PID Part 2 — Adding I, and Tuning

The mission 4 min

Close the gap that would not close — and learn the order the three gains must be tuned in.

Two lessons ago you found a gap on the curve that no gain could remove. Yesterday D let you raise the gain, which made the gap smaller without ever closing it. Today you add the term that closes it, and you leave with a tuning procedure you can apply to any controller, not just this one.

The same curve, one more time 5 min

The marked curve on your fast leg is the whole test today. It is the only place the steady gap appears, and it is the only thing I is for.

Measure the gap once with yesterday’s best Kp and Kd before you change anything. That is today’s starting number, and it is probably a few millimetres.

Keep the straight marked too. You will need it to check that adding I has not spoiled anything that already worked.

The technique — a term with a memory 12 min

The gap survives because proportional control needs an error to produce a correction. On a constant curve the robot needs a constant turn, so it settles wherever the error is just big enough to produce it, and stays there. Neither P nor D objects: P is producing exactly what it should, and D sees no change at all.

So add a term that objects to an error that lasts. Each pass round the loop, add the current error to a running total. If the error is small but never goes away, the total climbs and climbs, and eventually the correction it produces is enough to push the robot onto the line.

That is the I term — integral, meaning accumulated. Multiply the running total by its own gain Ki and add it in. Then the full controller is:

Steering = Kp × error + Ki × total + Kd × change

Three terms, three questions about the same error: how big is it, how long has it been there, and how fast is it changing. That is all PID is.

Two guards, both cheap:

• Reset the total to zero at the start of every Follow Line call. A new leg is a fresh problem and should not inherit the last leg’s accumulated error.
• Cap it. If the total goes past a limit you choose, hold it there. It cannot then wind up without bound however long things go wrong.

And note the scale. The total grows every single pass, so it becomes a much larger number than the error itself. Ki is far smaller than Kp — start around a hundredth of it. A Ki that looks like a reasonable number next to Kp will send the robot off the mat on the first curve.

Build it — the running total 10 min

One more variable, and it needs the same care as yesterday’s.

Before the loop: set the total to zero, and set the previous error to zero.

Inside the loop, each pass:

1. Read the sensor, work out the error.
2. Total = total + error. Then, if the total is above your cap, hold it at the cap; if below the negative cap, hold it there.
3. Change = error − previous error.
4. Steering = Kp × error + Ki × total + Kd × change.
5. Previous error = error.

Add Ki as a fourth input to Follow Line, alongside speed, Kp and Kd. Four numbers now describe a run completely, which is what makes the table worth keeping.

Set Ki to zero and run once. It must behave exactly as it did at the end of yesterday. If it does not, the arithmetic changed somewhere and that is the bug to find before any tuning starts.

Program it — three failures, three signatures 12 min

Before tuning, learn to tell the three gains apart by how they fail. This is the difference between diagnosing and guessing, and it is the most portable thing in this block.

• Too much P — fast weaving. Large, quick swings either side of the line that do not settle. The robot is overcorrecting.
• Too much D — a buzz. Small, rapid twitching, more audible than visible. The robot is chasing sensor noise.
• Too much I — a slow wallow. Big, lazy swings that take a long time to come back, often getting worse each cycle. The accumulated total is overshooting and then having to unwind.

Tune it — the order 9 min

This is the procedure. It works on any PID controller, on any robot, and it is what you are really taking away from this block.

1. Everything to zero but P. Raise Kp until the robot weaves steadily and will not settle. Then back off — around two thirds of that value.
2. Add D. Raise Kd from zero until the weaving damps out. Stop before the buzz.
3. Go back and raise P again now that it is damped, adding a little more D if the weaving returns.
4. Add I last, and only if a steady gap remains. Start at about a hundredth of Kp. Raise it until the gap closes. Stop the moment you see the slow wallow.

Change one gain at a time and run the leg after each change. Two changes at once and you have learned nothing about either.

Run it — including the nasty test 6 min

Run the marked leg twice with your final settings and record the three measurements: curve gap, swings, leg time. That row is what lesson 30 compares.

Then, if you used any I at all, test windup on purpose. Start the leg, hold the robot still against your hand for three seconds part-way along, and let go.

• If it recovers to the line reasonably, your cap and your reset are doing their job.
• If it lurches hard sideways, the total wound up. Lower the cap, or lower Ki, and try again.

This is not a contrived test. A robot gets nudged, blocked or held up in real rounds, and a follower that goes wild afterwards will lose a mission you had already scored.

The journal 4 min

This is a keep-forever entry:

• the five lines of the loop, in order
• your final Kp, Ki and Kd, with the speed they were tuned at
• the gap, swings and time they produced
• the three failure signatures in your own words, and what each one looked like when you caused it
• your I cap, and what the windup test did
• the tuning order, written out as four steps — this is the part that transfers to every other robot you will ever tune