CS909/maglev.html at master · foxtrotmike/CS909 · GitHub

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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Magnetic Levitation: Train Bang-Bang Controller (TF.js)</title>
<script src="https://cdn.jsdelivr.net/npm/@tensorflow/tfjs@4.16.0"></script>
<style>
  body { font-family: system-ui, -apple-system, Segoe UI, Roboto, Arial, sans-serif; background:#fff; color:#111; margin:18px; }
  .row { display:flex; gap:16px; flex-wrap:wrap; align-items:flex-start; }
  .card { border:1px solid #ddd; border-radius:12px; padding:12px; }
  label { display:block; margin:10px 0 4px; }
  input[type="range"] { width:100%; }
  button { padding:8px 10px; border-radius:10px; border:1px solid #bbb; background:#f7f7f7; cursor:pointer; }
  button:active { transform: translateY(1px); }
  .controls { min-width: 420px; }
  .mono { font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", monospace; }
  .small { color:#444; font-size:13px; line-height:1.35; }
  canvas { border:1px solid #ddd; border-radius:12px; background:#fff; }
  .pill { display:inline-block; padding:2px 8px; border:1px solid #ddd; border-radius:999px; margin-right:6px; }
  .grid2 { display:grid; grid-template-columns: 1fr 1fr; gap:10px; }
</style>
</head>
<body>

<h2>MagLev: learn a on–off controller model with position-only sensing</h2>
<div class="small">
In this simulation, a magnetic levitation system learns a simple on–off control program using only a position sensor, estimating motion from recent observations and adjusting when to fire the magnet so the ball stays near a target height. The controller observes only position and infers speed from recent measurements as a change in position over time, optionally smoothed. It should turn the magnet on when the target is above the current position or when the ball is moving downward, and turn it off when the ball is already above the target and moving upward, so it fires whenever upward correction is needed and stays off when the motion is already favourable. The controller computes a score from the position error and estimated velocity, with coefficients (kp and kv) that are learned to minimise tracking error over time. The forward action is a real bang-bang program that switches the magnet fully on or off, while training uses a straight-through estimator so gradients can still be propagated through this hard decision.
  <br>
  Representation: Input is position of the ball (x) and the output is an action A (1 or 0) to switch the magnet on or off
  <br>
  Estimate velocity from position: <span class="mono">v_hat = (x − x_prev)/dt</span> (optionally smooth with moving averages).<br>
  Controller model score parameterised by kp and kv: <span class="mono">z = kp(x* − x) − kv v_hat</span>.<br>
  Output Action (Magnetic on or off): <span class="mono">A = 1[z&gt;0]</span> (bang-bang).<br>
  <br>
  Evaluation:
  <br>
  Loss is essentially the absolute difference between the position of the ball and the and target position over time
  <br>
  Optimization:
  <br>
  Optimize the loss with respect to model parameters (Kp and Kv) Using Gradient Descent with a straight-through estimator (STE) as the model is non-differentiable (due to the step function) so we use a surrogate gradient from <span class="mono">sigmoid(βz)</span>.
</div>

<div class="row" style="margin-top:14px;">
  <div class="card controls">
    <h3 style="margin:0 0 6px;">Controls</h3>

    <label>Initial height x0: <span class="mono" id="x0Val">5.00</span></label>
    <input id="x0" type="range" min="0" max="10" step="0.01" value="5">

    <label>Initial true velocity v0 (physics only): <span class="mono" id="v0Val">0.00</span></label>
    <input id="v0" type="range" min="-10" max="10" step="0.01" value="0">

    <label>Target height x*: <span class="mono" id="tgtVal">5.00</span></label>
    <input id="tgt" type="range" min="0.5" max="9.5" step="0.01" value="5">

    <label>Training: <span class="mono" id="trainVal">ON</span></label>
    <input id="train" type="range" min="0" max="1" step="1" value="1">

    <label>Simulation speed: <span class="mono" id="speedVal">10</span> steps/frame</label>
    <input id="speed" type="range" min="1" max="40" step="1" value="10">

    <label>position sensor smoothing (EMA on v_hat): <span class="mono" id="smoothVal">0.30</span></label>
    <input id="smooth" type="range" min="0" max="0.95" step="0.01" value="0.30">

