Iterative approach of tire-coupled road simulator based on singularity threshold criterion

Abstract

For the tire-coupled road simulator, to get the required accelerations at the head of axes, the iterative approach is used to adjust the drive waveforms according to the particular measured Frequency Response Function (FRF) matrix. And for the iterative control task, this FRF matrix needs to be inverted. However, the matrix may be ill-conditioned, which will lead to the control instability. For this, the effect of condition number of matrix on the iterative instability is explored, and the singularity threshold criterion is proposed. The matrix condition number is defined as the ratio between the maximum and minimum singular values of a matrix, and is used to determine whether to use the pseudo-inversion of the FRF matrix for the impedance matrix identification. If the FRF matrix is identified as in ill-condition by the quantity, the pseudo-inversion will be calculated using Singular Value Decomposition (SVD), and the singular values, which are smaller than maximum singular value multiplied by the criterion threshold, are set to zero. For this case, the iterative control at this frequency line is similar to the average control. The typical value for the threshold is highly application dependent, and for our road simulator, when it is 0.05 to 0.1, the desired stability and accuracy can be gotten.