Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller
Само за регистроване кориснике
2019
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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 th...e 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.
Кључне речи:
Stochastic bifurcation / Stochastic averaging method / FOPID controller / Color-noiseИзвор:
Chaos Solitons & Fractals, 2019, 121, 30-38Издавач:
- Pergamon-Elsevier Science Ltd, Oxford
Финансирање / пројекти:
- Natural Science Foundation of China [11702201]
- Natural Science Basic Research Plan in Shaanxi Province of China [2015JM1028]
- Интегритет опреме под притиском при истовременом деловању замарајућег оптерећења и температуре (RS-MESTD-Technological Development (TD or TR)-35011)
- Динамика хибридних система сложених структура. Механика материјала (RS-MESTD-Basic Research (BR or ON)-174001)
DOI: 10.1016/j.chaos.2019.01.026
ISSN: 0960-0779
WoS: 000462143000003
Scopus: 2-s2.0-85061669101
Колекције
Институција/група
Mašinski fakultetTY - 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 . .