    <label>STE sharpness β (surrogate slope): <span class="mono" id="betaVal">8</span></label>
    <input id="beta" type="range" min="1" max="40" step="1" value="8">

    <div style="display:flex; gap:10px; margin-top:12px;">
      <button id="resetBtn">Reset simulation</button>
      <button id="toggleBtn">Pause</button>
    </div>

    <div class="grid2" style="margin-top:10px;">
      <button id="resetParamsBtn">Reset parameters</button>
      <button id="randomParamsBtn">Randomise parameters</button>
    </div>

    <div style="margin-top:12px;">
      <div class="small">Learned parameters:</div>
      <div style="margin-top:6px;">
        <span class="pill mono" id="kpVal">kp=0.800</span>
        <span class="pill mono" id="kvVal">kv=0.200</span>
      </div>
      <div class="small" style="margin-top:10px;">
        Mode:
        <span class="mono" id="modeText">TRAINING: hard forward + STE gradients</span>
      </div>

      <div class="small" style="margin-top:10px;">
        Hard control program (used in testing, and also as the forward pass in training):
        <div class="mono" style="margin-top:6px;">
          v_hat = (x − x_prev)/dt<br>
          z = kp(x* − x) − kv v_hat<br>
          if z &gt; 0: A = 1 else: A = 0
        </div>
      </div>
    </div>

    <div class="small" style="margin-top:10px;">
      Loss used in training (per episode):
      <div class="mono" style="margin-top:6px;">
        L = (1/T) Σ_t w_t |x_t − x*|,  w_t increases with t
      </div>
    </div>
  </div>

  <div class="card">
    <h3 style="margin:0 0 8px;">World view</h3>
    <canvas id="world" width="260" height="520"></canvas>
    <div class="small" style="margin-top:8px;">
      Blue line: target. Black circle: ball. Red bar: magnet action A.
    </div>
  </div>

  <div class="card">
    <h3 style="margin:0 0 8px;">Plots</h3>
    <canvas id="plot" width="820" height="520"></canvas>
    <div class="small" style="margin-top:8px;">
      Top: x* (blue) and x (black). Middle: true v (green) and inferred v_hat (grey). Bottom: A (red).
    </div>
  </div>
</div>

<script>
/* -----------------------------
   Physics
   ----------------------------- */
const m = 1.0;
const g = 9.8;
const F = 2.0 * g;
const dt = 0.05;

function stepJS(x, v, A){
  const a = (A * F / m) - g;
  let v1 = v + a * dt;
  let x1 = x + v * dt + 0.5 * a * dt * dt;

  // enforce physical bounds
  if(x1 <= 0.0){
    x1 = 0.0;
    v1 = 0.0;
  } else if(x1 >= 10.0){
    x1 = 10.0;
    v1 = 0.0;
  }

  return {x: x1, v: v1};
}

/* -----------------------------
   Learnable parameters (TF.js)
   ----------------------------- */
let kp = tf.variable(tf.scalar(0.8, "float32"));
let kv = tf.variable(tf.scalar(0.2, "float32"));
const opt = tf.train.adam(0.05);

/* -----------------------------
   Straight-through Heaviside with sigmoid surrogate gradient
   forward: y = 1[x > 0]
   backward: dy/dx = sigmoid(beta*x)*(1-sigmoid(beta*x))*beta
   ----------------------------- */
function steHeaviside(x, beta){
  return tf.customGrad((xTensor, save) => {
    const b = tf.scalar(beta, "float32");
    const z = xTensor.mul(b);
    const s = tf.sigmoid(z);
    const y = xTensor.greater(tf.scalar(0)).toFloat();
    save([s, b]);

    const gradFunc = (dy, saved) => {
      const [sSaved, bSaved] = saved;
      const ds_dx = sSaved.mul(tf.scalar(1).sub(sSaved)).mul(bSaved);
      return dy.mul(ds_dx);
    };
    return { value: y, gradFunc };
  })(x);
}

