In one embodiment, a vehicle braking system, for delivering pressurized air to a brake chamber to achieve a desired braking response, includes an air-pressure controlled relay valve for delivering the pressurized air to the brake chamber. A solenoid receives a variable control input pressure and delivers the control input pressure to the relay valve as a function of a state of the solenoid. An ECU controls the solenoid according to a control model for delivering the pressurized air to the brake chamber and achieving the desired braking response.