Tuning of NMPC controllers via multi-objective optimisation

• A systematic procedure for the tuning of NMPC controllers is proposed.
• The procedure highlights the intrinsic multi-objective nature of the NMPC.
• The proposed procedure is successfully tested on two challenging case studies.
• The proposed procedure is also successfully tested in presence of disturbances model mismatch and changing in the NMPC settings.
• The proposed procedure results to be particularly effective in disturbance rejection for application where one variable is of key importance.

Nonlinear Model Predictive Control (NMPC) is a powerful technique that can be used to control many industrial processes. Different and often conflicting control objectives, e.g., reference tracking, disturbance rejection and minimum control effort, are typically present. Most often these objectives are translated into a single weighted sum (WS) objective function. This approach is widespread because it is easy to use and understand. However, selecting an appropriate set of weights for the objective function is often non-trivial and is mainly done by trial and error. The current study proposes a systematic procedure for tuning Nonlinear MPC based on multi-objective optimisation methods. Advanced methods allow an efficient solution of the multi-objective problem providing a systematic overview of the controller behaviour. Moreover, through analytic relations it is possible to link a solution obtained with these novel methods to a set of weights for a weighted sum objective function. Applying this set of weights causes the WS to generate the same solution as obtained with the advanced method. Hence, an appropriate controller can be selected based on the alternatives generated by the advanced method, while the corresponding weights for a WS can be derived for implementing the controller in practice. The procedure is successfully tested on two benchmark applications: the Van de Vusse reactor and the Tennessee Eastman plant.