Exploring controller design techniques with minimum fragilities & defining risk limits for the closed loop system

Small perturbation in the parameters of a controller leads to a considerable change in the qualitative properties of the closed loop system. Such a controller is said to be "fragile." Uncertainties in the controller implementations cannot be avoided since there are some tolerances in the analog components whereas there would be some rounding of the controller parameters when controller is implemented digitally. All these facts make a controller, "fragile" to some extent no matter what design technique is used. In this paper we define a parametric stability band having fragile controllers within it and non-fragile controllers lying outside it. Controller design techniques are discussed exploring the methods of design having minimum fragility. Secondly the stability radii of different control systems before and after the reduction of fragility are measured so that they can be marked as fragile for the former case or stabilized in the latter case.