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

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Abstract

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.

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Abbreviations

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

\( \zeta_{f} \) :

Non-dimensional damping ratio of filter

ω :

Non-dimensional frequency

ω f :

Non-dimensional natural frequency filter

λ 1, λ 2 :

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

τ:

Non-dimensional time-delay parameter

a :

Real part of the merged poles

b :

Imaginary part of the merged poles

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, P.O. Botanic Garden, Howrah, West Bengal, 711103, India

    Akash Sarkar, Joy Mondal & S. Chatterjee

Authors
  1. Akash Sarkar
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  2. Joy Mondal
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  3. S. Chatterjee
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Correspondence to S. Chatterjee.

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Sarkar, A., Mondal, J. & Chatterjee, S. Controlling self-excited vibration using acceleration feedback with time-delay. Int. J. Dynam. Control 7, 1521–1531 (2019). https://doi.org/10.1007/s40435-019-00577-y

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  • DOI: https://doi.org/10.1007/s40435-019-00577-y

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