Session: 04-02-02: Advances in Aerodynamics & Novel Aerospace Propulsion Systems

Paper Number: 71173

Start Time: Tuesday, 10:45 AM

71173 - Bell 412 Full Flight Envelope Aircraft Simulation Model Development and Evaluation With Nonlinear Equations of Motion 

Aircraft simulation models are crucial for any aircraft development program with applications including pilot training, performance analysis, and control law development. To be useful, these models must be applicable throughout the aircraft’s entire flight envelope, including the possible range of speeds, altitudes, and aircraft configurations. It is common practice to use linearized small perturbation equations of motion for the system identification of the stability and control derivatives. The linearization renders these models valid only for a single flight condition and are aptly named “point models”. A “global model” can be formed by connecting these point models using a technique such as regression or interpolation to form a model that is valid and useful throughout the entire flight envelope. This fitting process, however, introduces additional sources of error thus creating a discrepancy between the quality of a point model and a global model. Despite the increased use and validity of the global model and the divide between global and point model matches, aircraft system identification literature typically evaluates the quality of a model by the quality of the point model match.

This study is motivated by observations that a high parameter variance exists for time-domain system identification performed on data at similar flight conditions. The high variance is especially problematic when forming a global model where a meaningful regression may not be possible. It is hypothesized that some of the variance in stability and control derivatives is due to the equation linearization error. Due in large part to recent advancements in computer technology and optimization techniques, the use of nonlinear equations of motion and nonlinear parameter constraints, such as to enforce model stability, is now feasible. This study develops and applies flight model system identification implementing these nonlinear equations and constraints for the National Research Council of Canada’s Bell 412 helicopter. The results are compared to a model developed from traditional small perturbation equations. A key component of this study is the evaluation of the overall global model instead of the point models.

It was observed that the use of the full nonlinear equations of motion produced a flight model with reduced parameter variance and improved static or trim characteristics when compared to the conventional linear model while maintaining a similar or better quality of time-history matches. Parameter variances and the number of outliers were both reduced for the nonlinear model. The nonlinear model also required smaller offsets to match the real aircraft trim condition. Further, the nonlinear model incorporated a nonlinear constraint enforcing stability of the output model, which was informed by observations made through flight testing. Accordingly, it is shown that the nonlinear model is stable across the entire range of dynamic pressures considered in this study while the state-space model has unstable zeros. Due to the presence of these unstable zeros, a simulator developed using the global model derived from the linear model will become unstable if a feedback loop with sufficiently high gain is closed. Thus, this places a limit on the performance of any stabilizing controllers. Furthermore, unlike unstable poles, unstable zeros cannot be moved to the left side of the Nyquist plot with a feedback controller, meaning there are speed ranges where the aircraft will be uncontrollable and unstable. In conclusion, this study compared a global flight simulation model developed using both linear and nonlinear equations of motion. The overall nonlinear global model quality was evaluated and concluded to have similar or improved performance to the linear model in terms of the parameter variance, model stability, trim characteristics, and time-history matches.

Presenting Author: Alexander Crain National Research Council Canada

Authors:

Alexander Crain National Research Council Canada
Joseph Ricciardi National Research Council Canada
Terrin Stachiw National Research Council Council