Fragility evaluation of PI and PID controllers tuning rules

Abstract

Currently, the design of Proportional Integral Derivative (PID) controllers must take into account the closed-loop control system performance to set-point and load-disturbance step changes, its robustness to the changes in the controlled process characteristics, the control effort smoothness and extreme requirements, and its fragility to the variation of the controller parameters. In this chapter, the early work on the controller fragility is revised and the Delta Epsilon Robustness and Performance Fragility Indices are presented as measurements of the loss of robustness and/or performance when the controller parameters change due to inaccuracies in its implementation or due to its final fine tuning. Using the Delta 20 Fragility Indices, the fragility index is defined when a controller may be considered as a robustness or performance resilient, non-fragile or fragile controller. The fragility of a tuning rule as a whole, its ability to produce robustness- and/or performance-non-fragile controllers, is evaluated using the fragility plots. It is shown that although a controller tuning rule can produce control systems with a constant nominal robustness over its entire range of application, the controller fragility is affected by the controlled process parameters and by the control algorithm implementation.