Non-linearity of the engine system creates a challenge in building a reliable control-oriented model (COM). The main source of non-linearity is the complex nature of the combustion process. Modern engine system configurations are increasingly complex and predicting their transient response poses additional difficulty. In the present paper, a COM is developed to address the challenges and capture the behaviour of a high-degree-of-freedom engine system. Engine combustion models are created by utilizing the high-fidelity engine cycle simulation to characterize the effects of main parameters, such as turbulence, air—fuel ratio, and residual fraction, and subsequently capturing the interrelationships with artificial neural networks. Then, system dynamics are accounted for by adding manifold and actuator dynamics models. The capabilities of the proposed COM are demonstrated using a spark-ignition engine with a dual-independent cam phasing as a test case. The results indicate the model's ability to accurately predict engine responses to an arbitrary schedule of engine control inputs over the feasible operating range.

Optimal engine calibration methodology at part-load operating conditions using a multi-scale simulation approach is proposed and demonstrated on a spark ignition engine with dual-independent variable valve timing and a charge motion control valve. Fuel economy is typically selected as a calibration objective at part-load operating conditions. However, to secure vehicle driveability and smooth engine operation with low vibration and harshness, the combustion variability is considered by introducing the coefficient of variation in the indicated mean effective pressure characterized through a statistical analysis of experimental data. Other engine responses are fully predicted through a co-simulation approach by implementing the quasi-dimensional combustion simulation into the one-dimensional gas exchange simulation, and subsequently captured by an artificial neural network for fast computation. The best actuator set points are determined by solving the constrained multiple-objective optimization problem with fuel economy and combustion variability objectives under partload conditions. The calibration eliminates a high combustion variability at low loads and low speeds, maintaining most of the fuel economy benefit achievable with variable valve timing, and it can be used for an implementable feedforward control strategy.

Significant excursions of engine variables occur during fast transients because of slow actuator responses and system dynamics. This creates adverse effects on dynamic performance and often causes emissions penalties. The challenge is particularly pronounced in engines with an increased number of actuators. In this paper, non-linear model predictive control (NMPC) is introduced to improve the dynamic response of a flexible engine system. NMPC combines advantages of both feed forward and feedback control while considering their constraints. The length of control horizon and prediction horizon are determined to achieve the dead-beat-like optimal control during transients and ensure smooth responses. The NMPC significantly improves the engine torque response and minimizes the excursions of in-cylinder variables under highly transient operation by adjusting each actuator control input simultaneously to achieve the control objectives.