Purely Analog Fractional Order PI Control Using Discrete Fractional Capacitors (Fractors): Synthesis and Experiments

Document Type

Conference Paper

Journal/Book Title/Conference

ASME 2009 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference


American Society of Mechanical Engineers


San Diego, CA

Publication Date



This paper presents the results of experiments related to analog fractional order PI control of a coupled tank system. A custom circuit board has been built to perform analog PID/FOPID control. Specialized circuit elements called ‘Fractors’ [1] are used to perform fractional order integration/differentiation of the error signals. The design of the board, subsequent experimentation and its comparison to similar digital control techniques have been presented. The benefits of purely analog control when dealing with non-linearities are also discussed. Further, methods of approximating a particular fractional order α* with any number of practically available orders α1,α2,....αn has also been presented. The conclusion of this work examines the need for purely analog control as opposed to widespread digital methods and also lays down definite directions for future work.

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