TY  - 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 . .