Nonlinear model reduction — method and CAE-tool development

Abstract

New methods for nonlinear model reduction of dynamic models, described by nonlinear differential equations have been developed. The methods are based on singular perturbations, weak coupling and cost functionals for computing and analyzing the reduced order model. By introducing a formally affine nonlinear model structure, the cost functional vector optimization yields closed expressions for the reduced order system. Via Lagrange multipliers even constraints with regard to the reduced order system can be considered, only extending these closed expressions. This leads to the notion of smaller and control-oriented realizations. The methods have been programmed and integrated into a MATLAB-based toolbox, termed as NEON (Nonlinear Order Reduction). NEON uses standard MATLAB/SIMULINK and the GUI, OPTIMIZATION, CONTROL and SYMBOLIC toolboxes. Via NEON the methods are here applied to a structural dynamic aircraft model, in order to achieve a very low order model, suited for integral structural dynamic and flight mechanical controller design.