An Economic Nonlinear Model Predictive Control Strategy for SI Engines: Model-Based Design and Real-Time Experimental Validation

This paper proposes a model predictive torque control strategy for spark-ignition engines with external exhaust gas recirculation. The proposed economic nonlinear model predictive controller (E-NMPC) tries to minimize fuel consumption, given an indicated mean effective pressure (IMEP) tracking reference and abnormal combustion constraints such as knock and combustion variabilities. A nonlinear optimization problem is formulated and solved in real time using sequential quadratic programming (SQP) to obtain the desired control actions. The SQP utilizes active set quadratic programming (QP) algorithms, with warm-start techniques that exploit the structural similarities between successive sub-QPs along the SQP sequence. This process reduces QP iterations by approximately 60% for each SQP update. Simulation results demonstrate that the proposed model predictive controller can track the IMEP reference with an rms error of 1.1% for engine cycles without active combustion constraints. When the IMEP reference conflicts with constraints, the SQP E-NMPC can efficiently find close-to-optimal control actions that are similar to those from off-line feed-forward calibration. The proposed algorithm is validated on an engine dynamometer. The algorithm executes in a prototype engine controller with a mean computation time of 1.07 ms, proving its feasibility for future engine control unit implementation.