TY  - JOUR
AU  - Li, Wei
AU  - Huang, Dongmei
AU  - Zhang, Meiting
AU  - Trišović, Nataša
AU  - Zhao, Junfeng
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3145
AB  - Fractional-order PID (FOPID) controller, as the results of recent development of fractional calculus, is becoming wide-used in many deterministic dynamical systems, but not in stochastic dynamical systems. This paper explores stochastic bifurcation of a generalized Van del Pol (VDP) system under the control of FOPID controller. Firstly, introducing the transformation between fast-varying and slow-varying variables of the system response, and utilizing the properties of fractional calculus, we obtain a new expression in the form of slow-varying variables for FOPID controller. Based on this work, the stochastic averaging method is applied to obtain the Fokker-Planck-Kolmogorov (FPK) equation and the stationary probability density function (PDF) of the amplitude response. Then a new numerical algorithm is proposed to testify the analytical results in the case of the coexistence of fractional integral and fractional derivative. After that, stochastic bifurcations induced by the order of the fractional integral, the order of the fractional derivative and the coefficient in FOPID controller are investigated in detail. The agreement between analytical and numerical results verifies the correctness and effectiveness of our proposed methods.
PB  - Pergamon-Elsevier Science Ltd, Oxford
T2  - Chaos Solitons & Fractals
T1  - Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller
EP  - 38
SP  - 30
VL  - 121
DO  - 10.1016/j.chaos.2019.01.026
ER  - 

@article{
author = "Li, Wei and Huang, Dongmei and Zhang, Meiting and Trišović, Nataša and Zhao, Junfeng",
year = "2019",
abstract = "Fractional-order PID (FOPID) controller, as the results of recent development of fractional calculus, is becoming wide-used in many deterministic dynamical systems, but not in stochastic dynamical systems. This paper explores stochastic bifurcation of a generalized Van del Pol (VDP) system under the control of FOPID controller. Firstly, introducing the transformation between fast-varying and slow-varying variables of the system response, and utilizing the properties of fractional calculus, we obtain a new expression in the form of slow-varying variables for FOPID controller. Based on this work, the stochastic averaging method is applied to obtain the Fokker-Planck-Kolmogorov (FPK) equation and the stationary probability density function (PDF) of the amplitude response. Then a new numerical algorithm is proposed to testify the analytical results in the case of the coexistence of fractional integral and fractional derivative. After that, stochastic bifurcations induced by the order of the fractional integral, the order of the fractional derivative and the coefficient in FOPID controller are investigated in detail. The agreement between analytical and numerical results verifies the correctness and effectiveness of our proposed methods.",
publisher = "Pergamon-Elsevier Science Ltd, Oxford",
journal = "Chaos Solitons & Fractals",
title = "Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller",
pages = "38-30",
volume = "121",
doi = "10.1016/j.chaos.2019.01.026"
}

Li, W., Huang, D., Zhang, M., Trišović, N.,& Zhao, J.. (2019). Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller. in Chaos Solitons & Fractals
Pergamon-Elsevier Science Ltd, Oxford., 121, 30-38.
https://doi.org/10.1016/j.chaos.2019.01.026

Li W, Huang D, Zhang M, Trišović N, Zhao J. Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller. in Chaos Solitons & Fractals. 2019;121:30-38.
doi:10.1016/j.chaos.2019.01.026 .

Li, Wei, Huang, Dongmei, Zhang, Meiting, Trišović, Nataša, Zhao, Junfeng, "Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller" in Chaos Solitons & Fractals, 121 (2019):30-38,
https://doi.org/10.1016/j.chaos.2019.01.026 . .