A novel interval dynamic reliability computation approach for the risk evaluation of vibration active control systems based on PID controllers

• Published in: Applied Mathematical Modelling Vol. 92; pp. 422 - 446
• Main Authors: Wang, Lei, Liu, Jiaxiang, Yang, Chen, Wu, Di
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.04.2021; Elsevier BV
• Subjects: Active control; Collocation methods; Control systems; Controllers; Mass-spring-damper systems; Mathematical analysis; Parameter uncertainty; PID control; Probabilistic methods; Proportional integral derivative; Reliability analysis; Risk assessment; Statistical analysis; The subinterval method; The time-dependent reliability; Time dependence; Uncertainty; Vibration active control systems; Vibration control; Uncertainty; The subinterval method; Vibration active control systems; PID control; The time-dependent reliability
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2020.11.007

•Non-probabilistic time-dependent reliability model for systems based on PID controllers is set up.•Sub-interval method is used to calculate the close-loop response more accurately.•The first-passage theory is utilized to calculate the time-dependent reliability. PID control is widely used in vibration control systems. However, there are various uncertainties present in practical engineering, and the PID parameters obtained from a deterministic system may fail. Thus, reliability estimation is necessary to solve this problem. To avoid the disadvantages of traditional probabilistic methods, a non-probability based method to calculate time-dependent reliability is introduced to estimate the safety of a vibration active control system of based on PID controller performance. Next, the subinterval method is used to calculate a closed-loop response with large uncertainties and the first-passage theory is utilized to calculate the time-dependent reliability. Finally, one discrete mass-spring-damper system is analyzed for comparison with the collocation method and two panel structures (an elastic panel and a solar panel) are reliability evaluated to show the effects of the number of PID controllers and the displacement constraints.