A method of controlling an air separation plant and a control system to optimize production of an argon product produced by the plant. A computer program is continually executed that has models of each column of the plant, a condenser reboiler and an argon reflux condenser. The models contain stage models of each stage of separation within each of the columns that when assembled are able to calculate current values of controlled variables in response to input variables applied to the models. The controlled variables serve as an input to a controller that controls manipulated variables comprising flow rates of an air feed stream to the air separation plant, a product oxygen stream removed from the lower pressure column and the crude argon feed stream such that the controlled variables are within a targeted range selected to optimize the production of the argon product.