/* -----------------------------
   Training (differentiable unroll)
   Controller observes position only and estimates v_hat from x history.
   Forward A is hard, gradients are straight-through.
   ----------------------------- */
function trainOneBatch(alpha, beta){
  const lossTensor = opt.minimize(() => tf.tidy(() => {
    let x = tf.scalar(Math.random() * 10.0);
    let v = tf.scalar((Math.random() - 0.5) * 20.0);
    const xStar = tf.scalar(0.5 + Math.random() * 9.0);

    let xPrev = x;
    let vHatSmooth = tf.scalar(0.0);

    const T = 120;
    let total = tf.scalar(0.0);

    for(let t=0; t<T; t++){
      const vHat = x.sub(xPrev).div(dt);
      vHatSmooth = vHatSmooth.mul(alpha).add(vHat.mul(1.0 - alpha));

      const zCtrl = kp.mul(xStar.sub(x)).sub(kv.mul(vHatSmooth));
      const A = steHeaviside(zCtrl, beta);

      const a = A.mul(F).sub(g);
      const v1 = v.add(a.mul(dt));
      const x1 = x.add(v.mul(dt)).add(a.mul(0.5*dt*dt)).clipByValue(0.0, 10.0);

      xPrev = x;
      x = x1;
      v = v1;

      const err = x.sub(xStar).abs();
      const w = 0.2 + 0.8 * (t / (T - 1)); // late-step emphasis
      total = total.add(err.mul(w));
    }
    return total.div(T);
  }), true);

  const lossVal = lossTensor.dataSync()[0];
  lossTensor.dispose();
  return lossVal;
}

/* -----------------------------
   UI elements
   ----------------------------- */
const x0Slider = document.getElementById("x0");
const v0Slider = document.getElementById("v0");
const tgtSlider = document.getElementById("tgt");
const trainSlider = document.getElementById("train");
const speedSlider = document.getElementById("speed");
const smoothSlider = document.getElementById("smooth");
const betaSlider = document.getElementById("beta");

const x0Val = document.getElementById("x0Val");
const v0Val = document.getElementById("v0Val");
const tgtVal = document.getElementById("tgtVal");
const trainVal = document.getElementById("trainVal");
const speedVal = document.getElementById("speedVal");
const smoothVal = document.getElementById("smoothVal");
const betaVal = document.getElementById("betaVal");

const kpValSpan = document.getElementById("kpVal");
const kvValSpan = document.getElementById("kvVal");
const modeText = document.getElementById("modeText");

function syncLabels(){
  x0Val.textContent = (+x0Slider.value).toFixed(2);
  v0Val.textContent = (+v0Slider.value).toFixed(2);
  tgtVal.textContent = (+tgtSlider.value).toFixed(2);
  trainVal.textContent = (+trainSlider.value === 1) ? "ON" : "OFF";
  speedVal.textContent = (+speedSlider.value).toFixed(0);
  smoothVal.textContent = (+smoothSlider.value).toFixed(2);
  betaVal.textContent = (+betaSlider.value).toFixed(0);
}
[x0Slider, v0Slider, tgtSlider, trainSlider, speedSlider, smoothSlider, betaSlider].forEach(el => el.addEventListener("input", syncLabels));
syncLabels();

/* -----------------------------
   Simulation state (display) and position sensor memory
   ----------------------------- */
let sim = {
  x: +x0Slider.value,
  v: +v0Slider.value,
  xStar: +tgtSlider.value,
  A: 0.0,
  running: true,

  xPrevObs: +x0Slider.value,
  vHatSmooth: 0.0
};

const N = 300;
let hist = {x:[], v:[], xStar:[], A:[], vHat:[]};

function historyReset(){
  hist = {x:[], v:[], xStar:[], A:[], vHat:[]};
}

function historyPush(vHat){
  hist.x.push(sim.x);
  hist.v.push(sim.v);
  hist.xStar.push(sim.xStar);
  hist.A.push(sim.A);
  hist.vHat.push(vHat);
  if(hist.x.length > N){
    hist.x.shift(); hist.v.shift(); hist.xStar.shift(); hist.A.shift(); hist.vHat.shift();
  }
}

