Methods for controlling the in-feed and discharge rates of materials flowing into and out of a mixing process where one priority is to achieve a target mixture flow rate from the mixing process and another priority can be to achieve a target value for a mixture property. Actuators can be operated to control material in-feed rates, the mixture composition, and discharge rate, and can maintain a hold-up of the mixture in the mixing process. A total flow rate controller provides a control signal to a controller acting on the discharge rate and a controller acting on the in-feed rates. The mixture discharge flow rate can be automatically reduced from its desired target when the commanded rate of at least one of the materials exceeds its available supply rate as inferred from an inability to maintain the targeted value for the mixture property.