International Journal of Dynamics and Control

, Volume 7, Issue 4, pp 1521–1531 | Cite as

Controlling self-excited vibration using acceleration feedback with time-delay

  • Akash Sarkar
  • Joy Mondal
  • S. ChatterjeeEmail author


This paper investigates the control of vibration of a self-excited system, namely Rayleigh Oscillator, by using Acceleration Feedback Control method. In this control scheme, acceleration of the vibrating system is fed back to a second-order compensator and the control force is produced by amplifying the signal obtained from the compensator. Linear and non-linear stability analyses are performed. Linear stability analysis is used to obtain the stability regions and the optimal system parameters. Non-linear analysis is performed using Describing Function method. Acceleration feedback control is found to be effective in controlling the self-excited vibration. The presence of time-delay is also studied in this paper. It is observed that the presence of uncertain time-delay in the feedback loop can be detrimental. The optimal system (optimized for no delay case) can result in instability of the static equilibrium leading to finite amplitude oscillation. However, one can improve the situation by increasing the loop-gain. In order to circumvent this problem, it is proposed that a pre-determined time-delay may be introduced in the feedback circuit and the control parameters are re-optimized considering this time-delay. As a result, the system equilibrium can be stabilized even in the presence of time-delay. The results of theoretical analysis are validated with the simulation results performed in MATLAB Simulink.


Self-excited vibration Stability Describing function Time-delay 

List of symbols


Non-dimensional amplitude


Non-dimensional negative damping coefficient


Non-dimensional positive damping coefficient


Non-dimensional controller gain


Non-dimensional sensitivity of the sensor

Kc = k1k2

Non-dimensional loop gain


Non-dimensional displacement


Non-dimensional filter variable

\( \zeta_{f} \)

Non-dimensional damping ratio of filter


Non-dimensional frequency


Non-dimensional natural frequency filter


Identical complex conjugate pair of poles used in pole cross-over design


Non-dimensional time-delay parameter


Real part of the merged poles


Imaginary part of the merged poles


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringIndian Institute of Engineering Science and Technology, ShibpurHowrahIndia

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