/* -----------------------------
   Buttons
   ----------------------------- */
document.getElementById("resetBtn").addEventListener("click", () => {
  sim.x = +x0Slider.value;
  sim.v = +v0Slider.value;
  sim.xStar = +tgtSlider.value;
  sim.xPrevObs = sim.x;
  sim.vHatSmooth = 0.0;
  sim.A = 0.0;
  historyReset();
});

document.getElementById("toggleBtn").addEventListener("click", (e) => {
  sim.running = !sim.running;
  e.target.textContent = sim.running ? "Pause" : "Resume";
});

document.getElementById("resetParamsBtn").addEventListener("click", () => {
  tf.tidy(() => {
    kp.assign(tf.scalar(0.8));
    kv.assign(tf.scalar(0.2));
  });
});

document.getElementById("randomParamsBtn").addEventListener("click", () => {
  tf.tidy(() => {
    // mild randomisation so it does not explode too often
    const kpInit = (Math.random() - 0.5) * 3.0;  // ~[-1.5, 1.5]
    const kvInit = (Math.random() - 0.5) * 3.0;
    kp.assign(tf.scalar(kpInit));
    kv.assign(tf.scalar(kvInit));
  });
});

/* -----------------------------
   World view drawing
   ----------------------------- */
const world = document.getElementById("world");
const wctx = world.getContext("2d");

function drawWorld(){
  const W = world.width, H = world.height;
  wctx.clearRect(0,0,W,H);

  const yFromX = (x) => (H - 20) - (x/10.0) * (H - 40);

  // rail
  wctx.strokeStyle = "#bbb";
  wctx.lineWidth = 2;
  wctx.beginPath();
  wctx.moveTo(W/2, 20);
  wctx.lineTo(W/2, H-20);
  wctx.stroke();

  // target
  const yT = yFromX(sim.xStar);
  wctx.strokeStyle = "#1f77b4";
  wctx.lineWidth = 2;
  wctx.beginPath();
  wctx.moveTo(30, yT);
  wctx.lineTo(W-30, yT);
  wctx.stroke();

  // magnet block
  wctx.fillStyle = "#222";
  wctx.fillRect(W/2 - 40, 8, 80, 14);
  wctx.fillStyle = "#fff";
  wctx.font = "11px system-ui, sans-serif";
  wctx.fillText("MAGNET", W/2 - 28, 19);

  // ball
  const y = yFromX(sim.x);
  wctx.fillStyle = "#111";
  wctx.beginPath();
  wctx.arc(W/2, y, 14, 0, 2*Math.PI);
  wctx.fill();

  // action bar
  const barH = 170;
  const barX = W - 28, barY = H - 20 - barH;
  wctx.strokeStyle = "#bbb";
  wctx.lineWidth = 1;
  wctx.strokeRect(barX, barY, 10, barH);
  wctx.fillStyle = "#d62728";
  const filled = sim.A * barH;
  wctx.fillRect(barX, (H - 20) - filled, 10, filled);

  // labels
  wctx.fillStyle = "#111";
  wctx.font = "12px ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, monospace";
  wctx.fillText(`x=${sim.x.toFixed(2)}`, 10, 34);
  wctx.fillText(`v=${sim.v.toFixed(2)}`, 10, 50);
  wctx.fillText(`A=${sim.A.toFixed(2)}`, 10, 66);
  wctx.fillText(`v_hat=${sim.vHatSmooth.toFixed(2)}`, 10, 82);
}

/* -----------------------------
   Plotting: three panes
   ----------------------------- */
const plot = document.getElementById("plot");
const ctx = plot.getContext("2d");

function drawFrame(){
  const W = plot.width, H = plot.height;
  ctx.clearRect(0,0,W,H);

  const L = 56, R = 20, T = 16, B = 26;
  const innerW = W - L - R;
  const innerH = H - T - B;

  const gap = 12;
  const paneH = (innerH - 2*gap) / 3;

  const panes = [
    {y0: T,                 h: paneH, title: "Position x and target x* (0..10)"},
    {y0: T + paneH + gap,   h: paneH, title: "Velocity: true v (green) and inferred v_hat (grey)"},
    {y0: T + 2*(paneH+gap), h: paneH, title: "Controller A (hard, 0 or 1)"}
  ];

  ctx.font = "12px system-ui, sans-serif";
  ctx.fillStyle = "#111";

