Accuracy Estimation of Digital Fractional Order PID Controller

  • Krzysztof OprzędkiewiczEmail author
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 407)


In the paper an accuracy estimation method for digital fractional order PID controller is discussed. Integral and derivative parts of a controller are approximated with the use of Power Series Expansion (PSE) and Continuous Fraction Expansion (CFE) methods. These approximations are fundamental tools to modeling fractional-order elements with the use of integer-order, discrete, proper transfer function in the form of FIR or IIR filter. The accuracy of each approximation is a function of its order and other parameters. It can be estimated via comparison of step responses: analytical and approximated in sample moments. The step response expressed by accurate analytical formula can be interpreted as a standard. Approach presented in the paper can be applied during implementation of FO PID at each digital platform (microcontroller, PLC). Results of simulations show, that the CFE approximation allows us to build a FO PID controller so accurate, as constructed with the use of PSE, but much more simple to implementation, because its order is significantly lower.


Digital fractional order PID controller PSE approximation CFE approximation 



This paper was supported by the AGH (Poland) – project no


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Faculty of Electrotechnics, Automatics, Informatics and Biomedical Engineering, Deptartment of Automatics and Biomedical EngineeringAGH University of Science and TechnologyCracowPoland

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