Scheduling Period Selection Based on Stability Analysis for Engagement Control Task of Automatic Clutches

The clutch engagement process involves three phases known as open, slipping, and locked and takes a few seconds. The engagement control program runs in an embedded control unit, in which discretization may induce oscillation and even instability in the powertrain due to an improper scheduling period for the engagement control task. To properly select the scheduling period, a methodology for control–scheduling co-design during clutch engagement is proposed. Considering the transition of the friction state from slipping to being locked, the co-design framework consists of two steps. In the first step, a stability analysis is conducted for the slipping phase based on a linearized system model enveloping the driving and driven part of the clutch, feed-forward and feedback control loop together with a zero-order signal hold element. The critical period is determined according to pole locations, and factors influencing the critical period are investigated. In the second step, real-time hardware-in-the-loop experiments are carried out to inspect the dynamic response concerning the friction state transition. A sub-boundary within the stable region is found to guarantee the control performance to satisfy the engineering requirements. In general, the vehicle jerk and clutch frictional loss increase with the increase in the scheduling period. When the scheduling period is shorter than the critical period, the rate of increase is mild. However, once the scheduling period exceeds the critical period, the rate of increase becomes very high.