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Idle speed performance improvement via torque balancing control in ignition-event scale for SI engines with multi-cylinders

Imbalance in torque generation leads to engine speed fluctuation. To improve the idle engine speed performance, the torque balancing control problem is addressed in this paper for multi-cylinder SI engines. To evaluate cylinder-to-cylinder imbalance, the average torque in ignition-event scale is introduced as controlled output, which enables a feedback control to be performed without measurement of instantaneous torque, and the individual spark advances are chosen as control inputs. A linear discrete time model with single input and single output is proposed to represent the dynamics of the imbalance, where a sequentially switching function is introduced to describe the spark advance signals delivered to each cylinder and the differences in torque generation caused by the individual cylinder characteristics are equivalently modelled as unknown offset in the inputs. An estimation algorithm with the proof of convergence is presented to provide on-line estimation of the unknown offset under the passivity assumption of the system. Furthermore, a feedback control law which combines the unknown offset estimation and the model predictive control is proposed. Finally, the unknown offset estimation and the feedback control approach are validated based on the experimental results carried out on a six-cylinder gasoline engine test bench.