Fragility and robustness level accomplishment of well known PI/PID robust tuning rules

The robustness of a control system is by now a well established issue. Especially within the PI/PID domain, this is a requirement that is included as part of the design specifications by some of the new design approaches. In this paper we analyze how recognized robust PI/PID tuning rules accomplish with respect to their robustness specification. A concrete analysis is conducted where the chosen PI/PID controller tuning rules are based on a precise quantitative robustness specification such as the Maximum Sensitivity; M_S; value. It is reported that the claimed robustness specification in most of the cases is not accomplished for some set of plants, on other cases it is accomplished with excessive margin therefore providing a not satisfactory robustness/performance trade-off. In addition, even some of the PI/PID tuning rules do not accomplish with the specified robustness level, a fragility analysis is conducted to evaluate how they perform with respect to the achieved robustness. The conclusion drawn from this study is that even if the robustness issue has been incorporated in the new approaches for tuning and design of PI/PID controllers, this does not suffice. In order to appropriately tackle the robustness/performance trade-off, the achieved robustness level should not only be an integral specification but its accomplishment should be checked.