While design optimization has been employed effectively in the past few years to address the integration of design and control, the implementation of advanced model-based control techniques in such a framework has largely been ignored despite their advantages. The reason is that the advanced control schemes involve solving an optimization problem on-line, leading to a drastic increase in the complexity of the design framework. In this work a novel method is presented for integrating advanced model-based predictive controllers in a simultaneous process and control design methodology. Parametric programming is used for the controller derivation, giving rise to an explicit controller structure and removing the need for solving an optimization problem online. The resulting parametric controller is readily incorporated in the design optimization framework, bringing about significant economic and operability benefits. The key features and advantages of our approach are highlighted via binary distillation and evaporator motivating examples.