A sensitivity measure for an electronic, proportional-integral (PI) controller and calculating optimum parameter tolerances

The PI controllers are one of the most important control elements used in process control industry. In this study, first a method is proposed to determine the optimum parameter tolerances by the use of the sensitivities of an electronic PI controller's transfer function. These tolerances keep the relative error of the output of the PI controller due to parameter variations, in tolerance region. Then a sensitivity measure is defined to be used to improve the sensitivity performance of the PI controller and to compare various PI controllers with different set of design parameter values which realize the same transfer function.