Realization of Fractional-Order Proportional Derivative Controller for a Class of Fractional-Order System in Delta Domain

  • Jaydeep SwarnakarEmail author
  • Prasanta Sarkar
  • Lairenlakpam Joyprakash Singh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 989)


The study of the fractional-order controller (FOC) is an emerging area of research in system and control at the present scenario. In this paper, a fractional-order proportional derivative \( \left( {PD^{\eta } } \right) \) controller is implemented for a class of fractional-order plant from certain design specifications of the frequency domain. The entire work has been accomplished in two stages. The first stage deals with the design of continuous-time FOC to satisfy the desired design criterions. In the second stage, a continued fraction expansion (CFE) based direct discrete-time approximation method has been employed to realize the continuous-time FOC in delta domain. The realization of the discrete-time FOC employs the transformed delta operator as a generating function. The efficacy of the controller design method is verified by engaging the discretized FOC with the fractional-order plant and subsequently verifying the frequency response of the discretized open-loop system with respect to the desired frequency response of the original open-loop fractional-order system. The robustness of the overall controlled system is also investigated by altering the plant gain. Simulation results are presented to justify the efficacy of the proposed FOC realization method.


Fractional-order controller Continued fraction expansion (CFE) Delta operator Delta domain 


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Jaydeep Swarnakar
    • 1
    Email author
  • Prasanta Sarkar
    • 2
  • Lairenlakpam Joyprakash Singh
    • 1
  1. 1.Department of Electronics & Communication EngineeringSchool of Technology, North-Eastern Hill UniversityShillongIndia
  2. 2.Department of Electrical EngineeringNational Institute of Technical Teachers’ Training and ResearchKolkataIndia

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