Assessing Nonlinear Robustness of Control Law Designs

This work is aimed at evaluating the extent to which numerical bifurcation analysis tools can contribute to the determination of Regions of Attraction (ROA) for stable solutions of a dynamical system. The focus is on different flight scenarios within a safe flight envelope for a mathematical model of an airliner, aimed at being able to contribute to the assessment of aircraft control law designs. The implications of the study can be applied to other similar dynamical systems. In a multi-dimensional nonlinear system, computation of an exact ROA is difficult, as is its graphical representation and interpretation. Problems become more complicated when the behavior of system parameters (such as aircraft control surfaces) is also taken into account. The system under consideration here is a polynomial representation of the NASA GTM aircraft model. Bifurcation analysis was carried out on this nonlinear aircraft model for understanding its steady state behavior with respect to input parameters and evaluating the multiple solution branches to give an indication as to the steady-state ROA for varying input parameters. Time history-based ROA analysis was then carried out, to understand the transient state response and for determining a multidimensional ROA for a constant input parameter value. This helped in specifying the maximum value of disturbance an aircraft can be subjected to and still return to the stable trim point. Differences between the bifurcation analysis and the time history results highlight the difficulty in estimating a ROA for a multi-attractor multi-parameter multi-state nonlinear aircraft system. The benefits of combining the results obtained from bifurcation analysis with time history-based region of attraction analysis is discussed; this offers the prospect of a ROA within which, for a range of predefined input parameters, an aircraft subjected to any disturbance will return back to a specific stable trim point. The solution hence provides a measure of robustness for aircraft systems and aircraft control law designs.