Development of Linear-Parameter-Varying Models for Aircraft

Abstract

This paper presents a comparative study of three linear-parameter-varying (LPV) modeling approaches and their application to the longitudinal motion of a Boeing 747 series 100/200. The three approaches used to obtain the quasi-LPV models are Jacobian linearization, state transformation, and function substitution. Development of linear parameter varying models are a key step in applying LPV control synthesis. The models are obtained for the up-and-away flight envelope of the Boeing 747-100/200. Comparisons of the three models in terms of their advantages, drawbacks, and modeling difficulty are presented. Open-loop time responses show the three quasi-LPV models matching the behavior of the nonlinear model when in the trim region. Differences between the models are more apparent as the response of the aircraft deviates from the nominal trim conditions. Nomenclature c 1 , . . . , c 9 = inertia coefficients c = wing chord, m F dec = decomposition function m = aircraft mass, kḡ q = dynamic pressure, N/m 2 S = reference surface area, m 2 s α , c α = sine, cosine AoA w(t) = nonscheduling states x, z cg = aircraft center of gravity position x, z axis, m z(t) = scheduling states z eng = engine position z axis, m α = angle of attack (AoA), deg α w = wing design plane α w = α + 2 deg ρ(t) = scheduling vector

Direct identification of continuous-time LPV models

“…This LPV modeling concept allows for a wide representation capability of physical processes, but the real practical significance of the LPV framework lays in its well worked out and industrially reputed control synthesis approaches, e.g. [1], [18], [24], that have led to many successful applications of LPV control in practice [3], [13], [14], [23].…”

Comparison of Aeroelastic Modeling and Robust Flutter Analysis of a Typical Section**This work has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 636307, project FLEXOP

“…The goal of each of those robust flutter studies was to provide an end-to-end process, from robust modeling to robust analysis, and demonstrate the validity of the approach. Since this was their focus, no detailed study or comparison was performed on the effect the modeling choices have on the analysis -although it is well-known in the robust control community that this is a fundamental issue (Marcos and Balas (2004);Magni (2004); Marcos et al (2015)). Thus, the goal of this article is to present a comparison of the modeling options and a better understanding of their effects on the flutter analysis.…”

Robust fault reconstruction for linear parameter varying systems using sliding mode observers

“…Despite the potential benefit of employing an LPV based design, the LPV model used as the basis of the observer will be imperfect, and this might cause false alarms or missed detections. For a LPV model generated using an interpolation of families of localized linear models (which is a commonly used approach), plant-model mismatch is present (especially) in the interpolated region where the model is not well defined (see for example [25], [29] for validation tests of an LPV plant comparing the actual plant states and LPV states). Other LPV generating methods will contain imperfect plant information due to simplifications and assumptions.…”

“…For example, in aircraft systems, a nonlinear FDI observer design often requires information about the aerodynamic coefficients, which is hard to obtain in the required form. However an LPV representation can easily be built from available families of linear systems over the entire flight envelope (see [8], [29] for examples of LPV system development and [32] for a recent generalized LPV model generation scheme). Through polynomial fitting, the LPV models may explicitly contain information about the aerodynamic coefficient variations over the flight envelope.…”