As the flotation process is multivariable, this work investigates the implementation of a predictive multivariable controller for operation a typical flotation column. This controller was tested using a model with delays of a prototype column mounted on Nuclear Technology Development Center (CDTN). Taking as input signals the flushing wash water, air feeding, and non floated fraction flow rates, the controller determines the froth layer height and air holdup in the recovery zone. This control maintains stability. The operation of the controller is based on the optimization of a cost function. The conducted tests were based on the change of setpoint of the controlled variables. It was intended to analyze the system behavior for different operation conditions, considering the constraints of the process and the response speed.