Claude Skills by ashfordeOU

Use when you must reduce a rotorcraft performance flight test from measured data: convert measured main rotor torque and rotor speed into shaft power, compute the measured figure of merit from the ideal induced power and the measured power, correct measured hover power to a reference weight and density altitude with the induced and profile fraction split, correct a measured vertical rate of climb for the test weight, reduce hover power-required points measured across density altitudes to a ho...

Use when you must determine the reference stall speed Vs1g for a flight test: derive it from the wing loading and the maximum lift coefficient, correct it for a weight change, and check the stall margin against the current flight speed. Produces the Vs1g reference stall speed in m/s, the weight-corrected stall speed, and the stall margin verdict that gate the performance assessment. Trigger: Vs1g, stall speed, wing loading, stall margin, flight test, weight correction.

Use when you must determine the takeoff distance for a flight test: integrate the measured ground speed samples over the ground roll, add the rotation distance at the rotation speed, and close the airborne climb segment to the 35 ft obstacle height with the climb rate. Produces the ground roll distance, rotation distance, climb distance, and total takeoff distance that gate the takeoff field length assessment. Trigger: takeoff distance, ground roll, rotation speed, 35 ft obstacle, climb segme...

Use when you must reduce post-flight flight test data: apply the calibration correction with the channel slope and intercept, align the time series from separate recorders with the offset, smooth the raw trace with the moving average filter, compute the corrected airspeed from the impact pressure and density, and combine the measurement uncertainty sources with the root sum square into the combined uncertainty. Produces the corrected and filtered channel time series, the corrected airspeed, t...

Use when you must design flight test instrumentation: select sensors for the measurement parameters (air data, accelerations, angular rates, strain, control positions, engine data) with the right range, accuracy, and bandwidth, size the data acquisition sample rate against the anti-aliasing and Nyquist limits, and verify the recording, telemetry, pre-test calibration, and measurement uncertainty chain before the test. Applies the Nyquist criterion, sensor range checks, ADC quantization, and c...

Use when you must plan a flight test program: order the test points with the build-up approach so risk increases step by step and every prerequisite is flown before the dependent point, check that the instrumentation covers the required sensors, and confirm the test matrix covers every test objective. Produces the risk-ordered flight sequence with missing prerequisites flagged, the missing instrumentation list with the completeness verdict, the uncovered objectives with the matrix verdict, an...

Use when the task concerns flight test safety: risk assessment, flight envelope limits, emergency procedures, safety pilot duties, go/no-go criteria, risk mitigation. Assess the flight test safety package: score the hazards on the severity by likelihood risk matrix, check that every test point stays inside the flight envelope limits, confirm the emergency procedures cover the required conditions, verify the safety pilot duties are assigned, run the go/no-go criteria gate, and list the mitigat...

Use when you must plan and analyze the noise certification flight test for a transport airplane: lay out the flyover, sideline, and approach measurement conditions with the reference geometry (6500 m flyover distance, 450 m sideline offset, 1200 m approach distance at 120 m altitude on a 3 degree glide slope), compute the effective perceived noise level (EPNL) from the measured tone corrected perceived noise level (PNLT) time history with the 10 dB down integration rule and the 10 s normaliza...

Use when you must decommutate a serial PCM telemetry stream: acquire frame sync by locating the sync word in the captured word stream, walk the locked minor frames and count sync misses, and demultiplex the recovered telemetry channels into time series, with fixed channels read from their word slot every frame, supercommutated channels read from their multiple word slots per frame, and subcommutated channels keyed by the subframe id into the per-subframe value lists. Produce the locked frame ...

Use when you must plan and reduce the airspeed position error calibration (PEC) flight test for a fixed-wing aircraft: schedule the tower fly-by, trailing cone, and GPS ground speed doublet test points across the speed range, compute the calibrated airspeed from the indicated airspeed and the position error correction, reduce the fly-by height error and the reciprocal-heading ground speeds into the position error at each point, fit the piecewise-linear position error correction curve against ...

