Where Proportional Control Breaks

The mission 4 min

Find the two things your proportional follower cannot do at any gain.

You built proportional steering in lesson 12 and it was a large improvement over the two-state follower. Today you find its ceiling — not by being told about it, but by trying every gain and watching one problem get worse each time the other gets better.

The test leg 5 min

Use the fast leg you marked in lesson 25 — the one you said was worth the fastest possible following. If it is a long diagonal like the loading yard down to the packing table, it is exactly right: it has straight and it has curve.

You need both parts and they test different things:

• A long curve — a section where the line bends the same way for a while. Somewhere near the greenhouses at C usually works. This is where the steady gap appears.
• A long straight — this is where weaving shows up, and where you count how many swings it takes to settle after the bend ends.

Mark both sections on the mat with a removable marker or a scrap of tape at each end, so every team member measures the same stretch.

The technique — why a curve defeats a gain 12 min

Recall what proportional steering actually computes. The error is how far the light reading is from your mid value, and the steering correction is that error multiplied by your gain. Small error, small correction. No error, no correction at all.

That last sentence is the whole problem, and it only bites on a curve.

On a straight, holding the line needs no steering. Zero error, zero correction — and zero correction is exactly what is wanted. Proportional control is perfect here.

On a curve, holding the line needs a steady turn, all the way round. But a steady correction requires a steady error. So the robot slides off the line until the error is just big enough to produce the turn the curve demands — and then it stays there, tracking the curve perfectly, from a fixed distance off the line. It is not drifting. It has settled, in the wrong place.

So raise the gain. Now the second problem appears. A high gain means a big correction from a small error, so a robot returning to the line arrives fast, cannot stop on it, and crosses to the other side — which produces a large error the other way, and a large correction back. It weaves. On a straight it never settles.

Lower the gain and the weaving stops, but the curve gap grows and sharp bends get cut. The two problems want opposite gains. That is the second wall, and no single number is on both sides of it.

Build it — the measuring rig 10 min

No bricks today. What you build is a way of seeing the two failures, because both are easy to argue about and hard to eyeball.

For the steady gap. Run the curve, and stop the robot part-way round with the program still holding position — or simply stop it and do not move it. Measure, in millimetres, from the centre of the colour sensor to the centre of the line. Do it at the same marked point every run so the numbers compare.

For the overshoot. Watch the straight after the bend and count the swings — how many times the robot crosses the line before it is running level. Zero is settled. Three or more and it is still fighting. Have one person count and only that person count, so the number means the same thing all lesson.

Draw the table now, before you run anything: a row for each gain value, a column for the curve gap in millimetres, a column for the swings, and a column for the time over the whole leg.

Program it — one number, exposed 12 min

Your Follow Line block from lesson 13 already takes speed as an input. Today, if the gain is buried inside the block, bring it out as an input too.

This is the same rule as lesson 14 and it matters more today than usual: you are about to change the gain five times, and a number you have to go inside a My Block to edit is a number somebody will forget to change back.

Keep everything else fixed. Same speed on every run, same starting position, same battery state as far as you can manage, same section of line. If two things change between runs, the table proves nothing.

One more thing worth checking before you trust any of today’s numbers: re-run your colour calibration. A follower tuned against yesterday’s light values will show you failures that belong to the calibration, not the controller.

Tune it — sweep the gain 9 min

Five values, spread wide. If your working gain from Block 2 is in the middle, go well below and well above it — you want to see both failures clearly, not politely.

For each value, run the leg twice and record the curve gap, the swings and the time. Two runs, because one run of anything on a mat is an anecdote.

Then read your two columns down the page. The gap column gets better as the gain rises. The swings column gets worse. Somewhere in the middle is the compromise you have been using all year without realising it was a compromise.

Run it — the impossible request 6 min

Now try to satisfy both at once. Find a single gain that gives you a curve gap under about five millimetres and no more than one swing on the straight.

Give teams a genuine attempt at it. They will bracket in, split the difference, and get close on one column at the cost of the other.

Then say plainly what has happened: this was not a hard tuning problem they failed at. It is a request that one multiplication cannot fill, because the two failures want opposite numbers.

To do better, the follower needs to know something it currently does not: how long the error has been there, and how fast it is changing. Neither is in the reading. Both are in the history of the readings. That is tomorrow.

The journal 4 min

Today’s entry is mostly the table, and it gets used twice more this block:

• the marked curve and straight, sketched on the leg
• the gain table — five gains, curve gap, swings, leg time
• the row you would race with, circled, and what is wrong with it
• your best attempt at the impossible request, and which column you had to give up
• one sentence in your own words on why a curve leaves a gap that a straight does not