Optimal tuning rules for proportional-integral-derivative and fractional-order proportional-integral-derivative controllers for integral and unstable processes

A set of tuning rules for standard (integer-order) proportional-integral-derivative (PID) and fractional-order PID controllers for integral and unstable processes is presented in this study. Based on a simple model of the process, the tuning rules have been devised in order to minimise the integrated absolute error. Both set-point tracking and load disturbance rejection tasks are considered. The achieved performance indexes can also be used for the assessment of the controller performance. A remarkable feature of the optimisation procedure employed for integral processes is highlighted. The provided results allow the user to quantify, for a given process, the performance improvement that can be obtained by using the fractional controller instead of the integer one.