Quantification of Linear Approximation Error for Model Predictive Control of Spark-Ignited Turbocharged Engines

Modern turbocharged spark-ignition engines are being equipped with an increasing number of control actuators to meet fuel economy, emissions, and performance targets. The response time variations between engine control actuators tend to be significant during transients and necessitate highly complex actuator scheduling routines. Model Predictive Control (MPC) has the potential to significantly reduce control calibration effort as compared to the current methodologies that are based on decentralized feedback control strategies. MPC strategies simultaneously generate all actuator responses by using a combination of current engine conditions and optimization of a control-oriented plant model. To achieve real-time control, the engine model and optimization processes must be computationally efficient without sacrificing effectiveness. Most MPC systems intended for real-time control utilize a linearized model that can be quickly evaluated using a sub-optimal optimization methodology. Online linearization of the engine model is computationally expensive so it should be performed as infrequently as possible. Since engine dynamics are non-linear, a local linearity approximation error occurs during this process. This research presents a method of evaluating the impact of local linear approximation error on the modeled engine torque for a range of operating conditions. Transient experiments show a clear deviation between a non-linear model and its linearized version, which also depends on the type of transient induced. Step transients in engine torque are generally more forgiving with respect to the number of model linearization calculations required as compared to sinusoidal transients. The sinusoidal transients clearly show a narrow frequency range where the deviation in the models is highest.