From Traditional to Fractional PI Control: A Key for Generalization

Abstract

Proportional-integral (PI) controllers are the most common form of feedback used in industrial applications today [1][3]. The use of proportional and integral feedback also has a long history of practical applications [4]. For example, in the middle of the 18th century, centrifugal governors as the proportional feedback were applied to regulate the speed of windmills [5]. By the 19th century, it was known that using integral feedback could remove the offsets appearing in working with governors [6]. At present, PI control, still a very basic form of feedback, is also one of the first solutions often considered in the control of industrial systems [7]. On the other hand, in some applications, using the PI controller in its traditional form may not be satisfactory, and a more advanced controller is needed to achieve control objectives. In such cases, modified versions of the PI controller have been proposed to enhance the controller's performance. The fractional-order PI controller is one of these modified versions, and it is attracting increased interest in control system design uses [8], [9]. The idea of using such a controller originated with fractional calculus, known as a generalization for classical calculus [10]. The following section presents a brief review of recent fractional calculus applications in control system design.