Fuel State Reconstruction for Maneuvering Aircraft

Abstract

Agile, high performance aircraft are based more and more on flight mechanical unstable airframes with control laws stabilizing the air vehicle. This requires an accurate knowledge of the center of gravity position, particularly during agile maneuvering. This theoretical investigation is intended to serve a systematic framework in form of a fuel system which tries to cover all aspects of defueling during flight. Measurement and process noise as well as biases are accounted for in the simulated performance characteristics of fuel pumps and fuel probes. A simple simulation delivers the rates and accelerations exerted on the tanks which are typical for agile maneuvering. Various approaches such as an output and filter error approach are compared with the simulated fuel probe measurement with respect to their fuel state prediction capability. Main outcome is that the fuel probe measurements fail to predict fuel states during agile maneuvering whereas their accuracy is acceptable during gentle course changing maneuvers. The integration of pump rates in the output error approach shows significant deviations in the fuel states during simulation since it fails to cope with the process and measurement noise. Only the filter error approach which fuses in an optimal manner probe data during gentle course changing maneuvering and integration of pump rates during agile maneuvering produces a significantly improved fuel state prediction capability which translates into an accurate cg calculation. I. Nomenclature= center of gravity f, f  = system state function F = process noise distribution matrix FF T = covariance matrix of process noise T F Fˆ = modelled covariance matrix of process noise FE = filter error approach FS = fuel stage g, g  = system observation function G = measurement noise distribution matrix GG T = covariance matrix of measurement noise T G Gˆ = modelled covariance matrix of measurement noise I = identity matrix I y = inertia around y-axis k 1 = measurement noise parameter K k = Kalman gain at k-th time sample L EngLH = left engine power lever r N = distance wing to horizontal stabilizer CG Tank Tank R R   , = empty tank cg position CG AC R  = aircraft cg position S = reference area S  = acceleration rate at tank t,t = time, time step T 2 = time to double u = control input vector v, v  = measurement noise with variance 1 V 0 , V  = freestream velocity w, w  = process noise with variance 1 x, x  = fuel content in tank/fuel state x max = maximum fuel content in tank x CG = x-position of c.g.  k x = predicted fuel state at k-th time sample k x = corrected fuel state at k-th time sample y, y  = simulated observation vector y CG = y-position of c.g. z, z  = measured observation vector Z  = normal force derivative  = angle of attack  = angle of sideslip § Professor in Aeronautics, Esplanade 10, 85049 Ingolstadt, Germany, and AIAA Senior Member. Downloaded by UNIVERSITY OF ILLINOIS on October 1, 2015 | http://arc.aiaa.org | L EngRH = right engine power lever L L ,L W = length and width of tank m = ma...