A rubidium-82 ((82)Rb) elution system is described for use with positron emission tomography. Due to the short half-life of (82)Rb (76 s), the system physics must be modelled precisely to account for transport delay and the associated activity decay and dispersion. Saline flow is switched between a (82)Sr/(82)Rb generator and a bypass line to achieve a constant-activity elution of (82)Rb. Pulse width modulation (PWM) of a solenoid valve is compared to simple threshold control as a means to simulate a proportional valve. A predictive-corrective control (PCC) algorithm is developed which produces a constant-activity elution within the constraints of long feedback delay and short elution time. The system model parameters are adjusted through a self-tuning algorithm to minimize error versus the requested time-activity profile. The system is self-calibrating with 2.5% repeatability, independent of generator activity and elution flow rate. Accurate 30 s constant-activity elutions of 10-70% of the total generator activity are achieved using both control methods. The combined PWM-PCC method provides significant improvement in precision and accuracy of the requested elution profiles. The (82)Rb elution system produces accurate and reproducible constant-activity elution profiles of (82)Rb activity, independent of parent (82)Sr activity in the generator. More reproducible elution profiles may improve the quality of clinical and research PET perfusion studies using (82)Rb.