Abstract
This paper presents a fractional-order PD\(^{\alpha }\) control method for the master and slave system under communication time delay. First, a fractional-order PD\(^{\alpha }\) controller is designed based on the dynamic model of the master and slave system in order to improve the precision and flexibility of operation. Then, the associated characteristic equation for the fractional-order system with time delay is analyzed by taking the time delay as parameter, and the sufficient conditions of asymptotic stability are established to ensure the synchronization of the considered system from eigenvalues point of view. Furthermore, the maximum upper bound of time delay is derived by considering the distribution of roots for characteristic equation. Finally, three numerical simulation examples are given to illustrate the accuracy of conditions and the validity of the novel control architecture.
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This work is supported by the Foundation of Hebei Education Department (QN2018006) and the Five Platform Foundation of Hebei University of Science and Technology (2015PT21)
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Ji, Y. Synchronization analysis for master and slave system under communication time delay using fractional-order PD\(^{\alpha }\) control. Int. J. Dynam. Control 7, 525–535 (2019). https://doi.org/10.1007/s40435-018-0475-2
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DOI: https://doi.org/10.1007/s40435-018-0475-2