A control system for an automatic transmission coupled to an engine by a torque converter includes a torque module and a first clutch control module. The torque module determines an input torque to the transmission based on an output torque of the engine. The first clutch control module adjusts an acceleration of a turbine of the torque converter during a down shift of the transmission based on the input torque. The first clutch control module adjusts the acceleration of the turbine by adjusting a first pressure of fluid supplied to an off-going clutch of the transmission based on the input torque. The first clutch control module adjusts the first pressure based on a mathematical model that relates a torque capacity of the off-going clutch, the input torque, and the acceleration. A method is also provided.