Fractional order PID controller design based on Laguerre orthogonal functions

• Published in: International journal of dynamics and control Vol. 5; no. 3; pp. 542 - 550
• Main Authors: Tabatabaei, Mohammad, Salehi, Romina
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2017; Springer Nature B.V
• Subjects: Basis functions; Complexity; Control; Control and Systems Theory; Controllers; Dynamical Systems; Engineering; Indexing; Order parameters; Orthogonal functions; Orthonormal functions; Performance indices; Process controls; Production planning; Transfer functions; Vibration; Fractional order Laguerre functions; Fractional order PID controller; Laguerre functions; Orthogonal functions
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-016-0248-8

This paper proposes a novel fractional order PID controller for commensurate fractional order systems based on Laguerre orthonormal functions. The transfer functions of the fractional order plant, the desired loop gain and the fractional order PID controller are expanded in terms of their Laguerre basis functions. Matching the first three coefficients of the Laguerre series of the loop gain with the desired one yields the fractional order PID controller parameters. The pole of the fractional order Laguerre basis function is adjusted to minimize an integral square error performance index subject to control signal constraint. The numerical examples are presented to show the effectiveness of this Laguerre based fractional order PID controller.