Controlling self-excited vibration using positive position feedback with time-delay

Abstract

This paper explores the vibration control of Rayleigh oscillator (a self-excited system), by using positive position feedback method. Both linear and nonlinear stability analyses are performed. The stability regions and optimal system parameters are obtained by performing linear stability analysis, and nonlinear analysis is performed using describing function method to get the amplitude and frequency of the system. The effect of time-delay on system performance is also studied in this paper. It is observed that the existence of time-delay can be unfavourable; however, the situation can be improved by increasing the loop gain. However, it is impossible to design a system without time-delay present in the feedback circuit. Therefore, to nullify the effect of uncertain time-delay, authors have intentionally introduced a preselected time-delay in the feedback circuit and re-optimized to stabilize the static equilibrium of the delayed system. Numerical simulations performed in MATLAB SIMULINK confirm the results of the theoretical analysis obtained. Keywords Self-excited vibration • Positive position feedback • Stability • Time-delay List of symbols A Non-dimensional amplitude c 1 Non-dimensional negative damping coefficient c 3 Non-dimensional positive damping coefficient k 1 Non-dimensional controller gain k 2 Non-dimensional sensitivity of the sensor K c = k 1 k 2 Non-dimensional loop gain x Non-dimensional displacement x f Non-dimensional filter variable f Non-dimensional damping ratio of filter c Damping ratio of closed-loop poles Non-dimensional frequency c Frequency of closed-loop poles f Non-dimensional natural frequency filter 1 , 2 Identical complex conjugate pair of poles used in pole crossover design Non-dimensional time delay parameter

Active Vibration Control of a Quarter-Car Model via a Time-Delayed Vibration Absorber

“…Proper time delay is effective in controlling the self-excited vibration, suppressing chaos movement, and reducing nonlinear resonant response, etc. [14][15][16] Therefore, time delay is intentionally introduced into an active control loop to enhance the vibration control effect and the concept of timedelayed feedback control (TDFC) emerges. Sun et al proposed a design methodology of variable time delay in TDFC for a nonlinear isolation system.…”