By H. H. E. Leipholz, M. Abdel-Rohman (auth.)
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Extra info for Control of structures
And a n _ 1 etc. 4) and a bl CI = a n-I n-2 -an- 3 a n-I etc. S) bla -a b2 n- 3 n- I bl etc. 6) The system is stable if the sign of the first column does not change. 2 n n-l n-2 1 a a a n-l n-2 n-3 b1 b2 cl Co an _4 • ••••••••• a2 a n-5 .......... al Root Locus It is a graphical way of factoring the characteristic equation. 7) imposes two conditions on the openloop transfer function. 9) Thus "root locus" determines the closed-loop roots by working with the open-loop transfer function KGH. 3 Hode Plots It is a graphical method which provides stability information for open-loop systems.
Assume, A could be determined properly. 5) yields which leads to p < 1 , where p is an appropriate constant smaller than one. 15) should hold, where E were a prescribed number, one would have introduced a performance criterion, which when satisfied, would also guarantee stability of the controlled structure if the response Yo of the uncontrolled structure were stable. E. Leipholz and M. 17) < Ep . This is of course a very vague condition for A, and it becomes obvious that control problems, involving an unknown operator to be determined, are usually undeterminant problems.
For example, using the deflection sensor, the closed-loop transfer function of the control system is G (s) = c ~(s) ~(s) (1. , one has u(t) fey, y, = y, Y; ... , c), (1. 24) in which the c are constants. 23). The servomechanism may have detrimental effects on the structure if the designer is only interested in controlling one of the structural parameters, keeping the others fixed. 2 This controller is similar to the servomechanism in its components up to a few differences. These differences occur in the servo- val ve and actuator equations.