Control of SCR System Having a Filtering Device

An emissions control system is disclosed. The emissions control system may have a power source that creates a flow of exhaust and a filtering device that receives the flow of exhaust. A first sensor may be located at or upstream of the filtering device, the first sensor being configured to measure a first temperature, and an SCR catalyst may be located downstream of the filtering device. The emissions control system may also have an injector configured to inject a reduction agent into the flow of exhaust in the presence of the SCR catalyst. The emissions control system may further have a controller in communication with the first sensor. The controller may be configured to predict a change in an ability of the SCR catalyst to store reduction agent using a measured change in the first temperature and adjust the injector according to the predicted change in the storage ability of the SCR catalyst.