Tuning rules for optimal PID and fractional-order PID controllers

In this paper we present a set of tuning rules for standard (integer-order) PID and fractional-order PID controllers. Based on a first-order-plus-dead-time model of the process, the tuning rules have been devised in order to minimise the integrated absolute error with a constraint on the maximum sensitivity. The achieved performance indexes can also be used for the assessment of the controller performance. Both set-point following and load disturbance rejection tasks are considered. By comparing the results obtained for the two kinds of controllers, it is shown that the use of fractional-order integral action is not advantageous, while the use of a fractional-order derivative action provides a performance improvement.