A method of regulating an amount of NH3 stored in a catalyst of an exhaust after-treatment system includes determining a mass of NH3 into the catalyst based on a dosing rate of a dosing agent that is injected into an exhaust stream upstream of the catalyst and determining a mass of NH3 out of the catalyst. An accumulated mass of NH3 within the catalyst is calculated based on the mass of NH3 into the catalyst and the mass of NH3 out of the catalyst. The dosing rate is regulated based on the accumulated mass of NH3 within the catalyst.