A control system for a transmission includes a memory module, a position module, an error module, an integral module, and an adjustment module. The memory stores a control value as a function of clutch torque. The position module controls a position of a clutch based on the control value. The error module periodically determines a slip speed error based on a difference between a target slip speed and an estimated slip speed of the clutch. The integral module periodically determines an integral of the slip speed error. The adjustment module adjusts the control value based on the integral. A method for controlling a transmission is also provided.