Real-Time Dynamic Modeling: Data Information Requirements and Flight Test Results
AIAA Atmospheric Flight Mechanics Conference and Exhibit
Practical aspects of identifying dynamic models for aircraft in real time were studied. Topics include formulation of an equation-error method in the frequency domain to estimate non-dimensional stability and control derivatives in real time, data information content for accurate modeling results, and data information management techniques such as data forgetting, incorporating prior information, and optimized excitation. Real-time dynamic modeling was applied to simulation data and flight test
... ata and flight test data from a modified F-15B fighter aircraft, and to operational flight data from a subscale jet transport aircraft. Estimated parameter standard errors and comparisons with results from a batch output-error method in the time domain were used to demonstrate the accuracy of the identified real-time models. Nomenclature x y z a , a , a = body-axis translational accelerometer measurements, g or ft/sec 2 e a r f , , , = elevator, aileron, rudder, and trailing-edge flap deflections, rad or deg c dc s ds , , , = canard, differential canard, stabilator, and differential stabilator deflections, rad or deg , , 2 = parameter vector = covariance matrix = frequency, rad/sec superscripts T = transpose † = complex conjugate transpose ˆ = estimate = time derivative -1 = matrix inverse subscripts o = reference value I. Introduction YNAMIC modeling in real time has many important practical uses, such as improving the efficiency of stability and control flight testing, flight envelope expansion, adaptive or reconfigurable control, vehicle health monitoring, and fault detection. Several methods 1-5 have shown potential for identifying local linear dynamic models from flight data in real time. One of these methods 4,6 is based on a recursive Fourier transform and equation-error modeling in the frequency domain. This method, sometimes called the Fourier Transform Regression (FTR) method, produces very accurate results with valid error measures and has many practical advantages. The FTR method has also been independently evaluated 7,8 as the best method available for real-time dynamic modeling. For these reasons, the FTR method was chosen for further study and application. The FTR method has been successfully applied 6-11 to identify accurate linear dynamic models in real time at individual flight conditions. While this capability is important and useful, further progress requires that this capability be extended to continuous application as the aircraft flies through a wide range of changing flight conditions throughout the flight envelope. Ultimately, local real-time modeling results could be integrated into a global aerodynamic model that could be updated in real time as the aircraft changes flight conditions, changes configuration, ages, or becomes damaged in some way. This vision of real-time global dynamic modeling has many important implications for efficient flight testing, accurate flight simulation, adaptive or reconfigurable control, and aircraft safety. One important aspect of applying real-time dynamic modeling for varying flight conditions and aircraft configurations is determining the data information content requirements for accurate dynamic modeling results. Changing aircraft flight conditions or aircraft configurations means that parameters in the approximating dynamic model change. Dynamic motion of the aircraft, either from ordinary flight operations or from control surface excitation, is necessary so that the measured data will exhibit the aircraft dynamics to be modeled. Naturally, if the real-time dynamic modeling is to be done continuously or on a regular basis, it is important that only the minimum necessary aircraft excitation be applied, and the resulting aircraft motion should be as small and unobtrusive as possible. This paper investigates data information requirements for accurate real-time dynamic modeling. Flight experiments on a modified F-15B fighter aircraft are used to illuminate issues related to data information content necessary for accurate real-time modeling. Real-time modeling is also applied to operational flight data from a subscale jet transport model, to evaluate the feasibility of real-time modeling without specific excitation. This is an important step in extending local real-time modeling to the case of changing conditions, interpreted broadly to include flight condition changes, configuration changes, damage, and failure scenarios. Issues such as data information content necessary for fast and accurate local modeling, model validation, necessary excitation, data forgetting, and methods for incorporating prior information are studied. The next section describes the methods used. A model formulation is developed that retains full nonlinear dynamics, with linearized aerodynamic models. The FTR method is described, along with explanations of methods for data forgetting and incorporating prior information into the real-time parameter estimation algorithm. Next, the flight test aircraft are described, including flight instrumentation and characteristics of the flight data. The results section includes simulation and flight test investigations examining data information requirements for accurately identifying local dynamic models in real time. Finally, the concluding remarks summarize progress made so far and outline next steps.