Discussion on: “Simple Fractional Order Model Structures and their Applications in Control System Design”

Abstract

Fractional calculus is about the integration or differentiation of non-integer orders. The use of “fractional” is purely due to historical reasons [1]. Using fractional order differential equations is believed to be able to better characterize the nature around us. Using an integer order model is only for our own convenience. Depending on the scale onwhich we characterize the dynamics of a system, more and more evidences are found that using fractional order model is ubiquitous and unavoidable [1, 2, 3]. For dynamic systems and controls, there are four possibilities 1) Integer-order plant model with integer order controller; 2) Integer-order plant model with fractional order controller; 3) Fractional-order plant with integerorder controller; and 4) Fractional-order plant model with fractional-order controller [2]. Case-1 is our traditional (integer-order) control. An example of Case 2) can be found in [3] and an example of Case-4 can be found in [4]. Examples for Case-3 are abundant such as conventional integer-order controls for flexible structures whose transfer functions are irrational or of fractional order. It is interesting to note that, reaction curve based rough modeling technique, although widely used in process industry to get a first order plus delay time (FOPDT) for initial tuning of a working PID controller with techniques such as Ziegler-Nichols tuning rule, has not been put enough emphasis in control textbooks.Webelieve that, every practicing control engineer and control engineering educator should pay attention to the importance of reaction