Convex Hull Manipulation Based Optimization

Abstract

This chapter presents various studies about the benefits of using the TP model manipulation. First, it focuses on a simple study on a 3DoF wing section control problem without friction, and point out the fact that the derivation and manipulation of different TP models (obtained by manipulating the convex hull of the representation) for the controller and observer design leads to further powerful opportunities in terms of optimization. Next chapters investigate the fact that the complexity relaxation of the TP model derived from the 3DoF model excluding friction leads to control performance improvement even in cases when the relaxed TP model is not exact. Finally, both convex hull manipulation and complexity relaxation of the TP model are combined, and a comprehensive investigation is provided on the benefits of using TP model manipulation based control design. In the final version of this example, the 3DoF model will include friction, which results in a considerably more complex model with a 3-dimensional parameter vector. A comprehensive analysis is provided on the effects of TP model manipulation on the stability region and on control performance.