System Theory

Download Active Control of Structures by Andre Preumont, Kazuto Seto PDF

By Andre Preumont, Kazuto Seto

With lively keep an eye on of buildings , worldwide pioneers current the cutting-edge within the conception, layout and alertness of lively vibration keep an eye on. because the call for for prime functionality structural platforms raises, so will the call for for info and innovation in structural vibration regulate; this e-book presents a good treatise of the topic that might meet this requirement. The authors introduce lively vibration keep an eye on by utilizing shrewdpermanent fabrics and buildings, semi-active keep watch over units and numerous suggestions strategies; they then speak about themes together with tools and units in civil buildings, modal research, lively keep watch over of high-rise constructions and bridge towers, energetic tendon regulate of cable constructions, and energetic and semi-active isolation in mechanical constructions.

lively keep an eye on of constructions:

  • Discusses new kinds of vibration regulate tools and units, together with the newly built reduced-order actual modelling technique for structural keep watch over;
  • Introduces triple high-rise constructions attached through lively keep an eye on bridges as devised by means of Professor Seto;
  • Offers a layout approach from modelling to controller layout for versatile constructions;
  • Makes prolific use of functional examples and figures to explain the subjects and expertise in an intelligible demeanour.

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Example text

70) are no longer guaranteed to be positive; however, if the actuator location a is close to the sensor location s, the modal amplitudes φi (a ) and φi (s) will be close to each other, at least for the low-frequency modes, and the corresponding residues will again be positive. The following result can be established in this case: If two neighboring modes are such that their residues φi (a )φi (s) and φi+1 (a )φi+1 (s) have the same sign, there is always an imaginary zero between the two poles (Martin, 1978).

125), and vice versa. f. 86) or ξi = g(bT φi )2 . e. the departure rate from the open-loop poles) is controlled by (bT φi )2 , the square of the modal amplitude at the actuator/sensor location. Now let us examine the asymptotic behavior for large gains. 83) is (Ms 2 + gbbT s + K )x = 0. 88) It follows that x = −(K + Ms 2 )−1 gsbbT x or bT x = −gsbT (K + Ms 2 )−1 bbT x. 90) sbT (K + Ms 2 )−1 b = 0. 63), that is, the eigenvalues of the constrained system. The fact that the eigenvalues are purely imaginary, s = ± jω0 , stems from the fact that K and M are symmetric and positive semi-definite.

8. Every imaginary pole at ± jωi introduces a 180◦ phase lag and every imaginary zero at ± j zi a 180◦ phase lead. In this way, the phase diagram is always contained between 0 and −180◦ , as a consequence of the interlacing property. For the same reason, the Nyquist diagram consists of a set of near-circles (one per mode), all contained in the third and fourth quadrants. Thus, the entire curve G(ω) is below the real axis (the diameter of every circle is proportional to ξi−1 ). 1 Transmission Zeros and Constrained System We now establish that the transmission zeros of the undamped system are the poles (natural frequencies) of the constrained system.

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