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Proportional-integral (PI) controllers are the most common form of feedback used in industrial applications today . The use of proportional and integral feedback also has a long history of practical applications . For example, in the middle of the 18th century, centrifugal governors as the proportional feedback were applied to regulate the speed of windmills . By the 19th century, it was known that using integral feedback could remove the offsets appearing in working with governors . 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 . 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 , . The idea of using such a controller originated with fractional calculus, known as a generalization for classical calculus . The following section presents a brief review of recent fractional calculus applications in control system design.