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Control Systems

Why too much proportional gain causes overshoot

Raise a proportional controller's gain and the system gets to its target sooner, until it starts to fly past the target, come back, and pass it again the other way. That's overshoot, and the swinging afterwards is ringing. The cause is momentum: when the error reaches zero, the push reaches zero, but the speed doesn't.

Zero error, not zero speed

A proportional controller pushes in proportion to the error: thrust = 9.8 + Kp × error, for a drone climbing to 10 m. The push is strongest when the drone is furthest away. With a big gain that's a hard shove from the start: at Kp 4, 10 m of error asks for 9.8 + 40, far more than the motors can give.

So the drone is moving fast when it reaches 10 m. The push has faded to nothing, but nothing is slowing it down except drag, and it coasts past. Now the error is negative, the push reverses, and the same thing happens on the way back. Each correction overdoes the last.

The sweet spot

Too little gain dawdles; too much overshoots. Between them is a gain that arrives quickly and only overshoots a little:

KpReaches 9.5 mHighest point
0.25about 9.5 s9.6 m: not there after 10 s
0.5about 4 s10.4 m
1about 2 s11.6 m
4about 1 s13.9 m, then rings

Kp 0.5 to 0.75 is the sweet spot for this drone: quick, and well under a 1.5 m overshoot limit.

Live experiment

Find the sweet spot

Same drone, same rule, thrust = 9.8 + Kp × error, at six gains. 0.25 dawdles. 0.5 and 0.75 reach 10 m in about four and three seconds and stay under the red line 1.5 m above it. 1 just crosses the line, and 4 and 16 rocket past to nearly 14 and 15 m and swing.

Try it yourself: free lesson

“Too much of a good thing” is lesson 3 of 6 in Feedback Falls, Control Systems World 1. Free with an account. Lessons unlock in order, so you’ll do the 2 before it first.

Tuning by eye

Read the response and turn the gain:

  • Overshoot: too much gain. Halve it.
  • No overshoot, but slow: too little. Add a third.
  • Quick, and only a little past: stop there.

It's the same loop engineers run on everything from drones to chemical plants: watch, adjust, watch again.

Beyond the sweet spot

This simple drone's swings always die away in the end. Real loops react a moment late, and with enough gain the swings grow instead of shrinking: the loop is unstable. And there's a limit to what tuning P alone can do, because it can't see speed. To be fast and clean, add a term that pushes against the speed, the D in PID, and the gain can be bold without the overshoot.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Too much of a good thing” is lesson 3 of 6 in Feedback Falls, Control Systems World 1. Free with an account. Lessons unlock in order, so you’ll do the 2 before it first.

Or start from the very first lesson, no account needed

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3The drone overshoots by a lot and swings for seconds. The gain is probably…
    Show the answer

    Answer: Too big. A big gain pushes hard all the way in, and the drone arrives with too much speed to stop.

    • Why not “Exactly right”? A well-tuned gain arrives quickly with little or no overshoot. Swinging for seconds is the sign of too much.
    • Why not “Too small”? A small gain gives a gentle push that arrives slowly and doesn't swing. Big swings come from too much push.
    • Why not “Negative”? A negative gain would push the wrong way and drive the drone away from its target, not swing it around it.
  2. Question 2 of 3The drone takes ages to reach its height but never overshoots. To arrive sooner you…
    Show the answer

    Answer: Raise the gain a little. Small gain, gentle push. Raise it until the overshoot just starts to appear, then stop.

    • Why not “Remove the hover thrust”? Without the hover thrust the drone needs a standing error just to stay up, so it sags below the target instead of arriving sooner.
    • Why not “Do nothing”? With the same gain it keeps the same slow response. Something has to change for it to arrive sooner.
    • Why not “Lower the gain”? Lowering the gain makes the push gentler still, so the drone takes even longer.
  3. Question 3 of 3You try gains of 0.3, 0.5 and 1.0. 0.3 is slow, 1.0 overshoots. The sweet spot is…
    Show the answer

    Answer: Around 0.5. The clean, fast gain sits between the one that's too slow and the one that overshoots. 0.5 lands there for this drone.

    • Why not “Below 0.3”? 0.3 is already too slow, so going lower makes it slower still.
    • Why not “Above 1.0”? 1.0 already overshoots, and a bigger gain overshoots more.
    • Why not “Exactly 1.0”? 1.0 is the gain that overshoots. The sweet spot sits between the slow gain and the one that overshoots.
Keep practising: free lesson

“Too much of a good thing” is lesson 3 of 6 in Feedback Falls, Control Systems World 1. Free with an account. Lessons unlock in order, so you’ll do the 2 before it first.

Questions people ask

What is overshoot in a control system?

How far the response goes past its target before coming back, often given as a percentage of the step. A drone asked to climb 10 m that peaks at 11.6 m has overshot by 1.6 m, or 16%.

What is ringing?

The swinging back and forth that follows an overshoot: past the target, back under it, past again, each swing smaller until it settles. Lots of ringing means too much gain or too little damping.

How do I stop overshoot without making the system slow?

Add damping, a D term that pushes against speed. With brakes, a bold gain becomes safe: on the same drone, Kp 16 alone rockets past to nearly 15 m, while Kp 16 with Kd 7 is up in under two seconds and stops dead on 10 m.

Can too much gain make a loop unstable?

Yes, once there's any delay in the loop. A real sensor, motor or heater reacts a moment late, and past a certain gain each swing comes back bigger than the last instead of smaller. That growing oscillation is instability.

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