Title:

Active vibration control for asymmetric systems by pole assignment

Most structural systems are symmetric and naturally stable but some are asymmetric and prone to instability. The asymmetric system is defined by a nonsymmetric matrix and generated by a nonconservative force. When the force is bigger than a critical point, poles are shifted from the lefthand side to the righthand 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 spillover effect. The algorithm of partial pole assignment with and without time delay can assign the required closedloop poles precisely when the nonconservative force is a certain value. However, it is changeable and makes the closedloop poles shifted away from desired locations. The closedloop system may be unstable if the force is highly uncertain. To deal with this problem, sensitivities of the closedloop poles must be minimised by using the robust pole assignment. A former algorithm is available for a case of frictioninduced vibration by using the singleinput control. In this thesis, a novel method of robust pole assignment to minimise sensitivities by using multipleinput control is proposed. Both frictioninduced vibration and aerodynamic flutter problems are considered. Furthermore, a new concept to minimise magnitudes of vibration responses by evaluating the optimal closedloop poles is focused. The power flow mode theory based on damping distribution may reveal the optimal locations of poles by maximising the timeaveraged power dissipation per unit characteristic velocity.
