Lee, T. and Filipi, Z., "Nonlinear Model Predictive Control of Advanced Engines Using Discretized Nonlinear Control Oriented Models," SAE Technical Paper 2010-01-2216, 2010, doi:10.4271/2010-01-2216.
This paper proposes a methodology to develop a nonlinear model predictive control (NMPC) of a dual-independent variable valve timing (di-VVT) engine using discretized nonlinear engine models. In multiple-input-multiple-output (MIMO) systems, model based control methodologies are critical for realizing the full potential of complex hardware. Fast and accurate control oriented models (COM) that capture combustion physics, actuator and system dynamics are prerequisites for developing NMPC. We propose a multi-scale simulation approach to generate the non-linear combustion model, where the high-fidelity engine cycle simulation is utilized to characterize effects of turbulence, air-to-fuel ratio, residual fraction, and nitrogen oxide (NOx) emissions. The input-to-output relations are subsequently captured with artificial neural networks (ANNs). Manifold and actuator dynamics are discretized to reduce computation efforts. The discretized models are capable of handling nonlinearity of dynamics models caused by varying time steps depending on engine speeds and other inherent characteristics. The models are realized using system identification based on autoregressive ANNs. Then, NMPC is designed to achieve requested torque responses and to track the optimal actuator responses closely. The latter is important for eliminating excursions of residual and associated emissions penalty during a transient. NMPC using discretized models is capable of achieving dead-beat like control with much shorter computation time and with short prediction and control horizons.