On the generation of LFT-based uncertainty models for flight control law robustness analysis

This paper considers the problem of generating Linear Fractional Transformation (LFT) based uncertainty models for the robustness analysis of flight control systems using the structured singular value μ. Two approaches to the problem are described. The first is an 'exact' approach based on physical modelling, which requires detailed information about the way in which the uncertain aircraft parameters enter the aircraft dynamic equations. This approach is compared with an easier and faster method which uses the differences in the linearised trims that arise from a simulation model of the aircraft evaluated at different points over the uncertain parameter space as a basis for LFT construction. Although this method could potentially be quite conservative, we show by an example robustness analysis for the lateral control law of a civil transport aircraft that the proposed 'difference-based' approach yields comparable bounds on μ to those generated via the exact method. This is due partly to the absence of repeated real uncertainty constraints in the LFT's generated via the difference based approach, resulting in a less conservative μ-analysis problem formulation than that generated by the exact LFT representation. Our results indicate that, for many practical aerospace analysis problems, it may be feasible to use simple, easily automated algorithms for LFT-based uncertainty modelling.