A rubidium-82 (⁸²Rb) elution system is described for use with positron emission tomography. Due to the short half-life of ⁸²Rb (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 ⁸²Sr/⁸²Rb generator and a bypass line to achieve a constant-activity elution of ⁸²Rb. 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 ⁸²Rb elution system produces accurate and reproducible constant-activity elution profiles of ⁸²Rb activity, independent of parent ⁸²Sr activity in the generator. More reproducible elution profiles may improve the quality of clinical and research PET perfusion studies using ⁸²Rb.