# Gain Scheduling > Use when you must design and schedule controller gains against dynamic-pressure across nonlinear flight envelope, interpolate gain schedule breakpoint table across Mach-number operating points, and select the scheduling variable (dynamic-pressure, Mach number, angle of attack, or altitude). Choose nearest, linear, or spline interpolation, apply scheduling-variable rate limiting, and distinguish gain scheduling from gain updating. Verify stability between operating points and handle anti-windup interaction when scheduling autopilot and flight control gains across the envelope. Produces the interpolated gain at the current operating point and the rate-limited scheduling variable value. Trigger: gain scheduling, gain-scheduling, scheduling variable, dynamic pressure, Mach number, angle of attack, altitude, breakpoint table, schedule table, interpolation, rate limiting, gain updating, anti-windup, flight envelope. - Skill: `ashfordeou/gain-scheduling` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/gain-scheduling` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/gain-scheduling/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/gain-scheduling --- # Gain Scheduling (gnc-autonomy/control/gain-scheduling) Use when the task is scheduling controller gains across a nonlinear flight envelope: picking the scheduling variable, building the breakpoint/gain schedule table, interpolating the gain at the current operating point, and rate limiting the scheduling variable so gain changes stay smooth between operating points. ## Domain quick reference - Scheduling variables: dynamic pressure (Pa), Mach number (dimensionless), angle of attack (deg), and altitude (m). Pick the variable that captures the nonlinearity that moves the plant dynamics, typically control effectiveness or hinge moment growth with dynamic pressure, or compressibility effects with Mach number. - Breakpoint/schedule table: strictly increasing breakpoints, each paired with a gain tuned at that operating point. The table is the schedule; gains between breakpoints come from interpolation. - Interpolation methods: nearest (stepwise, keeps the tuned gain until the midpoint), linear (default, straight segments between breakpoints), spline (overview: smoother across breakpoints but can overshoot between them; not implemented in the logic module). - Out-of-range behavior: clamp to the end gains (default) or raise an error when the flight condition sits outside the tuned envelope and must be flagged rather than silently held. - Rate limiting: limit how fast the scheduling variable can change, so the gain itself cannot step faster than the actuators can follow. Apply the rate limit to the scheduling variable, then interpolate. - Gain scheduling vs gain updating: scheduling is a deterministic function of the measured operating state; gain updating is online adjustment from adaptation or system identification. They differ in mechanism and in verification burden. - Stability between operating points: each operating point is locally stable by design; the transitions must be slow enough (rate limited) that the time-varying closed loop stays stable between points. - Anti-windup interaction: scheduled gains change the integrator authority; when gains are scheduled up, the integrator clamp should follow, or the loop winds up at the scheduled authority limit. - Application: autopilot and flight control gains across the envelope (pitch rate and roll rate gains scheduled against dynamic pressure, damper gains scheduled against Mach number, and so on). ## Workflow 1. Pick the scheduling variable for the nonlinearity at hand and the operating-point values it will take (dynamic pressure in Pa, Mach number, angle of attack in deg, or altitude in m). 2. Build the breakpoint/gain table from gains tuned at each operating point (for example with root-locus-design or pid-control-design), keeping the breakpoints strictly increasing. 3. Rate limit the commanded scheduling variable with rate_limited_scheduling_variable(prev_value, new_value, max_rate, dt) so gain changes stay within the actuator capability. 4. Interpolate the gain at the current operating point with schedule_gain(table, sched_var_value, method="linear", out_of_range="clamp"). 5. Choose the out-of-range policy: clamp for benign conditions, error mode when the flight condition must be flagged as outside the tuned envelope. 6. Before enabling the scheduled gains in the autopilot, check stability between adjacent operating points and re-check the anti-windup clamps against the scheduled authority limits. ## Pitfalls - Routing PID tuning questions here: Ziegler-Nichols gains, ultimate gain and period, and fixed-point tuning belong to pid-control-design. - Routing root locus gain selection here: choosing the gain K for a single operating point belongs to root-locus-design; gain scheduling sits on top of that per-point design. - Routing frequency response margin questions here: gain and phase margins at one flight condition belong to frequency-response-design. - Using a non-monotonic breakpoint list: the schedule table must be strictly increasing, or the interpolation is ambiguous; the logic module raises ValueError. - Interpolating without rate limiting: a fast gain step can destabilize the loop between operating points even when every point is locally stable. - Rate limiting after interpolation: limit the scheduling variable first, then interpolate, so the applied gain moves smoothly. - Clamping silently at the envelope edge: clamping hides the loss of tuned coverage; use error mode when the condition must be flagged. - Confusing scheduling with updating: a scheduled gain is a deterministic function of the operating state; adaptive gain updating is a different mechanism with its own verification burden. - Forgetting anti-windup: when gains are scheduled up, the integrator clamp must follow, or the loop winds up against the scheduled authority. - Treating spline as implemented: spline interpolation is covered as an overview only; the logic module raises NotImplementedError for method="spline", use linear or nearest for a concrete gain. ## Behavior contract (gate 3) The interpolation, clamping, monotonicity validation, and rate limiting logic is exercised by the gate 3 contract test: scripts/test_gain_scheduling_logic.py against scripts/gain_scheduling_logic.py (stdlib unittest, offline). Run: python3 scripts/test_gain_scheduling_logic.py ## Compliance - ARP4754A is proprietary (SAE); name + paraphrase only per standards-map.yaml. Gain scheduling interpolation math is standard control practice, summary only. - compliance: STANDARDS-REF, gated: false.