Parameter Estimation of Highly Unstable Aircraft Assuming Nonlinear Errors

Abstract

Flight test data of an unstable feedback controlled aircraft (Eurofighter) is artificially generated with added linear and nonlinear (de-)stabilizing error on the deri vati ves comprising also process and measurement noise that is analyzed with three estimators: equation error, output error, and wi th the new combi ned equati on/ output error methods estimati ng linear deri vati ves. The investigati on focuses on the estimation performance in the equation and output error domains when the estimators are applied on nonlinear errors wi th a linear error model. Main outcome is that when the error becomes nonlinear , the matching performance degrades and the s pread in the estimates of the various estimators increases considerabl y where underestimati on of the l ocal characteristics such as the stability characteristics occurs. Measurement and process noise influences particularl y the estimates of the secondary deri vati ves. If the error destabilizes the aircraft consi derabl y even small deviations in the estimates may produces very different maneuver responses in the output error domain which makes pure equation error estimation unrel iable in this respect. Moreover, the matching performance of the estimator is best in its own domain but compromising the other domain whereas the combi ned esti mator produces a g ood balance in matching performance for both equation and output error domains . Nomenclatureforce coefficient c l = rolling mo ment coefficient c m = pitching mo ment coefficient c n = yawing mo ment coefficient f = system state function F = process noise distribution matrix g = system observation function G = measurement noise distribution matrix I = inertia matrix J = cost function K = maximu m nu mber of time samp les l  = reference cord m = size of unknown parameter vector RMSE(x) = root mean square error o f x M  = mo ment vector N = maximu m nu mber of time samp les N = order of polynomial p = size of observation vector p,q,r = roll, p itch, and yaw rate S = reference area t = time t 0 = initial t ime u = control input vector v = measurement noise V = freestream velocity w = process noise w pi = diagonal elements of W W = normalizat ion matrix x = state vector x 0 = initial condit ion of state vector x 1,2,3 = input signals 1,2,3 y = simu lated observation vector z = measured observation vector  = angle of attack  = angle of sideslip  = flaperon deflection  = weighting between equation/output error  = normalizat ion factor  = unknown parameters to be estimated  = leading edge sweep   = angular rate vector  = aileron deflection  = rudder deflection § Professor in Aeronautics, Esplanade 10, 85049 Ingolstadt, Germany, and AIAA Senio r Member.Downloaded by MONASH UNIVERSITY on November 26, 2014 | http://arc.aiaa.org | q dyn = dynamic pressure s = half span Subscripts/Superscripts 0 = static offset ADM = aerodynamic model ctrl = control surface deflections Engine = engine related FT = flight test related G = gravity related i,j,n = i-th, j-th, n -th sample  = angle of attack derivative  ...