Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

Abstract

The X-56A aircraft is a remotely-piloted aircraft with flutter modes intentionally designed into the flight envelope. The X-56A program must demonstrate flight control while suppressing all unstable modes. A previous X-56A model study demonstrated a distributed-sensing-based active shape and active flutter suppression controller. The controller relies on an estimator which is sensitive to bias. This estimator is improved herein, and a real-time robust estimator is derived and demonstrated on 1530 fiber optic sensors. It is shown in simulation that the estimator can simultaneously reject 230 worst-case fiber optic sensor failures automatically. These sensor failures include locations with high leverage (or importance). To reduce the impact of leverage outliers, concentration based on a Mahalanobis trim criterion is introduced. A redescending M-estimator with Tukey bisquare weights is used to improve location and dispersion estimates within each concentration step in the presence of asymmetry (or leverage). A dynamic simulation is used to compare the concentrated robust estimator to a state-of-the-art real-time robust multivariate estimator. The estimators support a previously-derived mu-optimal shape controller. It is found that during the failure scenario, the concentrated modal estimator keeps the system stable. Nomenclature= maximum desired strain variation on sensors upstream of the fiber break = bias on sensor near the fiber break = current M-step = number of M-steps = current concentration step = number of concentration steps = squared Mahalanobis distance ( ) = squared Mahalanobis distance of the argument = upper bound of ( ) = deformations defined at time = reference deformations = finite residuals of all sensors = finite residual of the sensor = plant = tuning constant for weight function of M-estimator = controller = sensor station 1 Aerospace Engineer, PhD; NASA Armstrong, Controls Branch / 4840D; AIAA Member; peter.m.suh@nasa.gov. 2 Aerospace Engineer; NASA Armstrong, Aerostructures Branch / 4820; alexander.w.chin@nasa.gov. 2 = index of SFOS used for sensor feedback = row index vector of for reference deformations ( ) = median of the argument = number of mode shapes retained in the model = column index vector of for reference modal displacements = number of nodes in finite element model ( ) = normal distribution with argument parameters = airframe sensor noise = bias induced by simulated FOS failure on sensors = simulated fiber optic sensor noise = tuning constant ( ) = position of fiber break ( ) = positions of sensors in a radius upstream of the fiber break ( ) = vector of modal displacements at time ( ) = modal displacement at time ̂ = estimated modal displacements ̂( ) = estimated modal displacements at time step ( ) = modal displacement references = radius of sensors affected near the fiber break = set of all sensors = set of good sensors in concentration step = set of sensors upstream and near the fiber break ̂ ( ) = SFOS strain measurements ( ) = measured strain of sensor after the fiber break (...

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