Mixed H2/H∞ control of tall buildings with reduced-order modelling technique

In this paper, a reduced-order technique based on the dynamic condensation method is applied to obtain a reduced-order model of an experimental tall building which has 20 floors and is 2.5 m high. The experimental model is designed to imitate a practical tall building with an active mass driver, and is used to study the available modelling and active control strategies for real tall buildings. Using the acquired reduced-order model, a new approach which combines the pole placement method with the considerations on robust stability and constraint of control signal is presented to design a reduced (low)-order controller. This new design method is formulated as a mixed H-2/H-infinity optimization problem, which can be easily resolved by linear matrix inequalities. Because pole placement method can realize ideal damping characteristics for the vibrational modes, robust stability can avoid the spillover instability problem which is induced by neglecting the high-order modes, and constraint on control signal can provide more reasonable controller realization, the designed reduced-order controller can fulfil the performance and stability requirements for the vibration control of structures. Numerical simulations validate that the reduced-order model can represent the full-order model exactly in the targeted frequency range, and the designed reduced-order controller can effectively attenuate the excessive vibration to the full-order model excited by seismic disturbance. Copyright (c) 2007 John Wiley & Sons, Ltd.