Nonlinear Aerodynamic Modeling of Unstable Aircraft Using Flight Test

This paper presents five direct identification methods for estimation of nonlinear aerodynamics of unstable aircraft. This type of identification is hard under the best of circumstances. In the context of system identification, direct means that no knowledge of the stabilizing flight control system (FCS) is used. This makes the methods more general and they could thus be used easily for different aircraft. JAS 39 Gripen is designed to be subsonic pitch unstable and supersonic pitch stable to gain performance. For maneuvering close to trim conditions, the aerodynamics can be considered linear, but for aggressive, high angle-of-attack maneuvering and flight at transonic speeds where aerodynamic shocks are present there will be nonlinearities. This leads to the need for a flight control system that can handle these complexities. The FCS of JAS 39 Gripen is gain scheduled and has many different flight modes. In order to design the control laws, high quality simulation models are needed. This in turn makes system identification an important task. Here five methods that can be used to estimate nonlinear aerodynamic characteristics from flight test data will be presented. The first method that we will discuss here is a parameterized observer (PO) approach where the observer gain is added to the unknown parameters to be identified. This gives a simple but fast method. The second and Fig. 1 JAS 39 Gripen test aircraft. third approaches are the Extended (EKF) and the Unscented (UKF) Kalman filter, both nonlinear versions of the ordinary Kalman filter. These three first methods are versions of the prediction error method and involve iterative minimization of a cost function using a Levenberg-Marquardt optimization procedure. The fourth method add the unknown parameters as new states with zero dynamics and the state vector in this augmented system (AUG) is then estimated with an EKF in a single run. All these four methods rely on the possibility to predict the system output. The fifth method is a bit different. It uses a constrained Levenberg-Marquardt (CLM) optimization procedure to minimize a Lagrangian function which does not depend on simulation of the system at all. Therefore the instability is not a problem. Instead the method puts constrains on every time sample. In this paper, results are given for both simulations and a real flight test in the transonic envelop.