This paper addresses the design and implementation of a robust multivariable model predictive control (MPC) on a quadruple tanks system. Mismatch between the MPC's model and the process may cause constraint violation, non-optimized 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 how this model mismatch is compensated by augmented state disturbances, and also how the steady state error is eliminated. In this 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 implementation.