A novel design methodology on cascaded fractional order (FO) PI-PD control and its real time implementation to Cart-Inverted Pendulum System

Abstract

The tune up of fractional order (FO)-PIλDμ controllers is largely advocated in available literature which mostly requires evolutionary optimization techniques or solution of complex non-linear equations thereby leading to lack of practical solutions in terms of selecting the controller parameters. It may be quite feasible if one can consider PID control in the form of cascaded PI−PD control with which the task of attainment of the control objectives can be accomplished methodically. In extension to this, studies related to FO PIλ−PDμ controller are not too exhaustive. Generally, graphical methods are adopted to compute the controller parameters. There is still paucity of comprehensive design algorithms for these controllers to which end this work comes up with a novel and simple specification driven design methodology of the cascaded structures of FO PIλ−PDμ and [PI]λ−[PD]μ controllers following the classical control theory Keeping away from the complex and implicit design strategies they assist with an exact and unique solution to design these FO controllers in frequency domain with satisfactory dynamic performance in time domain which may not be possible with the FO-PIλDμ controllers. Illustrative examples and experimental validations aid to substantiate the reliability of the proposed method.