This paper presents the development of a State Space Constrained Multivariable Predictive Controller and its implementation in an industrial process control problem. Compared with other model based predictive controllers, the state-space formulation gives better numerical stability, with the additional advantage that can be applied to Multivariable systems without modifying its structure. Moreover, it is possible to consider constraints in the states of the process. So, by selecting an adequate state-space representation of the plant, it is possible to consider constraints in non-measured variable. After developing a Constrained Multivariable Predictive Controller based on a State-Space representation and a discussion of the constraints that are usually considered in process control problem, the application of this technique to the control of a milk of lime blending tank is presented. This system is part of the purification process of a sugar factory.