An optimal pole placement technique is proposed for the vibration control of a structure modeled as a one-degree-of-freedom (DOF) 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. With the use of independent modal space control theory, the algorithm is extended to the control of multiple DOFs system with incomplete state measurements using limited number of sensors. The performance and stability of the control algori...[ Read more ]

An optimal pole placement technique is proposed for the vibration control of a structure modeled as a one-degree-of-freedom (DOF) 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. With the use of independent modal space control theory, the algorithm is extended to the control of multiple DOFs 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. One modeled as one DOF system subjected to white noise excitation. The other modeled as eight DOFs system subjected to the SE component of the ground acceleration record of 1940 El-Centro Earthquake. 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 easy and effective design methodology for these two control devices to mitigate structural response due to earthquake excitation.