Disclosed are SCR predictive control systems, methods for using such control systems, and motor vehicles with SCR employing predictive control. A method for regulating operation of an SCR system includes receiving sensor signals indicative of NOx output downstream from an SCR catalyst, and sensor signals indicative of exhaust gas temperature upstream from the SCR catalyst. The method determines if a model error condition has occurred for the NOx output signal and, responsive to such an occurrence, modulating dosing injector output for at least a calibrated designated time period. Upon expiration of the designated time period, the dosing injector is activated and commanded to inject reductant in accordance with a modulated dosing value. After the dosing injector injects the modulated dosing value of reductant, the method determines if the SCR system is underdosing or overdosing based on a response shape of signals received from the outlet NOx content sensor.