Pilot Induced Oscillation

Pilot-Induced Oscillation (flight-mechanics/handling-qualities/pilot-induced-oscillation)

Use when the task is pilot-induced oscillation (PIO) analysis: the category of the oscillation, the phase-lag-at-crossover risk band, the suppression measures, and the flight test detection of the closed-loop phenomenon.

Domain quick reference

• A pilot-induced oscillation is an unintentional, sustained oscillation of the aircraft that develops from the close coupling between the pilot's control inputs and the aircraft response: the pilot's corrective inputs add energy to the oscillation instead of damping it. It is a pilot-vehicle system phenomenon, not an aircraft instability alone.
• Category I (linear aircraft response): the aircraft responds essentially linearly; the oscillation develops because the pilot-vehicle loop (pilot gain and lag plus aircraft and actuation lags) is unstable. Classic triggers: a high gain task with excessive phase lag.
• Category II (quasi-linear response, rate-limited actuators): the actuator or control surface rate limit saturates during the oscillation, so the rate-limited element reduces effective gain and adds phase lag. Describing-function methods are needed and the oscillation often appears at a frequency different from the linear prediction.
• Category III (nonlinear response): the response is dominated by transitions, such as control law mode switching, surface saturation, or reversion to alternate modes during the task.
• Typical causes: excessive phase lag (equivalent time delay) in the pilot-vehicle loop, including pilot reaction delay, digital flight control transport delay, actuator lag, and sensor and filter lag; high control sensitivity that keeps the loop gain high and shrinks the phase margin; actuator rate limiting under large rapid commands; and structural notch filters that add phase lag in the piloted frequency band.
• Phase-lag-at-crossover risk check: the crossover frequency is the frequency where the open-loop pilot-vehicle gain passes through unity. The phase lag there gives the phase margin, margin = 180 + phase_lag for the negative lag, and the equivalent time delay tau_e = |phase_lag| / (360 * f_crossover). Bandwidth-style bands: tau_e below 0.10 s is low risk, 0.10-0.20 s is medium, above 0.20 s is high. Worked: phase_lag_risk(-30.0, 2.0) returns the low band with a 150 degree margin and a 0.0417 s delay; (-100.0, 1.0) returns high with a 0.2778 s delay.
• Suppression measures: reduce the loop gain and add phase lead compensation to recover phase margin; reduce the equivalent time delay (faster actuators, less transport delay); increase the actuator rate limit or add command-rate shaping; retune or relocate the structural notch filter; and add control logic that prevents mode switching or reversion during the critical task.
• Flight test detection: closed-loop test techniques track a defined task (for example a discrete attitude capture) and watch for an oscillatory response that grows after the input stops, with the oscillation frequency well below the short period; open-loop frequency sweeps measure the phase lag at crossover directly; pilot comments such as "the aircraft got ahead of me" are a classic symptom.

Workflow

1. Collect the loop data: the crossover frequency and the phase lag at crossover of the open-loop pilot-vehicle response, from a frequency sweep or from the equivalent time delay estimate.
2. Categorize the oscillation with categorize_pio(rate_limiting, nonlinear): both false gives Category I, rate limiting alone gives Category II, and any nonlinear response gives Category III.
3. Run the risk check with phase_lag_risk(phase_lag_deg, crossover_freq_hz), which returns the band, the phase margin, and the equivalent time delay; confirm the margin with phase_margin and the delay with equivalent_time_delay.
4. Interpret the band: low needs no action, medium warrants mitigation before further flight test, high demands suppression before the task is cleared.
5. Select the suppression measures with suppression_measures(...) against the causes present (rate limiting, high sensitivity, structural filters, nonlinear response) and the risk band.
6. Plan the flight test detection: a closed-loop task with defined tolerances, monitoring for divergent oscillation after the input stops, plus an open-loop sweep to confirm the phase lag at crossover.

Pitfalls

• Routing mode analysis here: short period damping, natural frequency, and eigenvalue classification belong to dynamic-stability; the PIO analysis works on the pilot-vehicle loop, not on the bare aircraft modes.
• Routing control power here: actuator sizing, authority margins, and hinge moments belong to control-surface-effectiveness; rate limiting matters here only as a PIO cause, not as an actuator sizing number.
• Routing pilot ratings here: assigning a Cooper-Harper rating to the task belongs to cooper-harper-rating; a low rating may accompany a PIO but the rating is not the oscillation analysis.
• Routing flight control system analysis here: gain and phase margin of the autopilot or flight control loop without the pilot belong to the gnc-autonomy control leaves; the pilot must be in the loop for a pilot-induced oscillation.
• Treating a divergent aircraft mode as a PIO: flutter or a divergent eigenmode grows without pilot input; a PIO requires the pilot's corrective inputs in the loop.
• Confusing the categories: Category II is specifically the quasi-linear case where rate limiting is the dominant nonlinearity and describing-function methods apply; a linear response is Category I even when the pilot oscillates.
• Sign errors in the risk check: the phase lag is negative degrees, the margin is 180 plus the lag, and the equivalent time delay uses the magnitude of the lag; a flipped sign turns a high risk band into a low one.
• Using the wrong crossover: the risk check needs the pilot-vehicle loop crossover frequency, not the flight control system crossover or a structural mode frequency.
• Confusing equivalent time delay with measured transport delay: tau_e is derived from the phase lag at one frequency and lumps all lag sources; the measured transport delay is one contributor, not the whole result.

Behavior contract (gate 3)

The PIO categorization, phase-lag risk check, and suppression measure selection are exercised by the gate 3 contract test: scripts/test_pilot_induced_oscillation.py against scripts/pilot_induced_oscillation_logic.py (stdlib unittest, offline). Run: python3 scripts/test_pilot_induced_oscillation.py

Compliance

• Standards referenced, not reproduced: FAR-25 and CS-25 flight characteristics requirements frame the handling qualities assessment for transport aeroplanes; the three-category PIO categorization, the equivalent time delay measure, and the suppression measures are common flying qualities methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.