A reduced‐order modeling technique for tall buildings with active tuned mass damper

It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reduced-order control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reduced-order system is updated repeatedly until a desired one is obtained, the accuracy of the reduced-order system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. Another advantage of the method is that the reduced-order system is defined in the subspace of the original physical space, which makes the state vectors have physical meaning. An eigenvalue shifting technique is applied to accelerate the convergence of iteration and to make the reduced system retain all the dynamic characteristics of the full system within a given frequency range. Two schemes to establish the reduced-order system by using the proposed method are also presented and discussed in this paper. The results for a tall building with active tuned mass damper show that the proposed method is efficient for the reduced-order modelling and the accuracy is very close to exact only after two iterations. Copyright © 2001 John Wiley & Sons, Ltd.

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