Sensitivity of active vibration control to structural changes and model reduction

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Virginia Polytechnic Institute and State University

The analytical study presented here is concerned with by two types of sensitivity of active vibration control of large space structures (LSS). The first one required for assessing robustness, is the sensitivity of the performance and stability of the control system to changes in structure and to model reduction. The second type is the sensitivity of the optimum design of the control system to changes in the structure. This sensitivity is of interest in assessing the need for integrated structure/control design.

Three direct rate feedback (DRF) control techniques are studied for a laboratory structure which has characteristics of LSS and then compared to standard linear quadratic (LQ) control. The baseline design of each control system is obtained first and then sensitivity analysis conducted.

An uncoupled DRF control law which minimized the sum of gains subject to requirements on performance was not robust to structural changes, and small changes in the structure caused notable increase in performance compared to that of the baseline design and therefore a potential gain from simultaneous structure/control design was indicated.

Two coupled DRF techniques are proposed. A Minimum Force DRF (MF-DRF) law minimized maximum force of any actuator, while a Linear Quadratic DRF (LQ-DRF) law minimized the standard quadratic performance index for initial conditions in the shape of the first six natural modes. Both techniques guaranteed system stability. The LQ control law was found to be only slightly better than the simpler MF·DRF law in terms of the quadratic performance index and poorer than the LQ-DRF law. However the LQ control requires model reduction and was found to be sensitive to errors in that process. For example, the LQ design lost its stability when the structure was modified by adding a non-structural mass to it.

A separate experimental study was conducted simultaneously with this study to verify theoretical results. Good agreement was found between analytical results and experimental measurements for the investigated control techniques.