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Multi-parametric model predictive control (mp-MPC) makes possible the application of MPC controllers with a low on-line computational demand and rapid sampling. It is appealing for low-level control applications, where the disturbance-rejection properties are very important. This study explores two important issues in the transition from mp-MPC theory to the implementation of an industrial controller: offset-free output-feedback tracking, and controller tuning based on local linear analysis of the closed-loop system. An experimental case study on a two-input single-output system for pressure control in the vacuum chamber of a wire annealer is presented.