Observer pole placement limitations for a class of offset-free model predictive controllers

Model predictive control (MPC) algorithms achieve offset-free control by augmenting the nominal system model with a disturbance model. The disturbance vector is used to predict the mismatch between the measured and predicted output vectors. In this paper, we consider an offset-free MPC framework that includes an output disturbance model and a Kalman filter to estimate the state and disturbance vectors. Using root locus techniques, we identify sufficient conditions for a class of nominal systems with at least one real positive pole for which the closed loop estimator poles cannot be arbitrarily selected. We present several examples illustrating the limitations of the closed loop estimator pole locations.