Dynamic Analysis of a Modular Test Stand for Multi-Axis Vibration Testing 117 Fig. 8 The inverse FRFs reported by Testlab 2021.2.1 for the four MIMO tests: (a) inverse FRFs for control DOF 23Y+, (b) inverse FRFs for control DOF 26X+ alarm/abort line violations is 5% and 2% respectively. The undamped, damped, and stiffened/truncated MIMO tests were again well below these thresholds. The results from this metric agree with our findings from the previous metric, suggesting little impact from the test stand on the MIMO tests. Inverse FRF Comparison Our previous results showed that the dynamics of the test stand in the range of identified modes (20-300 Hz) did not appear to influence the control performance of the MIMO tests. However, the question remained whether the controller overcame the test stand dynamics, or was not affected by them at all. To understand the impact the test stand dynamics on the controller, we analyzed the inverse FRFs between the control DOFs and input voltage from our MIMO tests. These FRFs inform the controller’s decisions concerning how much voltage to apply to get a desired acceleration response. Resonances from the test stand would appear in the inverse FRFs as peaks and valleys if the controller were making an effort to overcome them. Figure 8 plots the inverse FRFs reported by the Testlab 2021.2.1 MIMO random module for each of the MIMO test cases. The inverse FRFs from Figure 8 were relatively flat in the range of 20-200 Hz, where many of our identified test stand modes lie (16-25 modes depending on the test stand configuration). Since there were no peaks or valleys, one can conclude that the test stand resonances had no noticeable impact on the controller in this range. It is observed that there was a resonance and anti-resonance in the inverse FRF between 200-300Hz, and the test stand had resonances in this range. However, if this behavior were caused by variations in the test stand, it would be expected that the inverse FRF would vary between configurations. Instead, the system dynamics had almost no change from test to test. The inverse system FRFs were nearly identical regardless of test stand configuration. This implies that the behavior of the test article, as a result of the shaker input, was independent of the test stand dynamics. The inverse FRFs, see Figure 8b, were observed to have more distortion than the curves in Figure 8a. The audible rattling describe in earlier sections emanated from the shaker located at DOF 26X+. This rattling increased the level of noise in the measured data, and was likely the cause of the added distortion. Because the distortion appears in all of the curves, the rattling may have been a issue in all of the MIMO tests, progressively getting worse until the controller could no longer handle it in the stiffened MIMO test. Limiting the frequency range of the stiffened/truncated MIMO test cut off the rattle frequency, and allowed the controller to replicate the specification with greater accuracy.
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