Use when the task is flight test telemetry and data acquisition planning, PCM frame or IRIG time coding, data latency budgeting, signal conditioning, ground station link checks, or telemetry quality checks. Design and check the flight test telemetry and data acquisition chain: size the PCM minor frame and bit rate, assign supercommutated and subcommutated channels against the frame rate, encode the time of year in IRIG time format, condition the sensor signal to the ADC span, budget the end-t...

Use when the task is building the test point matrix for a flight test program, laying out condition sweeps, choosing repeat points, or ordering the points for efficient flying. Design the flight test point matrix: expand the altitude, speed, and weight sweeps across the aircraft configurations into the full grid of test conditions, mark the repeat points for data quality, sequence the points so configuration changes and altitude hops are minimized for flight efficiency, and check the flown po...

Use when you must reduce the measured control force records of a longitudinal flight test: calibrate the force transducer from applied loads and recorded counts with a closed-form least-squares fit, derive the stick force gradient versus calibrated airspeed from a speed sweep with the stable-gradient verdict, compute the stick force per g from pull-up maneuvers, extract the breakout force from the push-pull hysteresis width, and run the control centering check of the residual control position...

Use when the task is dynamic stability flight testing, mode damping estimation, log decrement analysis, or handling qualities assessment. Plan and analyze a dynamic stability flight test: select the excitation technique for each mode (elevator doublet for the short period, elevator pulse for the phugoid, rudder pulse for the Dutch roll, aileron step for roll subsidence, rudder step for the spiral), reduce the decaying oscillation records to the log decrement, damping ratio, damped and undampe...

Use when you must plan and reduce the static lateral-directional stability flight test from steady-heading sideslip data: build the rudder-fixed and rudder-free sideslip sweep matrix at constant airspeed, fit the rudder and aileron deflection gradients versus sideslip angle, estimate the directional stability from the fitted rudder gradient with a declared rudder control power and the lateral dihedral stability from the fitted aileron gradient with a declared aileron control power, record the...

Use when the task is static stability flight testing, trim curve reduction, neutral point location, or static margin estimation. Evaluate the static stability flight test results: fit the trim curve to the elevator angle versus speed points, derive the trim curve slope, locate the stick fixed neutral point from the slope, estimate the static margin, and assess the elevator angle per g from the incremental elevator angle per load factor step. Produces the trim curve fit, the slope, the stick f...

Use when assessing the operational risk of a small UAS (drone) operation: check FAA Part 107 applicability (weight under 55 lb, visual line of sight, daylight, below 400 ft AGL, airspace class, remote pilot certificate), classify the operation under EASA SORA into open, specific or certified from kinetic energy and population density, compute the ground risk class (GRC), the air risk class (ARC) from airspace type, apply SORA robustness levels and containment, evaluate BVLOS waiver considerat...

Use when a task concerns guidance, navigation, and control for aerospace vehicles: guide the router to the gnc-autonomy pack: orbit-dynamics Hohmann and J2 drift, rendezvous-phasing phasing maneuvers, attitude-dynamics quaternion kinematics, navigation-frames ECEF/NED/WGS-84, inertial-navigation INS drift and Schuler, dilution-of-precision GDOP/PDOP, python-control-design PID margins, root-locus-design closed-loop poles, state-space-analysis controllability, pid-control-design Ziegler-Nichols...

Use when you must design and simulate an active-disturbance-rejection-control law for a second-order plant with an unknown total disturbance: run the linear-extended-state-observer with bandwidth-parameterized observer gains placing every observer pole at omega_o to estimate the state and the total disturbance, cancel the estimate with the disturbance-rejection term divided by the plant-gain estimate b0, and close the outer loop with the bandwidth-parameterized PD law on the estimated states ...

