Generalized State-Space Realization of Parameter-Dependent Unsteady Aerodynamic Models

Abstract

There is increasing interest in the development of next-generation optimal controllers in the aerospace industry, focused on reducing aircraft environmental impact by mass reduction and enabling higher flight velocities for flexible wing structures. A key challenge in designing an optimal control system for this purpose is modeling the unsteady aerodynamic loads in a form convenient for control analysis, namely, a state-space form. In this thesis, three novel approaches for generating state-space realizations of unsteady aerodynamic loads, with one varying parameter, are presented. The approaches are based on parametric Loewner frameworks, namely, transfer matrix interpolation, global basis, and multivariate interpolation. The parametric Loewner frameworks are combined with additional techniques for reducing the system to standard, stable form. The input to the realization problem is the aerodynamic transfer matrix, calculated with a compressible potential solver for a pitching and plunging flat plate at discrete values of reduced frequency and the parameter of interest, free-stream Mach number. An extensive analysis on accuracy, dimension, and dynamic behavior of the parametric state-space models is carried out to determine the approach most suitable for aeroservoelastic applications. It is shown that for the considered aerodynamic model, all the approaches are time efficient and generate highly accurate and low dimensional state-space representations of the unsteady loads. However, when applied to aeroservoelastic modeling, the approach based on multivariate interpolation method is expected to suffer from numerical instabilities due to the high numbers of degrees of freedom. The other two approaches, based on transfer matrix interpolation and global basis, are more suitable for modeling multiple input-multiple output systems and model reduction. Therefore, these approaches are considered appropriate for control design. The conducted research and gained experience suggest that the approach based on global basis is generally preferred over the transfer matrix interpolation based approach. However, in the cases with large sampled sets or drastically changing aerodynamic data over the parameter range of interest, the approach based on transfer matrix interpolation is recommended.