Research ArticleTwo-stage observer based offset-free MPC

•We design a MPC controller for dynamic systems in the presence of disturbances.•We focus on the decoupling principal and present an efficient method for observer design.•We show that observer design can be done separately by solving a norm minimization problem.•The proposed approach can be applied to both eMPC and online-MPC in same manner.

This paper addresses design of model predictive control (MPC) for dynamic systems in the presence of disturbances. For the systems with disturbances, it is common to use observers to estimate states and disturbances, allowing control algorithm to reject disturbances. In this paper, we demonstrate how one can extend model predictive control for systems with disturbances by applying full state and disturbance observer. To this aim, a two-stage approach is proposed where the observer design procedure is completely decoupled from the MPC problem, known as the separation principle. We focus on the decoupling principal and it is shown that the observer can be designed independently via a norm minimization problem to reduce effects of disturbances and model mismatch. On the other hand, the MPC law is obtained using the multi-parametric quadratic programming approach where the parameters are the components of the state vector.