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Robustness Analysis of Nonlinear Dynamic Inversion Control Laws for Flight Control Applications.

Papageorgiou C.

2003

Abstract

This thesis evolves around a nonlinear control design technique, which is popular in the design of flight control laws. The technique is called Nonlinear Dynamic Inversion. It can explicitly address the nonlinearities in the aircraft dynamics and can provide a control law which is valid for the whole of the flight envelope without the need for gain-scheduling linear controllers. The purpose of this thesis is to extend the applicability of the technique to aircraft with significant interactions between the rigid and flexible modes and to derive nonlinear tests for analysing the robustness of the NDI controller in the presence of parametric uncertainties. A modified inversion technique is proposed for the control of aeroservoelastic aircraft, that provides good tracking of the rigid body modes and suppression of the flexible modes' vibrations. The design problem is formulated as an optimisation over the allowable positions on the aircraft structure on which to measure the variables to be controlled, so that the controlled output response is matched to a target response that satisfies handling qualities and vibration suppression. The technique is demonstrated on a nonlinear, F/A-18, merged model and is shown to exhibit good performance under rather strict assumptions about the uncertainty of the flexible modes. It is concluded that the proposed technique is more suited to aeroservoelastic aircraft whose flexible modes are within the desired rigid modes' bandwidth. The problem of analysing the robustness of a nonlinear, closed-loop system under NDI control is transformed into analysing the robustness of a quasi-LPV model. The quasi-LPV model captures both the nonlinearities via the endogenous scheduling variables, and the uncertainty via the external parameters. The derived tests are local tests and are based on quadratic Lyapunov functions. The robust stability is assessed using estimates of the region of attraction of an equilibrium point and the robust performance is assessed using the Ltwo-induced gain from reference inputs of a certain energy to the performance outputs. Both problems are formulated using LMI's and solved using either a gridding procedure or an LFT formulation. A robust model matching criterion is proposed for the comparison of different NDI controllers, and it is demonstrated via an example that NDI control laws with explicit integral action, attain better performance than the ones with simple, proportional gain. Keywords: nonlinear dynamic inversion, robustness analysis, aeroservoelasticity, quasi-LPV modelling, quasi-LPV analysis.

BibTex Entry

@PhdThesis{,: author = {Papageorgiou C.},; title = {Robustness Analysis of Nonlinear Dynamic Inversion Control Laws for Flight Control Applications. },; year = {2003}
}



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