Response And Reliability Of Nonlinear Systems With Time Delay Feedback Under Wide-band Noise Excitation

With the acceleration of the intelligent manufacturing process,engineering instruments in various fields are developing towards automation,and automatic control system has become an indispensable part of various automated machinery.However,due to the inevitable defects of the control signal transmission or the control equipment itself in the actual controlled system,there is a time difference or time delay between the control and the system actuation.A time-delay dynamic system is formed.Although in the past,people often ignore the influence of time delay to solve many engineering problems.But as the requirements for the dynamic behavior of the controlled system become more and more accurate,it is necessary to consider the influence of time delay on the system.Therefore,it is of great significance to study the dynamic characteristics of time-delay dynamic systems and explore the influence of time delay on dynamic systems.In this thesis,the stochastic response and reliability of nonlinear systems with timedelay feedback control under wide-band noise excitation are studied.Firstly,based on the generalized harmonic function,the state variable with time delay in the system is approximately equivalent to the expression of the state variable without time delay.The original time-delay control system is transformed into a non-time-delay control system,and the non-time-delay control system is transformed into an average It? stochastic differential equation about the response amplitude of the system by using the stochastic averaging method,which is convenient to study the stochastic dynamics of the system and retains the main dynamic characteristics of the original system.Then,by establishing and solving the Fokker-Planck-Kolmogorov(FPK)equation associated with the mean Ito stochastic differential equation,the statistics on the system response are obtained.Based on this,the influence of time-delay feedback control on the random response of typical nonlinear systems such as van der Pol oscillator and Duffing-van der Pol oscillator under wide-band noise excitation is studied.Finally,based on the average Ito stochastic differential equation,the backward Kolmogorov equation satisfied by the conditional reliability function and the Pontryagin equation satisfied by the average first passage time are established.By solving these equations,the effects of time-delay feedback control on the reliability function,the probability density of the first passage time and the average first passage time of typical nonlinear systems such as van der Pol oscillator and Duffingvan der Pol oscillator under wide-band noise excitation are studied.All the theoretical results are verified by Monte Carlo digital simulation.The results show that the method can accurately predict the influence of time delay on the controlled system under wideband noise excitation.