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An expert 2DOF fractional order fuzzy PID controller for nonlinear systems

Abstract

This work presents a generic two-degree-of-freedom fractional order fuzzy PI-D (2DOF FOFPI-D) controller dedicated to a class of nonlinear systems. The control law for proposed scheme is derived from basic 2DOF fractional order PID controller in discrete domain. Expert intelligence is embedded in overall derived control law by utilizing formula-based fuzzy design methodology. The controller structure comprises of fractional order fuzzy PI (FOFPI) and fractional order derivative filter to handle multiple issues and provides flexibility in design and self-tuning control feature. Further, the proposed scheme is compared with its integer order counterpart and 2DOF PI-D controller for coupled nonlinear 2-link robotic arm in real operating environment. The parameters of designed controllers are optimally tuned using multi-objective non-dominated sorting genetic algorithm-II for attaining low variation in control effort and error index. Intensive simulation studies are performed to analyze trajectory tracking, model uncertainty, disturbance due to cogging, sensor noise and noise as well as disturbance rejection simultaneously. Results demonstrate the superior performance of 2DOF FOFPI-D controller as compared to other designed controllers in the facets of different operating conditions.

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Correspondence to Vijay Mohan.

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Mohan, V., Chhabra, H., Rani, A. et al. An expert 2DOF fractional order fuzzy PID controller for nonlinear systems. Neural Comput & Applic 31, 4253–4270 (2019). https://doi.org/10.1007/s00521-017-3330-z

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  • DOI: https://doi.org/10.1007/s00521-017-3330-z

Keywords

  • 2DOF FOFPI-D
  • Formula-based fuzzy design
  • Multi-objective optimization
  • Robustness testing