Use when you must design and simulate the tuning-functions adaptive backstepping control law for a second-order strict-feedback plant x1_dot = x2 + theta f1(x1), x2_dot = u + f2(x1, x2) with the unknown constant plant parameter theta inside the recursion: update the single parameter estimate theta_hat with the second tuning function carried through the z1 z2 error recursion, assemble the adaptive virtual control and the final control, and audit the augmented Lyapunov function with the paramet...

Use when you must design and simulate a model-reference adaptive controller (MRAC) for a first-order plant with an unknown plant coefficient: run the reference model from the command, form the control as the sum of a state-feedback term and a feedforward term with adaptive gains, update the gains online with the gradient (Lyapunov-motivated) adaptation law scaled by the tracking error, and assess convergence of the tracking error and of the gains toward the ideal-cancellation values. Produces...

Use when you must design and simulate the backstepping control law for a second-order strict-feedback plant x1_dot = x2 + f1(x1), x2_dot = u + f2(x1, x2) tracking a reference: choose the virtual control that stabilizes the first error variable z1 = x1 - x1d, propagate the inner-state mismatch z2 = x2 - alpha1 as the second error variable, differentiate the virtual control analytically along the plant, and assemble the final control from the recursion so the composite Lyapunov function V2 = (z...

Use when you must allocate a commanded roll, pitch, yaw moment vector across redundant aerodynamic and propulsive effectors: assemble the control effectiveness matrix, solve the pseudoinverse allocation or the weighted least squares problem, enforce the position limits with the redistributed pseudoinverse, distribute the moment between the aerodynamic and thrust vectoring groups with the daisy chain scheme, and report the achieved moment, allocation error and saturated effectors. Produces the...

Use when you must design a deadbeat-control law for a discrete-time plant given by its pulse transfer function: verify admissibility for direct deadbeat synthesis (every plant pole and zero strictly inside the unit circle), solve the deadbeat design equation that places every closed loop pole at the origin of the z plane, form the finite-settling-time controller difference equation from the plant polynomials, and simulate the closed loop to confirm the output reaches and holds the reference i...

Use when you must design a sampled-data digital control loop in the z-domain: discretize a continuous plant with a zero-order hold, emulate a continuous compensator with the Tustin bilinear transform with frequency prewarping, compute discrete PID coefficients in the position and velocity forms, check the sampled poles against the unit circle for stability, and select the sample rate from the closed-loop bandwidth. Produces the discretized plant coefficients, the emulated compensator, the dis...

Use when you must apply feedback linearization to a nonlinear plant with a known exact model: compute the Lie derivatives of the output along the drift and control vector fields to establish the relative degree, invert the decoupling scalar at the operating state, form the linearizing control that cancels the nonlinear terms so the output channel obeys the linear relation y^(r) = v, apply the outer linear tracking loop with the assigned closed-loop pole placement, and check the internal dynam...

Use when the task is bode analysis, frequency response, gain crossover, phase crossover, gain margin, phase margin, or stability from the margins. Compute the Bode frequency response of an open loop transfer function for flight control design: evaluate the magnitude and phase at a frequency from the numerator and denominator coefficients at s = j*w, find the gain crossover and phase crossover frequencies, derive the gain margin in dB and the phase margin in degrees, and judge closed loop stab...

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-windu...

Use when you must run the h-infinity mixed-sensitivity norm analysis of a feedback loop: given the plant transfer function, a candidate controller, the sensitivity weight and the control-effort weight, verify the closed loop is stable and compute the h-infinity norms of the weighted sensitivity functions by gamma iteration over the imaginary-axis frequency response, locating the worst-case peak magnitude of each channel. Produces the weighted-sensitivity norm, the weighted control-sensitivity...

Use when you must synthesize the state-space h-infinity controller of the generalized plant with the dgkf two-Riccati method: given the state matrices and the performance and control channels, iterate the gamma level while the x-infinity and y-infinity algebraic Riccati equations admit stabilizing positive-semidefinite solutions and the spectral-radius coupling stays below gamma squared, then form the central h-infinity controller state matrices from the state-feedback gain and the observer g...

