The Vibration Suppression Of Delayed Feedback Control In The Nonlinear Vibration System

In recent years, with the rapid development of control technique, computer technology, and thehigh precision and high sensitivity of the sensor and actuator development, active vibrationsuppression control technology has been rapid development in the fields of aviation, aerospace,machinery, building, transportation etc.. In this paper, the vibration of the nonlinear dynamicalvibration system is studied. The delayed feedback control is applied to suppress the harmfulvibration of the vibration system. The focus of this paper is to analyze the effect of gain and timedelay on the performance of the vibration.First, the recent status and progress of delayed feedback control is introduced. The theory andrecent progress of the delayed feedback control are mainly introduced. In the second chapter basictheories about nonlinear vibration system are conclude and summarized. For example, stabilitycriteria of linear system, Routh-Hurwit criterion, multiple scales method, bifurcation and chaos. Inthe third chapter, a mass-spring nonlinear vibration system of mass-spring with cubic nonlinearstiffness is studied. The primary resonance of the vibration system is studied by using the delayedvelocity feedback control. The multiple scales is employed to obtain the approximate analyticalsolutions. The effect of damping coefficient, nonlinear stiffness coefficient, the gain of delayedfeedback and time delay on the amplitude-frequency of the primary system is analyzed. The stabilityof the vibration system is analyzed by the method of Routh-Hurwit criterion. The numericalsimulation is agree with the analytical solution well. In the forth chapter, a mass-spring vibrationsystem with auto-parametric excited pendulum is studied. The saturation phenomenon of thevibration system exists when the primary resonance and1:2internal resonance is considered. Thedistribution of the frequency bandwidth of the saturation control is not reasonable because of theexistence of the internal detuning parameters. The frequency bandwidth of saturation control isunstable at some ranges of internal detuning parameters. The delayed feedback control is used tocontrol the distribution of the frequency bandwidth of the saturation control. The unstable region ofthe frequency bandwidth of saturation control is eliminated and the bandwidth of the frequency ofthe saturation control is enlarged by appropriate tuning the value of time delay. In the fifth chapter, asecond order controller is applied to control the saturation control of a steel beam. The effect ofdelayed feedback control on saturation control is analyzed. The results show that the vibrationsystem can be switched between the single-mode motion and saturation control, and the bandwidth of saturation control can be enlarged by tuning values of time delay.The results of this paper can help to improve the delay dynamical theory, to promote thedevelopment of nonlinear dynamics. The study of this paper has theoretical significance andpractical application value.