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The scientific world has recently witnessed a rapid growth in the number of articles, addressing the importance of fractional-order controllers with a primary focus on fractional-order proportional integral derivative controller. The purpose of this article is to provide a detailed analysis of fractional-order proportional integral derivative controller, including architecture, classification, control design, toolboxes, and applications. Further, this article also presents an extensive overview on fractional-order controllers, their tuning methods, and the role of multiple classical and artificial intelligence-based algorithms in calculating optimal controller gains. The main focus of this article is to analyze various single and multi-objective functions adopted for controller tuning in various applications. In addition to this, the presented work also provides a comprehend comparative analysis through a rigorous literature survey of fractional-order proportional integral derivative controllers exploited in power system applications, electric drive applications, power electronics applications, biomedical and health science applications, chemical and process industry applications, agricultural applications, etc., in the support of superiority of fractional-order proportional integral derivative controller over conventional proportional integral derivative controller.
Bashishtha et al. (Wed,) studied this question.