Nonlinear Predictive Control

Authors:

• Piotr Tatjewski,
• Maciej Ławryńczuk

Abstract

Model Predictive Control (MPC) algorithms using nonlinear process models are the subject of consideration in this chapter. The applied nonlinear models are in the form of general difference equations or state-space equations. MPC algorithms using directly nonlinear models in the optimization of the trajectory of the manipulated variables are described in the first part of the chapter. This leads to strictly optimal solutions, but is practically restricted to processes with slow dynamics due to difficult, time consuming nonlinear optimization. For the case of state-space models, the original authors’ approach to the modeling of disturbances and state estimation is presented. The most extensive part of the paper is devoted to effective, suboptimal MPC algorithms with successive linearizations, which enables us to replace nonlinear optimization by a quadratic one. Several versions of such algorithms are presented, with different linearization structures. This class of algorithms enables us to apply nonlinear modeling to fast dynamical systems, leading generally to suboptimal results, but usually fully acceptable in engineering practice. This is confirmed by the presented results of simulation studies of two processes. Finally, augmentations of MPC algorithms to incorporate current set-point optimization are described, to increase economic efficiency of the control structures.