Adaptive inverse control of random vibration based on the filtered-X LMS algorithm

Yang Zhidong, Huang Qitao, Han Junwei and Li Hongren

National Key Laboratory of Robots Technique and System, Harbin Institute of Technology, Harbin 150080, China

Abstract: Random vibration control is aimed at reproducing the power spectral density (PSD) at specified control points.
The classical frequency-spectrum equalization algorithm needs to compute the average of the multiple frequency response
functions (FRFs), which lengthens the control loop time in the equalization process. Likewise, the feedback control algorithm
has a very slow convergence rate due to the small value of the feedback gain parameter to ensure stability of the system.
To overcome these limitations, an adaptive inverse control of random vibrations based on the filtered-X least mean-square
(LMS) algorithm is proposed. Furthermore, according to the description and iteration characteristics of random vibration tests
in the frequency domain, the frequency domain LMS algorithm is adopted to refine the inverse characteristics of the FRF
instead of the traditional time domain LMS algorithm. This inverse characteristic, which is called the impedance function of
the system under control, is used to update the drive PSD directly. The test results indicated that in addition to successfully
avoiding the instability problem that occurs during the iteration process, the adaptive control strategy minimizes the amount
of time needed to obtain a short control loop and achieve equalization.

Keywords: random vibration; power spectral density; frequency response function; adaptive inverse control; filtered-X
LMS algorithm