Robustness of Nonlinear MPC for Dead-time Processes*

This paper studies the effect of the predictor structure and tuning in the robustness of model predictive controllers (MPC) when controlling dead-time processes. It is shown that although MPC techniques can easily cope with systems with dead time because of their internal predictor structure, this implicit predictor can make the stability margins of the controller dependent on the nominal dead-time. This delay dependency can be an important drawback of the controller, causing instability even for small modelling errors when controlling processes with large delays. Therefore, it is necessary to define a proper predictor for the MPC algorithm in order to improve robustness. In this paper a predictor structure derived from the Filtered Smith Predictor is proposed which simplifies the tuning and allows improved robustness. The analysis of stability and robustness is first done for the linear MPC case, and then generalized for nonlinear MPC for a class of nonlinear systems. The key idea of this approach is to separate the predictor structure from the optimization stage in such a way that input-to-state stability and constraint satisfaction can be guaranteed by using an equivalent dead-time free system.