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A comparative evaluation of a set of bio-inspired optimization algorithms for design of two-DOF robust FO-PID controller for magnetic levitation plant

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Abstract

Design, tuning and implementation of various control structures, such as one-degree of freedom (DOF) and two-DOF structures of both integer-order and fractional-order proportional integral derivative controller to stabilize the magnetic levitation plant, is proposed in this paper. The two-DOF structure has been formulated by incorporating a separate control loop in the existing one-DOF control structure. The parameters of all the controller structures have been tuned using evolutionary algorithms, namely, particle swarm optimization (PSO), teaching learning-based optimization (TLBO), genetic algorithm (GA) and black widow optimization (BWO). The performance of the algorithms has been compared on the basis of Wilcoxon signed-rank test and Friedman test. The controller structures have also been tested for disturbance rejection, by applying a periodic pulse distribution at the output of the closed loop. It is found that the system achieves iso-damping characteristic, exhibiting flat phase-plot at the vicinity of the gain cross-over frequency. It is also observed that the two-DOF FOPID controller structure exhibits an improvement of 45.02%, 7.6% and 7.81% in peak overshoot (OS), settling time (Ts) and rise time (Tr), respectively, over two-DOF IOPID, in case of GA. In comparison with GA, the improvement of 73.02%, 4.31% and 5.7% is witnessed for OS, Ts and Tr in case of PSO and 20.029%, 11.03% and 10.60% improvement is observed for OS, Ts, Tr in the case of TLBO algorithm. In contrast, the BWO-tuned two-DOF FOPID controller exhibits superior time-domain response as it generates an improvement of nearly 100%, 29.28% and 14.76% for OS, Ts and Tr. The proposed controller achieves superior disturbance rejection ability measured in terms of sensitivity and complementary sensitivity compared to other state-of-art algorithms.

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Authors and Affiliations

  1. Department of EEE, Centurion University of Technology and Management, Bhubaneswar, Odisha, India

    Amit Kumar Sahoo

  2. Department of EEE, Birla Institute of Technology, Mesra, Ranchi, India

    Sudhansu Kumar Mishra, Deep Shekhar Acharya, Sarbani Chakraborty & Subrat Kumar Swain

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Sahoo, A.K., Mishra, S.K., Acharya, D.S. et al. A comparative evaluation of a set of bio-inspired optimization algorithms for design of two-DOF robust FO-PID controller for magnetic levitation plant. Electr Eng 105, 3033–3054 (2023). https://doi.org/10.1007/s00202-023-01867-7

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