Feedback control and PID

Learn

What you’ll learn

• Why on/off (“bang-bang”) control wobbles
• P, I and D in plain words
• How to tune a controller step by step

Bang-bang control

The two-sensor line follower only knows “left”, “right” or “centre”, so it jerks between full turns: bang-bang control. It works, but it zig-zags and can’t go fast.

Error

Proportional control needs a number: the error, how far you are from where you want to be. In the simulator, linePosition() gives the line’s position under a 5-sensor bar, from −1 (far left) to 1 (far right), so the error is just that value (target = 0).

P: proportional

correction = Kp × error

Small error → small correction; big error → big correction. Too little Kp and the robot drifts off on curves; too much and it oscillates.

D: derivative

+ Kd × (error − lastError)

Reacts to how fast the error is changing, which damps the wobble, like a shock absorber.

I: integral

+ Ki × (sum of all errors)

Fixes a small error that stays for a long time (one motor slightly weaker). Line followers often don’t need it; balancing robots and heaters do.

Tuning recipe

1. Set Ki = Kd = 0. Increase Kp until it follows well but starts to wobble.
2. Add Kd until the wobble calms down.
3. Only if it settles slightly off-target, add a little Ki.
4. Change one number at a time and note what happens.

Examples

Example: P line follower (simulator)

const BASE = 50, KP = 40;

function loop() {
  const error = linePosition();
  if (error === null) { motors(30, -30); return; }   // lost: search
  const turn = KP * error;
  motors(BASE + turn, BASE - turn);
}

Line to the right (error > 0) → left wheel faster → robot turns right towards it.

Example: adding D

let last = 0;
function loop() {
  const error = linePosition();
  if (error === null) { motors(30, -30); return; }
  const turn = 40 * error + 120 * (error - last);
  last = error;
  motors(60 + turn, 60 - turn);
}

Example: P control with encoders (Arduino)

long error = leftCount - rightCount;   // target: equal counts
int correction = 3 * error;            // Kp = 3
setMotors(150 - correction, 150 + correction);

Practice

Try it

P controller

▶ Run↺ Reset

Your code (JavaScript)const BASE = 50, KP = 40; function loop() { const error = linePosition(); if (error === null) { motors(30, -30); return; } // lost: search const turn = KP * error; motors(BASE + turn, BASE - turn); }Load starter code

Robot commands

• motors(left, right): wheel power, −100 to 100
• lineLeft(), lineRight(): true over the black line
• distance(): cm to the nearest thing ahead (max 200)
• distanceLeft(), distanceRight(): cm to the sides
• linePosition(): where the line is, −1 (left) to 1 (right), or null
• millis(): milliseconds since Run
• print(value): show a message below
• setup() runs once; loop() runs 50 times a second

Too little, too muchEasy

Try KP = 10 and KP = 150. Describe what happens in each case. KP 10: turns too gently and runs off on the curves. KP 150: over-corrects and wobbles from side to side.

Go fasterMedium

Raise BASE to 80. Re-tune KP until it completes laps. Is it faster than the bang-bang follower?

Add DHard

Add a derivative term and find a Kd that lets it run at BASE = 90 without wobbling off. Start Kd around 2–4 times Kp and adjust.

Quick check

1. What is the “error” in a controller?

A bugHow far you are from the targetThe battery levelA random number

2. Kp is too high. The robot…

Drifts off slowlyOscillates (wobbles)StopsGoes faster with no side effects

3. Which term reacts to how fast the error is changing?

PIDNone

Check my answers