In a powertrain including an engine controlled by the position of the throttle valve, a hydrodynamic torque converter and multiple ratio automatic transmission connected to the drive wheels of the vehicle, a solenoid-operated hydraulic valve supplies pressurized fluid to engage and release the clutch that controls torque transfer between an offgoing clutch and an oncoming clutch. The position of the throttle valve and the speed of the engine are applied as input to a mathematical model programmed in algorithmic form for execution by a digital microprocessor. The engine produces a signal representing net torque output by the engine and torque converter, which signal is applied as input to an inverse mathematical model of the solenoid-operated valve that supplies hydraulic fluid to the controlling clutch. The unique relationship of phase to gain, the frequency response of the solenoid valve, is inverted within the frequency range of interest to remove the effects of delay. Torque converter turbine speed error is determined as it is applied as input to a PID compensated feedback control, whose output is summed with the inverse of the solenoid valve frequency response to produce a duty cycle supplied to the solenoid that controls pressure in the transmission friction element.