Aeroservoelastic Model Uncertainty Bound Estimation from Flight Data

Abstract

Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust ight control system development. There has been a serious de ciency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from ight data using both parametric and nonparametric identi cation techniques. The model validation problem addressed here is to identify aeroservoelastic models with associated uncertainty structures from a limited amount of controlled excitation inputs over an extensive ight envelope. The challenge is to update analytical models from ight data estimates while also deriving nonconservative uncertainty descriptions consistent with the ight data. Transfer function estimates are incorporated in a robust minimax estimation scheme to update models and get error bounds consistent with the data and model structure. Uncertainty estimates derived from the data in this manner provide an appropriate and relevant representation for model development and robust stability analysis. The method incorporates parametric and nonparamteric uncertainty into various uncertainty structures for quantitative measures of robust stability relating to parameter variations and unmodeled dynamics. This model-plus-uncertainty identi cation procedure is applied to aeroservoelastic ight data from the NASA Dryden Flight ResearchCenter F-18 Systems Research Aircraft. Nomenclature f A; B; C; Dg = plant state-space matrices f O A; O B; O C ; O Dg = estimated plant state-space matrices K = controller P = aeroservoelasticplant O P = updated aeroservoelasticplant T = complementary sensitivity function W = uncertainty weightings y = output frequency response vector 1C = uncertainty in C matrix 1H = uncertainty in model-multiplier parameter vector 1 a = complex additive uncertainty 1 i = complex input-multiplicativeuncertainty 1 o = complex output-multiplicativeuncertainty 1 r = real output-multiplicativeuncertainty 1 r o = mixed output-multiplicativeuncertainty ² = minimum upper bound of " " = frequency-dependentadditive uncertainty H = model-multiplier parameter vector O H = estimated model-multiplier parameter vector ¹ = structured singular value U = matrix of modal frequency responses Á = model frequency response vector

The mu-k Method for Robust Flutter Solutions

“…(17)(18)(19)(20). Also note that the sign of each partition in V( p, q, M) can be chosen arbitrarily because if the system is stable subject to ∆ M it is also stable subject to −∆ M and so on.…”

“…(17)(18)(19)(20) only considers a linear dependence on the uncertain parameters δ j . If higher-order parametric perturbations or nonparametric uncertainty need to be considered, 18 the LFT framework from robust control 15 can be utilized to form the corresponding flutter loop. The LFT framework is also convenient for posing different subsystems as LFTs, which will be utilized in the subsequent case study.…”

Robust Eigenvalue Analysis Using the Structured Singular Value: The µ-p Flutter Method

“…So far, the framework has relied on model validation based on single-input/ single-output frequency responses of the system [4,22,23]. Although this transfer-function model-validation technique can still be applied, the -p framework also enables model validation based on modal flight data, as described in the following sections.…”

Integration of Aeroservoelastic Properties into the NASA Dryden F/A-18 Simulator Using Flight Data from the Active Aeroelastic Wing Program

“…This can make discrimination between the source and responses of components affecting aeroservoelasticity difficult to determine [11]. Thus in order to be able to distinguish system component dynamics and determine the expected response of an aircraft in flight, structural, aerodynamic, and control system disciplines can no longer be treated independently and must be studied together to fully understand the phenomena associated with aeroservoelasticity [10,22].…”

“…The process to convert this information into a working model that the F/A-18 simulator can use is based on a modeling process derived by Brenner, Prazenica, and Lind [11,20,21]. In order to create an accurate model from flight data that takes into account the elastic dynamics of the aircraft, a nominal model was first created as an initial estimate to represent the true aircraft.…”