Nonlinear QFT Based on Local Linearization

Abstract

Nonlinear QFT have been developed using two different approaches: a global approach based on the subtitution of the nonlinear plant by a equivalent linear set (depending of acceptable outputs), and another class of techniques in which the nonlinear plant is substituted by a equivalent linear set and a disturbances set. This work explores the potentials of a technique based on the second class, where the equivalent linear set is computed using local linearization about acceptable trajectories or equilibrium points. A comparison of the local and global approaches is made for several examples, giving as a result that local linearization is more conservative, in the sense that more control effort than needed is used. Finally, a pH control problem is solved by using the local approach, giving good results. As a result, local synthesis seems to be more conservative than global synthesis. A reason may be that there is some loss of structure in the model used for local synthesis. On the other side, local synthesis is easier to apply in practice, and is the unique option when only a set of local models is available. It is our belief that an integration of both techniques will be the most suitable one to achieve a solution with minimum control effort.