control bandwidth

Control bandwidth is a measure of how fast-changing a command a controller can actually keep up with. Think of someone steering a boat to follow a wiggling line in the water. If the line bends slowly, the helmsman tracks it easily; if it zigzags faster and faster, at some point the boat just cannot turn quickly enough and starts cutting corners and lagging behind. Bandwidth marks roughly where that limit sits: it is the highest rate of change — the highest frequency of wiggle — that the system can still follow reasonably well before it gives up and falls behind.

The same number also describes which disturbances a controller can fight off. Slow shoves — a gradual headwind, a slowly draining battery, a load gently added — fall inside the bandwidth, so the controller has time to notice and correct them. Fast jolts — a sharp bump, a sudden gust, electrical noise — happen quicker than the loop can react, so they slip through and show up in the output. In short, a wider bandwidth means faster tracking of commands and stronger rejection of quick disturbances; a narrower bandwidth means a sluggish but often calmer, steadier system.

You might think more bandwidth is always better, but it is a trade-off. Pushing bandwidth up makes the system twitchier and more eager, which amplifies sensor noise and can edge it toward instability or oscillation. It is also capped by physical reality: motors, gears, and the mass being moved can only respond so fast no matter how clever the controller. Good design sets the bandwidth high enough to do the job and no higher, leaving a safe margin below the speeds where the hardware and stability start to complain.