Adaptive Iterative Control for Road Simulation Using the Frequency Domain Filtered-X LMS Algorithm

For a hydraulic or electro-dynamic shaker test rig, the goal of the iterative control is to reproduce the structural deformations of vehicles, measured under normal operating conditions for a vehicle driven on public roads or test tracks. The approach is based on the correct calculation of the excitation signals applied to the actuators of the multi-axis test rig. The conventional iterative control approach adjusts drive waveforms according to the particular Frequency Response Function (FRF) matrix, measured prior to the test and fixed. To ensure the system stability, the feedback gain should be small, which will lead to a very slow convergence rate. To overcome these defects, an adaptive inverse model based on the filtered-X least mean-square (LMS) algorithm is proposed to continuously improve the identification precision of the inverse characteristic of the FRF, which is called the impedance function of the system under test. And the frequency domain LMS algorithm is introduced to make sure the inverse characteristic is not critical to the iterative gain and thus allow for a bigger feedback gain. The experimental results indicate that the adaptive control strategy can not only solve the system instability problem arising from the improper feedback gain selection in the conventional iteration process, but also has the higher convergence rate.