Use when you must design and simulate an l1-adaptive-control law for a first-order plant with an unknown coefficient: run the state-predictor from the design model, drive the projection-based-adaptation-law with the prediction error, pass the adaptive signal through the low-pass filter omega_c/(s + omega_c) and form the control as the feedforward minus the filtered estimate. Produces the tracking-error and prediction-error time histories, the sigma_hat and filtered-signal histories, the proje...

Use when the task is lead lag compensation, phase margin improvement, steady state error reduction, or compensator design for a flight control loop. Design phase lead and phase lag compensators for aerospace flight control and GNC loops: compute the plant phase margin at gain crossover from the open loop transfer function, size the phase boost the lead network must add to meet the phase margin specification, derive the lead ratio alpha from the boost, place the lead zero and pole at the new c...

Use when you must design a full-order Luenberger state observer for a linear time-invariant system whose states are not all directly measurable: build the observability matrix and check observability, compute the estimator gain matrix by pole placement with the Ackermann formula so the observer error dynamics eigenvalues sit at the desired locations, verify the error dynamics are Hurwitz stable with the characteristic polynomial, confirm the separation principle so observer poles and controll...

Use when the task is PID tuning, proportional integral derivative terms, anti-windup, integrator clamping, pole placement, or gain and phase margin checks. Design PID controller gains for aerospace flight and GNC control loops: compute the controller output from the proportional, integral, and derivative error terms, tune the gains from the plant model with Ziegler-Nichols using the ultimate gain and ultimate period, or place closed loop poles directly for a first or second order plant, add i...

Use when designing and validating feedback control laws with Python control-systems tooling: evaluate gain and phase margins against acceptance limits (6 dB and 45 degrees), classify closed-loop stability from the margins, and apply Ziegler-Nichols tuning to get initial PID gains. Supports controller sanity checks (positive proportional, non-negative integral and derivative gains) before simulation or root-locus and Bode iteration. Pairs with the ARP4754A development-assurance context for con...

Use when you must design a feedback loop with the classical root locus method: compute the closed loop pole locations as the forward-path gain K varies, find the gain that places the dominant poles at a target damping ratio zeta, and judge closed loop stability from the characteristic equation 1 + K*G(s) = 0. Applies to the canonical type-1 plant G(s) = 1/(s(s + a)) used in flight control analysis. Produces the pole pair, the gain for the requested zeta, and the stability verdict that feeds c...

Use when you must design a sliding-mode-control law for a second-order plant with matched uncertainty: choose the sliding surface from the tracking error and its derivative, compute the equivalent control that holds the surface on the nominal model, add the switching term sized above the uncertainty bound inside the boundary layer to enforce the reachability condition, and suppress chattering with the saturation thickness. Produces the surface and equivalent-control histories, the sliding-con...

Use when you must compensate the dead time of a feedback loop with the smith-predictor structure: given a first-order-plus-dead-time plant model and given PI controller gains, run the delay-free plant model on the controller output, hold the model output in the delay line by the dead time, and subtract the delayed model output from the measured plant output to form the predictor feedback signal, so the primary controller closes on a delay-free compensated error. Produces the compensated error...

Use when you must analyze a linear time-invariant system in state space: form the controllability and observability matrices, decide controllability and observability from their ranks, compute the 2x2 eigenvalue stability verdict, build the state transition matrix by the Cayley-Hamilton method, and produce the controller or observer canonical forms. Applies to flight control and GNC state-space models written as x_dot = A x + B u with output y = C x. Produces the controllability and observabi...

Use when you must design and run an alpha-beta tracking filter for a constant-velocity target in SI units: predict the target position and velocity at the next sample time, form the residual from a noisy position measurement, apply the alpha and beta gain update to track position and velocity, and select the steady-state alpha and beta gains from the smoothing factor and the target maneuverability index. Produces the predicted and updated position and velocity, the residual sequence, and the ...

