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**Extra resources for Active Structural Control: Theory and Practice (Longman structural engineering & structural mechanics series)**

**Sample text**

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;.