Method of controlling a transmission clutch

During the inertia phase of a shift, the oncoming clutch is controlled to alleviate shift quality degradation due variability of clutch friction coefficient. The friction coefficient sometimes increases as the slip speed nears zero. The commanded clutch pressure is a sum of an open loop term and a closed loop term. The open loop term decreases as the clutch slip decreases. Thus, when the friction coefficient increases at the end of the inertia phase, the clutch torque remains nearly constant. When the friction coefficient does not increase at the end of the inertia phase, the closed loop term responds to the resulting decreasing rate of slip speed reduction.