LPV Model Order Reduction by Parameter-Varying Oblique Projection

A method to reduce the dynamic order of linear parameter-varying (LPV) systems in grid representation is developed in this paper. It consists of an oblique projection and is novel in its use of a parameter-varying nullspace to define the direction of this projection. Parameter-varying state transformations in general lead to parameter rate dependence in the model. The proposed projection avoids this dependence and maintains a consistent state space basis for the reduced-order system. This extension of the projection framework lends itself very naturally to balanced truncation and related approaches that employ Gramian-based information to quantify the importance of subspaces. The proposed method is first compared to LPV balancing and truncation on a numerical example and then used to approximate two LPV systems: the longitudinal dynamics model of an aeroservoelastic unmanned aerial vehicle and the far wake model of a wind turbine.