Uncertainty-oriented optimal PID control design framework for piezoelectric structures based on subinterval dimension-wise method (SDWM) and non-probabilistic time-dependent reliability (NTDR) analysis

Abstract

Piezoelectric system is widely used in vibration control, but due to the influence of uncertainty in the system, the control rate designed for determined system may not meet the design requirements in practical application. In order to solve the uncertainty problems in the system, a set of NTDR reliability optimization framework for piezoelectric active control system is proposed in this paper. Taking the most widely used PID controller as an example, a new controller design method is proposed: the response interval of the closed-loop system is calculated by the novel SDWM. Based on the first crossing theory, a new time-dependent reliability index is defined to calculate the time-dependent reliability of the piezoelectric system. Through an example of piezoelectric laminate, the layout of different piezoelectric materials is compared. Then, taking piezoelectric curved shell as an example, the influence of piezoelectric uncertainty and uncertainty parameter radius on vibration control of piezoelectric system is studied. Finally, the accuracy of the method is verified by Monte Carlo algorithm.