Active Structural Control: Theory and Practice (Longman by T. T. Soong

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By T. T. Soong

Lively structural keep watch over capability making buildings aware of exterior forces like earthquakes and hurricanes. Large-scale experimentation is now happening during this box and this booklet brings jointly a wealth of knowledge at the perform and concept of lively structural keep an eye on. in addition to documenting the latest advances within the box, the booklet additionally seems to be on the speedy improvement in allied applied sciences akin to electronics, fabrics and size concepts, that have fuelled the expansion of this region.

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Are of practical importance when applied to civil engineering structures. An approach to bounded state control is discussed 21 · " using linear state feedback laws. Based on an extension of the Lyapunov function methods, it 49 Active strncturnl control: theory and prnctlec follows, in a sense, the pole assignment concept to achieve bounded state control. In addition, all pulse control strategies proposed in the literature fall into this category 23 - 34 The objective of pulse control advanced by Masri et af2>-z> and by Udwadia and Tabaie 32 •33 is to destroy the gradual rhythmic build-up of the structural response in the case of resonance by means of short-interval high-energy pulses, A continuous monitoring of the system state variables is required.

I Tile Case of Output Feedback The procedure described above is based on state feedback as indicated by Eq. 31 ). 41) where Cis the p x 2n measurement matrix. 42) where G' is the output feedback gain matrix. l be thejth column of CI/J(>/), we have ei = G'I/Jj(>/;) and Eq. I' are made up of the vectors I/Jj(>i 1). 45) It is important to point out that the number of linearly independent columns that can be obtained from CI/J(•il will not exceed the rank of C. I' is invertible. Thus, the control gain G' as found from Eq.

47) z(t) = Ty(t) where Tis the 2n x 2n modal matrix whose columns are the eigenvectors of A. The decoupled slate-space equation governing y(t) has the form, upon substituting Eq. 47) into Eq. 49) ' is diagonal whose diagonal elements are the complex eigenvalues 2i, j 1, 2, ... t . jllt). The vector d(t- Llt) contains all the dynamic quantities at time t- Llt. With Eq. 52) as the motion constraint, the minimization of J(t) given by Eq. 1. (t) is the Lagrange multiplier. rr au Oz =O, = O, a:rt a;.

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