= 12
        voltage = 12* (abs(voltage)/voltage)
    end

    integrator.u[6] = voltage

end

cb_controller = DiscreteCallback(condition, control_loop_new!)


function predict_neuralode(p, angle)
    u0 = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
    tmp_prob = remake(prob, u0 = u0, p = vcat(p, angle))
    solve(tmp_prob, MethodOfSteps(Tsit5()), callback = cb_controller, tstops=timesteps, sensealg = ReverseDiffAdjoint(), )
end

function loss_neuralode(p)

    angle = deg2rad(45.0)
    pred = predict_neuralode(p, angle)
    pos = pred[3, :]
    voltage = pred[6, :]
    loss = sum((pos.-angle).^2)

    return loss, pred, pos, voltage, angle
end


index = 0 # training epoch counter

# callback function after each training epoch
callback = function (p, l, pred, pos, voltage, angle; doplot = true)
  global index += 1

  # ouput every few epochs
  if index % 50 == 0

    goal_position = ones(size(pred.t)[1])*rad2deg(angle)

    println("loss:", l," angle:", angle)
    plot(pred.t, rad2deg.(pos), label = ["position"])
    display(plot!(pred.t, goal_position, label = ["goal position"]))

    display(plot(pred.t, voltage, label = ["voltage"]))
  end

  return false

end

result = DiffEqFlux.sciml_train(
  loss_neuralode,
  weights,
  ADAM(0.05),
  cb = callback,
  maxiters = 1500,
  save_best=true
)

The problem is the controller learning it some times and not learning another time. I didn’t understand why it failing to learn sometimes. Is it because it need more iterations for learning a better control input.

The console log while controller learn to move towards the target position is given below.

`**loss:32.92571892751448 angle:0.7853981633974483
loss:32.627985828601574 angle:0.7853981633974483
loss:32.66226410447133 angle:0.7853981633974483
loss:32.567279853922514 angle:0.7853981633974483
loss:32.39154175827185 angle:0.7853981633974483
loss:32.81732092780774 angle:0.7853981633974483
loss:32.68729051161607 angle:0.7853981633974483
loss:32.74095819476493 angle:0.7853981633974483
loss:32.68435789697162 angle:0.7853981633974483
loss:33.09537254216951 angle:0.7853981633974483
loss:32.21350057852734 angle:0.7853981633974483
loss:33.71009342429282 angle:0.7853981633974483
loss:20.667760968747295 angle:0.7853981633974483
loss:20.65695448742362 angle:0.7853981633974483
loss:20.656843169457485 angle:0.7853981633974483
loss:20.65684311701577 angle:0.7853981633974483
loss:20.65684312504848 angle:0.7853981633974483
loss:20.6568431080726 angle:0.7853981633974483
loss:20.656843096951825 angle:0.7853981633974483
loss:20.65684310399092 angle:0.7853981633974483
loss:20.6568431122952 angle:0.7853981633974483
loss:20.656843098994212 angle:0.7853981633974483
loss:20.656843072282655 angle:0.7853981633974483
loss:20.65684304326965 angle:0.7853981633974483
loss:20.656843033931708 angle:0.7853981633974483
loss:20.656843053280774 angle:0.7853981633974483
loss:20.656843033519785 angle:0.7853981633974483**`

The console log while controller fail to move towards the target position is given below.


loss:32.641555388495185 angle:0.7853981633974483
loss:32.39069355004289 angle:0.7853981633974483
loss:32.43803035943642 angle:0.7853981633974483
loss:32.44203212699004 angle:0.7853981633974483
loss:32.325860035952495 angle:0.7853981633974483
loss:32.51288608170606 angle:0.7853981633974483
loss:32.4815533535547 angle:0.7853981633974483
loss:32.52985186829405 angle:0.7853981633974483
loss:32.46712305262051 angle:0.7853981633974483
loss:32.458913219436454 angle:0.7853981633974483
loss:32.445410725124525 angle:0.7853981633974483
loss:32.32018348205613 angle:0.7853981633974483
loss:32.38906862376797 angle:0.7853981633974483
loss:32.41120510538121 angle:0.7853981633974483
loss:32.48788975351786 angle:0.7853981633974483
loss:32.343650732335576 angle:0.7853981633974483
loss:32.30791129886353 angle:0.7853981633974483
loss:32.34361485838685 angle:0.7853981633974483
loss:32.328218206659635 angle:0.7853981633974483
loss:32.30852924469172 angle:0.7853981633974483
loss:32.345039342464716 angle:0.7853981633974483
loss:32.43607365411419 angle:0.7853981633974483
loss:32.36205242715388 angle:0.7853981633974483
loss:32.44062731662369 angle:0.7853981633974483
loss:32.50512118025965 angle:0.7853981633974483
loss:32.26274936510309 angle:0.7853981633974483
loss:32.30490991398758 angle:0.7853981633974483
loss:32.44811765382228 angle:0.7853981633974483
loss:32.48192486772814 angle:0.7853981633974483
loss:32.50304027000976 angle:0.7853981633974483

I really interested to investigate further deep into this issue. Any suggestions or help will be highly appreciated.

2

That would just mean that the learning rate might be too high.

3

Thanks for the suggestion. I will reduce the learning rate and examine the result.