The design and implementation of a robust multivariable model predictive control (MPC) on a quadruple tanks system (QTS) is addressed in this paper. Mismatch between the MPC's model and the process may cause constraint violation, nonoptimized performance, and even instability. It is the objective of this paper to offset-free control the process in the presence of constraints and model mismatch. It is shown in this paper how this model mismatch is compensated by augmented state disturbances, and also how the steady-state error is eliminated. In the proposed method, an observer is designed to estimate the disturbances and states. The results show how the proposed control method increases the robustness of the model predictive controller in simulation and in real-time implementations on a new QTS proposed in this work together with techniques designed to identify the parameters of this novel plant.