Idle speed control with low-complexity offset-free explicit model predictive control in presence of system delay

The requirement for continual improvement of idle speed control (ISC) performance is increasing due to the stringent regulation on emission and fuel economy these days. In this regard, a low-complexity offset-free explicit model predictive control (EMPC) with constraint horizon is designed to regulate the idle speed under unmeasured disturbance in presence of system delay with rigorous formulation. Particularly, we developed a high-fidelity 4-stroke gasoline-direct injected spark-ignited engine model based on first-principles and test vehicle driving data, and designed a model predictive ISC system. To handle the delay from intake to torque production, we constructed a control-oriented model with delay augmentation. To reject the influence of torque loss, we implemented the offset-free MPC scheme with disturbance model and estimator. Moreover, to deal with the limited capacity assigned for the controller in the engine control unit and the short sampling instant of the engine system, we formulated a low-complexity multiparametric quadratic program with constraint horizon in presence of system delay in state and input variables, and obtained an explicit solution map. To demonstrate the performance of the designed controller, a series of closed-loop simulations were performed. The developed explicit controller showed proper ISC performance in presence of torque loss and system delay.