Active vibration control for asymmetric systems by pole assignment

Abstract

Most structural systems are symmetric and naturally stable but some are asymmetric and prone to instability. The asymmetric system is defined by a non-symmetric matrix and generated by a non-conservative force. When the force is bigger than a critical point, poles are shifted from the left-hand side to the right-hand side of the complex plane leading to instability. To stabilise the unstable asymmetric system, partial pole assignment by using an unobservability condition is implemented to assign unstable poles and keep others unchanged. It requires both unassigned poles and mode shapes in order to keep the poles unchanged. Nonetheless, the mode shapes of the asymmetric system is difficult to evaluate. This thesis proposes a new algorithm of partial pole assignment by using the unobservability condition which requires only unassigned poles to keep them unchanged. Both single and couple time delays are also included in the control algorithm to avoid spill-over effect.

The algorithm of partial pole assignment with and without time delay can assign the required closed-loop poles precisely when the non-conservative force is a certain value. However, it is changeable and makes the closed-loop poles shifted away from desired locations. The closed-loop system may be unstable if the force is highly uncertain. To deal with this problem, sensitivities of the closed-loop poles must be minimised by using the robust pole assignment. A former algorithm is available for a case of friction-induced vibration by using the single-input control. In this thesis, a novel method of robust pole assignment to minimise sensitivities by using multiple-input control is proposed. Both friction-induced vibration and aerodynamic flutter problems are considered. Furthermore, a new concept to minimise magnitudes of vibration responses by evaluating the optimal closed-loop poles is focused. The power flow mode theory based on damping distribution may reveal the optimal locations of poles by maximising the time-averaged power dissipation per unit characteristic velocity.

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Identifiers

ORCID for Yeping Xiong: orcid.org/0000-0002-0135-8464

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