  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.
