PID Part 1 — P and D

The mission 4 min

Kill the weaving — so the gain can finally go up.

Yesterday you proved that raising the gain shrinks the curve gap and makes the straights weave. Today you add one term that stops the weaving, which lets you raise the gain further than you ever could before.

The same leg, the same marks 5 min

Same fast leg, same marked curve, same marked straight, same speed as yesterday. Everything about the test stays fixed so that today’s numbers sit under yesterday’s in the same table.

If a mark has come off the mat, put it back in the same place before you run anything. A test section that has quietly moved ten centimetres is a very convincing way to prove something false.

Battery too. A tired battery turns more slowly, which changes how the robot returns to the line — and you will read that as a gain effect if you are not watching for it.

The technique — a term that sees the arrival coming 12 min

Think about what happens as a weaving robot comes back to the line. The error is large and shrinking fast. Proportional control looks at the error and says: still large, keep pushing hard. So the robot is at full correction at the exact moment it arrives, and it sails straight across.

The missing information is not in the reading. It is in the change in the reading:

• Error large and shrinking fast → the robot is about to arrive. Ease off.
• Error large and not changing → nothing is working yet. Keep pushing.
• Error small but growing fast → something has pushed the robot off. Respond now, before it becomes a big error.

That is the D term — derivative, meaning rate of change. Each time round the loop you keep the previous error, subtract it from the current one, and the difference is your D value. Multiply it by its own gain Kd, and add it to the proportional part.

Two practical warnings, both of which will otherwise cost a team half a lesson:

D amplifies noise. The colour sensor reading jitters a little every pass, and D looks precisely at those jitters. Too much Kd turns a smooth follower into a buzzing, twitching one. If you see small fast twitching rather than large slow weaving, Kd is too high — the fix is a smaller number, not a bigger one.

D depends on loop speed. “How fast the error is changing” means per pass round the loop. Add a Display block or a Sound block inside the follow loop and every pass takes longer, so the same physical wobble produces a different D value. Keep the follow loop lean, and keep it the same between runs.

Build it — the previous error 10 min

One variable is all this needs, and it is the first time this course has asked a loop to remember something between passes.

Inside Follow Line, each time round:

1. Read the sensor and work out the error, as you already do.
2. D value = this error − the previous error.
3. Steering = Kp × error + Kd × D value.
4. Store this error as the previous error, ready for next pass.

Step four is the one teams forget, and the failure is confusing: the previous error stays at whatever it was first set to, so the D term becomes a strange constant that never changes. The robot behaves oddly rather than badly, which is harder to spot.

Set the previous error to zero before the loop starts, not inside it. Inside, it gets wiped every pass and D is always zero.

Program it — Kp and Kd as inputs 12 min

Follow Line already takes speed and, since yesterday, Kp. Add Kd as a third input.

The reason is the same as it has been since lesson 14, and it is worth stating once more because today is when it pays off properly: you are about to run a dozen combinations, and any number you have to open a My Block to change is a number that will be wrong on some run and nobody will know which.

With three inputs, a run is fully described by three numbers written in a table row. That is what makes today’s tuning honest instead of remembered.

Set Kd to zero and run once. It should behave exactly as it did yesterday at the same Kp. If it does not, the arithmetic is wrong somewhere and no amount of tuning will fix it — find that first.

Tune it — Kp first, then Kd, never both 9 min

There is an order to this and it is not optional. A team that changes two gains at once cannot say which one did anything.

Step one — find the edge with Kd at zero. Raise Kp until the robot weaves steadily on the straight and does not settle. That is the edge. Write the number down. Yesterday this was the wall; today it is the starting point.

Step two — bring Kd up from zero. Small steps. Watch the swings count on the straight. It should fall: three swings, then two, then one, then none. Stop as soon as it settles cleanly.

Step three — watch for the buzz. Keep raising Kd past the settled point and the robot starts twitching rapidly. That is noise, not control. Come back down to where it was smooth.

Step four — now raise Kp again. With the weaving damped, the gain can go higher than it could yesterday. Go up until the weaving returns, then damp it with a little more Kd, and stop when either the buzz appears or the improvement gets small.

Run it — the same two columns 6 min

Run the marked leg with your best Kp and Kd, twice, and fill in the same three measurements as yesterday: curve gap in millimetres, swings on the straight, and leg time.

Put the row directly under yesterday’s circled row. You should see:

• Swings: much better, ideally zero or one. That is D doing its job.
• Leg time: better, because the higher gain holds the line at speed.
• Curve gap: smaller, but still there. The higher gain shrank it. Nothing today closed it.

The journal 4 min

Today’s entry:

• the four lines of the loop, written out in order
• the Kp at which it weaved with Kd at zero — the edge you found
• the Kd sweep: swings against Kd, and the value where the buzz started
• your best Kp and Kd, with the gap, swings and time they produced, under yesterday’s row
• one sentence on why D contributes nothing when the error is steady