Technical solutions described herein include an emissions control system for treating exhaust gas in a motor vehicle including an internal combustion engine. The emissions control system includes a model-based controller to control reductant injection into the exhaust gas. Controlling the reductant injection includes determining an amount of NOx and an amount of NH3 at an outlet of the first SCR device, and at an outlet of the second SCR device. The controlling further includes computing an amount of reductant to inject to maintain a first predetermined ratio between the amount of NH3 and the amount of NOx at the outlet of the first SCR device and to maintain a second predetermined ratio between the amount of NH3 and the amount of NOx at the outlet of the second SCR device. Further, the controlling includes sending a command for receipt by the reductant injector to inject the computed amount of reductant.