Robustness analysis and design of fractional order I^λ D^μ controllers using the small gain theorem

ABSTRACT

In this paper, a simple method is proposed to tune the parameters of Fractional Integral-Fractional Derivative (FIFE) I^λ D^μ controllers based on the Bode diagram. The proposed technique provides a practical approach for tuning FIFE controllers to compensate stable plants. Using the small gain theorem and based on the sensitivity functions analysis, it is proved that by applying the designed FIFE controller the robustness of the compensated system in the presence of plant uncertainties is improved in comparison to the PI controller in a similar structure. Moreover, the closed-loop phase margin and gain crossover frequency are adjustable by tuning the free controller parameters. Simulation results are presented to demonstrate the simplicity of application and effectiveness of the tuned controller.

Keywords:

• Fractional order I^λ D^μ controllers
• robustness analysis
• small gain theorem
• Bode diagram
• sensitivity functions

Acknowledgements

The authors would like to thank the respected reviewers for their valuable comments and constructive suggestions to enhance the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.