Use when you must run a Mahony-style explicit complementary filter attitude observer on so3 to fuse a spacecraft or air-vehicle rate gyro with sun sensor and magnetometer vector measurements into a continuous, drift-free attitude quaternion estimate with online gyro bias estimation: form the cross-product innovation from each body measurement against the reference vector rotated by the estimated attitude, drive the proportional and integral correction gains, update the bias estimate, and inte...

Use when you must compute the cramer-rao-lower-bound on the variance of an unbiased parametric estimator before data arrives: build the fisher-information-matrix as the negative expected second derivative of the log-likelihood for the scalar dc level in white gaussian noise, the gaussian mean with known variance, the vector gaussian mean with known covariance, the sinusoid phase in noise, or the poisson rate, and invert the information matrix to report the best achievable variance. Produces t...

Use when the task is nonlinear state estimation, Jacobian linearization, or extended Kalman filtering for tracking. Estimate the state of a nonlinear system with an extended Kalman filter: linearize the nonlinear dynamics and measurement model about the current estimate with the state Jacobian F and the measurement Jacobian H, run the predict step x_hat = f(x_hat), P = F P F^T + Q, then the update step with the innovation y = z - h(x_hat), the innovation covariance S = H P H^T + R, the Kalman...

Use when you must calibrate an IMU from laboratory static test data: reduce the six-position accelerometer test, the mean specific force with each body axis held up and down against the known plus/minus 1 g references, to the per-axis bias and scale factor from the paired holds, and extend the least-squares fit over all six positions to the scale and misalignment sensitivity matrix; reduce the rate-table gyro test, the measured rates regressed on the commanded rates of each axis, to the per-a...

Use when you must track a maneuvering target with an interacting multiple model filter: run a two-mode IMM bank of constant velocity (CV) and constant acceleration (CA) Kalman filters per planar axis, mix the mode-conditioned estimates through the Markov mode-transition probabilities, refresh mode probabilities from innovation likelihoods, and combine the per-mode estimates into the mixed state estimate. Produces mode probabilities that gate maneuver detection, per-mode estimates, the combine...

Use when you must estimate the state of a nonlinear or non-Gaussian system with a bootstrap particle filter: draw an initial particle ensemble from a Gaussian prior, propagate the particles through a constant-velocity or random-walk motion model with additive Gaussian process noise, weight them with a Gaussian measurement likelihood, normalize the importance weights, track the effective sample size, and trigger systematic resampling when the effective sample size drops below half the particle...

Use when you must discretize the continuous white noise of a linear system into the discrete-time process noise covariance for a Kalman filter with the van-loan method: given the continuous plant matrices F and G and the continuous-spectral-density Qc, compute the discrete-noise-covariance Qd as the exact integral of the propagated noise strength over the filter step and the state transition matrix from the matrix exponential of F times the step. Produces the discrete noise covariance Qd, the...

Use when you must run a fixed-interval Rauch-Tung-Striebel (RTS) smoother over a stored forward Kalman-filter output for a discrete constant-velocity model in SI units: propagate the position and velocity state with the constant-velocity transition matrix, run the linear forward pass that stores the predicted and filtered means and covariances at every step, then execute the backward recursion with the smoother gain to combine each filtered estimate with the future measurements. Produces the ...

Use when you must estimate the state of a nonlinear system with an unscented Kalman filter: generate sigma points from the state mean and covariance with the scaled unscented transform, propagate each point through the nonlinear dynamics, compute the weighted predicted mean and covariance, form the innovation covariance and the cross covariance, calculate the Kalman gain, and correct the state and covariance from a nonlinear measurement. Produces the predicted and corrected states, the state ...

Use when you must compute augmented proportional navigation guidance commands for a planar intercept of a maneuvering target: line of sight rate from the relative position and velocity vectors, closing velocity, the pure proportional navigation command as the baseline, the augmented command that adds the target lateral acceleration perpendicular to the line of sight scaled by half the effective navigation ratio, the time to go estimate, and the commanded lateral acceleration in g. Produces th...