# Pilot Induced Oscillation > Use when you must assess pilot-induced oscillation (PIO) susceptibility and pilot-in-the-loop coupling for a piloted aircraft: categorize the oscillation into Category I (linear aircraft response), Category II (quasi-linear response with rate-limited actuators), or Category III (nonlinear response with mode transitions or control logic changes), identify the typical causes: excessive phase lag, high control sensitivity, actuator rate limiting, structural notch filters, run a phase-lag-at-crossover risk check that returns a low, medium, or high band with the equivalent time delay and phase margin, and select suppression measures such as phase compensation, gain reduction, notch filter retuning, and control logic changes. Supports flight test detection of divergent oscillation. Framed by FAR-25 and CS-25 flight characteristics requirements. Trigger: pilot-induced-oscillation, pio, phase lag, crossover frequency, equivalent time delay, actuator rate limiting, pilot-in-the-loop coupling, pio suppression. - Skill: `ashfordeou/pilot-induced-oscillation` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/pilot-induced-oscillation` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/pilot-induced-oscillation/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/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.