Local Jacobian based Galerkin Order Reduction for the Approximation of Large-Scale Nonlinear Dynamical Systems

In automotive applications large-scale nonlinear dynamical models are utilized for hardware-in-the-loop simulations and model-based controller design. A projection-based order reduction of these models, on the one hand, yields substantial advantages in computational speed and on the other hand, simplifies the controller design procedure. In this work a mathematical-empirical approach is chosen for the order reduction of a real-time diesel engine model. It is based on recorded time-snapshots for typical system excitations. Flat and nonlinear Galerkin approximations are obtained by projection onto a lower-dimensional sub-space. In the nonlinear Galerkin approach a novel scheme for the reconstruction of the omitted states is introduced. It makes use of the local model parameters in the local Jacobian matrix, obtained from a linearization of the complete nonlinear model for various points of a local model network. The results from the application of the reduction methods to the engine model are presented and discussed for different reduced model orders and the benefits of the iteration scheme are demonstrated. Keywords—Diesel engine modeling, Model order reduction, Singular value decomposition, Snapshot method, Galerkin methods, Local model network