  for(const p of panes){
    ctx.strokeStyle = "#ccc";
    ctx.strokeRect(L, p.y0, innerW, p.h);
    ctx.fillText(p.title, 10, p.y0 + 12);

    ctx.strokeStyle = "#eee";
    for(let i=1;i<=4;i++){
      const yy = p.y0 + (p.h * i / 5);
      ctx.beginPath();
      ctx.moveTo(L, yy);
      ctx.lineTo(L + innerW, yy);
      ctx.stroke();
    }
  }

  ctx.fillStyle = "#444";
  ctx.fillText("time (recent →)", W/2 - 44, H - 8);

  return {L, innerW, panes};
}

function plotLine(arr, pane, yMap, strokeStyle, width){
  const W = plot.width;
  const L = 56, R = 20;
  const innerW = W - L - R;
  if(arr.length < 2) return;

  ctx.strokeStyle = strokeStyle;
  ctx.lineWidth = width;
  ctx.beginPath();
  for(let i=0;i<arr.length;i++){
    const x = L + innerW * (i / (N - 1));
    const y = pane.y0 + pane.h * yMap(arr[i]);
    if(i === 0) ctx.moveTo(x,y); else ctx.lineTo(x,y);
  }
  ctx.stroke();
  ctx.lineWidth = 1;
}

function drawPlots(){
  const frame = drawFrame();
  const panes = frame.panes;

  const yPos = (x) => 1.0 - (x / 10.0);
  const yVel = (v) => 1.0 - ((v + 10.0) / 20.0);
  const yAct = (a) => 1.0 - a;

  plotLine(hist.xStar, panes[0], yPos, "#1f77b4", 2);
  plotLine(hist.x,     panes[0], yPos, "#111111", 2);

  plotLine(hist.v,    panes[1], yVel, "#2ca02c", 2);
  plotLine(hist.vHat, panes[1], yVel, "#777777", 2);

  plotLine(hist.A, panes[2], yAct, "#d62728", 2);

  ctx.fillStyle = "#111";
  ctx.font = "12px system-ui, sans-serif";
  ctx.fillText("x* (blue), x (black)", 60, panes[0].y0 + panes[0].h - 6);
}

/* -----------------------------
   Main loop
   ----------------------------- */
function tick(){
  const trainingOn = (+trainSlider.value === 1);
  modeText.textContent = trainingOn
    ? "TRAINING: hard forward + STE gradients"
    : "TESTING: hard controller (same program)";

  kpValSpan.textContent = `kp=${kp.dataSync()[0].toFixed(3)}`;
  kvValSpan.textContent = `kv=${kv.dataSync()[0].toFixed(3)}`;

  sim.xStar = +tgtSlider.value;

  const alpha = +smoothSlider.value;
  const beta = +betaSlider.value;

  // Train a bit per frame if enabled
  if(trainingOn){
    for(let i=0;i<2;i++) trainOneBatch(alpha, beta);
  }

  if(sim.running){
    const stepsPerFrame = +speedSlider.value;

    for(let i=0;i<stepsPerFrame;i++){
      // position sensor speed estimate
      const vHatRaw = (sim.x - sim.xPrevObs) / dt;
      sim.vHatSmooth = alpha * sim.vHatSmooth + (1.0 - alpha) * vHatRaw;

      // hard program in display simulation
      const kpValNow = kp.dataSync()[0];
      const kvValNow = kv.dataSync()[0];
      const z = kpValNow * (sim.xStar - sim.x) - kvValNow * sim.vHatSmooth;
      sim.A = (z > 0) ? 1.0 : 0.0;

      // physics evolution (true v is hidden from controller)
      const out = stepJS(sim.x, sim.v, sim.A);

      // update position sensor memory and state
      sim.xPrevObs = sim.x;
      sim.x = out.x;
      sim.v = out.v;

      historyPush(sim.vHatSmooth);
    }
  }

  drawWorld();
  drawPlots();
  requestAnimationFrame(tick);
}

// init
historyReset();
sim.xPrevObs = sim.x;
sim.vHatSmooth = 0.0;
tick();
</script>
<div style="margin-top:12px; font-size:12px; color:#666;">
  (c) Fayyaz Minhas
</div>
</body>

</html>