By Wodek Gawronski Dr (auth.), Wodek Gawronski Dr (eds.)
Methods of structural keep watch over and dynamics are brought during this ebook. those comprise aid of enormous structural versions by means of 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 process functionality, and controller aid tools that defend the closed-loop functionality. The booklet explores the original homes of versatile constructions to procure effective equipment of dynamic research and controller layout. The provided 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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Additional info for Balanced Control of Flexible Structures
Two variables, x and y, are approximately equal (x=-"y) if x = y + e , and Ile:tl~llyll. For example, if M is a diagonal matrix, then S is diagonally dominant, (S~bt) if the diagonal terms s a and Pii satisfy the condition Sii'Jc'E'~tii, and the off-diagonal terms of S satisfy the condition Isijl < e , where c is small, and i d = l ..... n. ), i=1 ..... nz), the balanced and modal representations of flexible structures are closely related, as it is expressed in the following properties: Property 1.
10 -2 I I I ! I I 10 -3 10 -~ exact --- lO-So I 5 N_. 2: antenna. 56). 3. The inputs are azimuth and elevation pinion torques, the 16 outputs include azimuth and elevation position and rates, pinion rates, elevation and cross-elevation pointing errors, and subreflector position in three-dimensional space. 2 again show good coincidence between the exact and the approximate Hankel singular values. The first four Hankel singular values correspond to the antenna rigid body motion in azimuth and elevation and are not shown in this figure, since their values tend to infinity.
54a) Wo=-diag(woilz), Woi > O, i = 1 ..... 54b) and therefore their product is also diagonally dominant. 43). , Wc=E(xxr). Thus, its diagonal dominance corresponds to the almost independent, or almost orthogonal states. Property 2. The "conservation law" for the approximate Hankel singular values. 56) holds. This property can serve as a tool for checking the correctness of the approximation. For example, if all the approximate Hankel singular values are larger than the exact ones, the approximation cannot be considered correct.