Stability in Feedback Systems
A feedback system is stable when its output converges to the desired state after a disturbance, rather than diverging or oscillating indefinitely (Wikipedia).
Types of stability
- Asymptotically stable — output returns to the setpoint and stays there
- Marginally stable — output neither grows nor decays (permanent oscillation at constant amplitude)
- Unstable — output grows without bound
Practical stability concerns
Every controller must balance competing goals:
| Concern | Description |
|---|---|
| Overshoot | Output exceeds the setpoint before settling — caused by too-aggressive correction |
| Oscillation | Output swings above and below the setpoint repeatedly — caused by lag in the loop |
| Settling time | How long until the output stays within acceptable range of the setpoint |
| Steady-state error | A persistent gap between output and setpoint after transients die out |
Maxwell identified this trade-off in 1868: the centrifugal governor could self-oscillate when lags caused overcompensation.
Stability mechanisms
- Dead band — a range where the controller deliberately does nothing, preventing oscillation around the setpoint
- Damping (the D in PID) — opposing the rate of change to prevent overshoot
- Gain tuning — reducing proportional gain trades slower response for less oscillation
Beyond engineering
The same dynamics appear in management feedback loops:
- A team that over-corrects after a bad sprint (hiring spree, process overhaul) may oscillate between extremes
- Quarterly OKR reviews (xettel) have high latency — by the time the error is detected, the correction may already be stale, producing overshoot
- Shortening the feedback cycle (xettel) reduces lag, which improves stability — but only if the measurement is reliable