By Wodek Gawronski Dr (auth.), Wodek Gawronski Dr (eds.)
Methods of structural keep an eye on and dynamics are brought during this e-book. those contain relief of huge structural types through balanced truncation, placement of actuators and sensors for dynamic trying out and regulate, structural id of the minimum-order balanced illustration, balanced dissipative controller layout, balanced LQG and H( controller designs with the closed-form relationships among controller parameters and method functionality, and controller aid tools that protect the closed-loop functionality. The ebook explores the original homes of versatile constructions to acquire effective tools of dynamic research and controller layout. The offered tools of structural dynamics, identity, sensor/actuator placement, and passive, LQG and H( controller layout were checked either with simulations and commercial implementations.
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Extra info for Balanced Control of Flexible Structures
This large and complex structure presents many difficulties in the controller design, and also violates the narrow definition of a flexible structure provided earlier. Yet, its flexible properties are dominating that the controller design methods derived for the narrowly defined structure can be applied in the antenna case as well. 19 Chapter 3 Balanced Open-Loop Systems Controller design relies heavily on the plant controllability and observability properties. , a property that all states are excited by the input actuators).
Cri'--,ri+l>0, i=1 ..... n-1. 16) is close to the smallest entries value of z. , if IICtII>>uC~II, and IIBtlI>>IIB,II do not hold. , riz~'i+l>0, i = 1 ..... 19) This condition says that the reduction is near-optimal if the sum of the Hankel singular values of the truncated states is much smaller than the sum of the Hankel singular values of the retained states. The question arises as to whether the reduced model (Ar,Br, C r) is stable. The results of Moore , Parnebo and Silverman , and Glover  confirm it.
The results of Moore , Parnebo and Silverman , and Glover  confirm it. ~, i = 1 ..... n, have their entries ri in decreasing order, ~'~r = d i a g ( r r, Ft~, where i ~i+l -0 ' and if 1" is partitioned such that l~r is positive definite, and if the triple (A,B,C) is partitioned accordingly, then (Ar,B~,C~) is stable. For a system with complex poles, such as flexible structures, each pair of coordinates, rather than each single coordinate, is evaluated for reduction. , related to two complex conjugate poles) are almost equal (~'i--~'i+l).