A limit cycle is a constant-amplitude oscillation from a nonlinearity — stiction, backlash, a travel stop — not from the constants. Detuning stretches the period and leaves the amplitude.
Trend showing valve stiction: the controller output ramps smoothly while the process variable moves in abrupt steps, producing a limit cycle that does not decay. A sawtooth or square-cornered cycle on the process variable against a smooth, slowly ramping output. The cycle amplitude stays constant instead of decaying. Put the loop in manual and the cycle stops — that single test separates stiction from every tuning problem.
A limit cycle is an oscillation that neither grows nor decays. It sits at a fixed amplitude indefinitely, and that is the signature — every oscillation caused by linear tuning either decays or grows.
Limit cycles come from nonlinearities: stiction, backlash, a valve against a travel stop, an on/off element in the loop. Detuning stretches the period without touching the amplitude, which is why a loop can be detuned to the point of uselessness and still be cycling.
Trend showing valve stiction: the controller output ramps smoothly while the process variable moves in abrupt steps, producing a limit cycle that does not decay. A sawtooth or square-cornered cycle on the process variable against a smooth, slowly ramping output. The cycle amplitude stays constant instead of decaying. Put the loop in manual and the cycle stops — that single test separates stiction from every tuning problem.
Questions that come up
What is a limit cycle in a control loop?
A sustained oscillation of constant amplitude caused by a nonlinearity rather than by tuning. Linear tuning either decays or grows; a limit cycle sits still. Fix the valve.
Written by PIDSnap control engineering.
Published 2026-08-01, last reviewed 2026-10-22.
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