Nonlinear Model Order Reduction for Predictive Control of the Diesel Engine Airpath

In this paper, balanced truncation based on empirical gramians is explored for nonlinear model order reduction of a diesel airpath (DAP) model to facilitate effective nonlinear model predictive control (NMPC) design and implementation. Several issues are identified for the standard empirical gramian formulations, especially for the DAP model whose inputs, states, and outputs are constrained and have very different scales, and a modified formulation of the empirical gramians to mitigate the issues is proposed. The reduced order model, derived using balanced truncation based on the proposed empirical gramian, is applied to design the NMPC for the DAP system. The resulting performance is evaluated through simulations and compared with those obtained using other gramian based nonlinear model order reduction methods to demonstrate the effectiveness of the proposed approach.