A simple optimal pole location technique for structural control

An optimal pole placement technique is proposed for the vibration control of a structure modeled as a single-degree-of-freedom system subjected to a white noise ground excitation. The objective of the proposed technique is to shift the closed-loop poles into a prescribed region in the complex plane using the smallest amount of control force variance. The Kuhn-Tucker necessary condition and the second order necessity and sufficiency theorem are used to solve for the control gain and the corresponding optimal pole locations in the prescribed region. Using independent modal space control theory, the algorithm is extended to the control of a multiple-degree-of-freedom system with incomplete state measurements using limited number of sensors. The performance and stability of the control algorithm are numerically verified on the control of two buildings. Two control devices, active tendon and active mass driver, are used to demonstrate the implementation of the current development. The results show that the technique provide an alternative design methodology for these two control devices to mitigate structural response due to earthquake excitation.