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.