Automated controller design using linear quantitative feedback theory for nonlinear systems

A method to design simple linear controllers for mildly nonlinear systems is presented. In order to design the desired controller we approximate the behavior of the nonlinear system with a set of linear systems which are derived through linearizations. Classical local linearization is carried out around stationary points but in order to have a better approximation of the nonlinear system selected non-stationary points are taken into account as well. This set of linear models are considered as an uncertainty description for a nominal plant. Quantitative Feedback theory (QFT) may be used to guarantee specification to be fulfilled for all linear models in such an uncertainty set. Traditionally QFT design is carried out in a Nichols diagram by loop shaping of the nominal linear plant. This task highly depends on the experience of the designer and is difficult for unstable systems. In order to facilitate this task an optimization algorithm based on Genetic algorithm is used to automatically synthesize a fixed structure controller. For illustration and evaluation the method is successfully applied to a Wiener system and a nonlinear Bioreactor benchmark problem.