Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller
Само за регистроване кориснике
2018
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
In this paper, the reliability of stochastic dynamical systems under Gaussian white noise excitations with fractional order proportional-inegral-derivative (FOPID) controller is estimated. First, the FOPID controller is approximated by a set of combination of displacement and velocity based on the generalized van der Pol transformation. Then, the stochastic averaging method of energy envelope is applied to obtain a diffusive differential equation, from which the Backward Kolmogorov equation, governing the conditional reliability function, and the Generalized Pontryagin equation, governing the statistical moments of first-passage time, are derived from the averaged equation and solved numerically. Finally, in the two examples, the critical parameters in the FOPID controller are shown to be capable of improving the reliability of the stochastic dynamical system apparently, and all numerical results are verified to be efficient and correct by the Monte Carlo simulation.
Кључне речи:
stochastic averaging method / reliability estimation / Monte Carlo simulation / FOPID controller / first-passageИзвор:
International Journal of Structural Stability and Dynamics, 2018, 18, 6Издавач:
- World Scientific Publ Co Pte Ltd, Singapore
Финансирање / пројекти:
- Natural Science Foundation of China [11302157, 11672111]
- Natural Science Basic Research Plan in Shaanxi Province of China [2015JM1028]
- Fundamental Research Funds for the Central Universities [JB160706]
- Chinese-Serbian Science and Technology Cooperation [3-19]
- Research Award Fund for Outstanding Young Researcher in Higher Education Institutions of Fujian Province
- Research Fund for Excellent Young Scientific and Technological Project of Huaqiao University [ZQN-YX307]
DOI: 10.1142/S0219455418500839
ISSN: 0219-4554
WoS: 000434116600008
Scopus: 2-s2.0-85035326035
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Li, Wei AU - Chen, Lincong AU - Zhao, Junfeng AU - Trišović, Nataša PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2768 AB - In this paper, the reliability of stochastic dynamical systems under Gaussian white noise excitations with fractional order proportional-inegral-derivative (FOPID) controller is estimated. First, the FOPID controller is approximated by a set of combination of displacement and velocity based on the generalized van der Pol transformation. Then, the stochastic averaging method of energy envelope is applied to obtain a diffusive differential equation, from which the Backward Kolmogorov equation, governing the conditional reliability function, and the Generalized Pontryagin equation, governing the statistical moments of first-passage time, are derived from the averaged equation and solved numerically. Finally, in the two examples, the critical parameters in the FOPID controller are shown to be capable of improving the reliability of the stochastic dynamical system apparently, and all numerical results are verified to be efficient and correct by the Monte Carlo simulation. PB - World Scientific Publ Co Pte Ltd, Singapore T2 - International Journal of Structural Stability and Dynamics T1 - Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller IS - 6 VL - 18 DO - 10.1142/S0219455418500839 ER -
@article{ author = "Li, Wei and Chen, Lincong and Zhao, Junfeng and Trišović, Nataša", year = "2018", abstract = "In this paper, the reliability of stochastic dynamical systems under Gaussian white noise excitations with fractional order proportional-inegral-derivative (FOPID) controller is estimated. First, the FOPID controller is approximated by a set of combination of displacement and velocity based on the generalized van der Pol transformation. Then, the stochastic averaging method of energy envelope is applied to obtain a diffusive differential equation, from which the Backward Kolmogorov equation, governing the conditional reliability function, and the Generalized Pontryagin equation, governing the statistical moments of first-passage time, are derived from the averaged equation and solved numerically. Finally, in the two examples, the critical parameters in the FOPID controller are shown to be capable of improving the reliability of the stochastic dynamical system apparently, and all numerical results are verified to be efficient and correct by the Monte Carlo simulation.", publisher = "World Scientific Publ Co Pte Ltd, Singapore", journal = "International Journal of Structural Stability and Dynamics", title = "Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller", number = "6", volume = "18", doi = "10.1142/S0219455418500839" }
Li, W., Chen, L., Zhao, J.,& Trišović, N.. (2018). Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller. in International Journal of Structural Stability and Dynamics World Scientific Publ Co Pte Ltd, Singapore., 18(6). https://doi.org/10.1142/S0219455418500839
Li W, Chen L, Zhao J, Trišović N. Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller. in International Journal of Structural Stability and Dynamics. 2018;18(6). doi:10.1142/S0219455418500839 .
Li, Wei, Chen, Lincong, Zhao, Junfeng, Trišović, Nataša, "Reliability Estimation of Stochastic Dynamical Systems with Fractional Order PID Controller" in International Journal of Structural Stability and Dynamics, 18, no. 6 (2018), https://doi.org/10.1142/S0219455418500839 . .