Tuning the implementable structures of fractional-order PID controllers for control of FOPDT processes

This study presents a set of rules for optimal tuning a class of integer-order controllers, known as implementable fractional-order PID controllers, to be applied in control of first-order-plus-dead-time (FOPDT) processes. To this aim, the approach of so-called “tuning based on the implementable form of the controller” is applied instead of the common approach of “tuning based on the ideal form of the controller”. Consequently, no contradiction is found between the behavior of the tuned controller and that of the implemented controller. Also, algebraic relations between the values of cost functions, which are defined based on integral square error (ISE) and integral square time error (ISTE) performance indices, and free parameters of the implementable controller are established. Tuning implementable fractional-order PID controllers via the proposed rules guarantees that the values of performance indices are reduced in comparison with the case of using optimal PID controllers. In addition to numerical results, experimental results are also provided to demonstrate the effectiveness of the proposed tuning rules in practical applications.