H_∞ control for morphing aircraft via non-affine parameter dependent LPV model

Morphing aircraft can adaptively alter configuration according to the different flight conditions or a variety of missions to ensure the optimal aerodynamic performance in flight. A class of variable-span morphing aircraft were considered, and the controller design synthesis for linear parameter varying (LPV) systems with non-affine parameter dependent configuration was researched. Jacobian linearization approach, as well as exact fitting method, was used on multiple balance points to transform the nonlinear model of morphing process into the LPV structure which regards the ratio of variable-span as the varying parameter. In contrast to most LPV systems, the obtained structure was polynomial instead of affine parameter dependent. An equivalent linear time-invariant (LTI) system for the non-affine LPV structure can be obtained by linear fractional representation (LFR). On basis of the sufficient condition of linear matrix inequality(LMI) for quadratic Lyapunov stability, a design methodology of the state feedback H_∞ controller was presented to guarantee the stability of morphing process. Its effectiveness for the globally stable performance was illustrated with simulation results, even when the external disturbance was taken into account. Therefore, the controller synthesis based on LFR transformation is no longer limited to the affine parameter dependent form, and can be widely applied to universal LPV system.