On a Property of a Class of Offset-Free Model Predictive Controllers

We consider a model predictive control framework that includes a discrete-time linear time-invariant nominal plant model augmented with an output integrator disturbance model and a Kalman filter to estimate the state and disturbance vectors. While the application of this framework can guarantee offset-free control, it has shown a consistent limitation in the achievable closed loop estimator performance. Using root locus techniques, we identify sufficient conditions for a class of nominal plant models with at least one real pole for which the closed loop estimator poles cannot be arbitrarily selected regardless of the augmented system's statistics. We present several examples illustrating the limitations of the closed loop estimator pole locations.