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

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.