A#18-1 - (h)(7). Now use to bring down the overshoot, i.e.,...

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Assignment #18 ECSE-2410 Signals & Systems - Spring 2007 Fri 04/13/07 1(75). Given the system, D ( s ) Assign#18. p.1 X ( s ) H 1 ( s ) H 2 ( s ) Y ( s ) H 3 ( s ) - + + + where , s K K s H 1 1 ) ( + = ) 2 )( 1 ( 1 ) ( 2 + + = s s s H , and 1 ) ( 3 = s H . The purpose of K is to provide proportional feedback and the purpose of is to provide derivative feedback. In practice, K is used to minimize steady-state errors and is used to keep down overshoot, i.e., add damping. 1 K 1 K (a)(7). Find ) ( ) ( s X s Y when . 0 ) ( = s D (b)(6). Find , when and ) ( lim t e t ) ( ) ( ) ( t y t x t e = ) ( ) ( t u t x = . What is this steady-state error when K =34? (c)(7). Find ) ( ) ( s D s Y when . 0 ) ( = s X (d)(6). In (c) above, find when is a unit step. What is the steady-state output due to the disturbance, D ( s ), when K = 34? ) ( lim t y t ) ( s D (e)(5). Find the characteristic equation of the closed-loop system in terms of K and . 1 K (f)(7). For 4 and =0, find the closed loop poles, and the corresponding values of 3 = K 1 K ζ and n ω . Note that the choice of K =34 helps the steady-state errors, but contributes greatly to overshoot.
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Unformatted text preview: (h)(7). Now use to bring down the overshoot, i.e., increase 1 K . With the proportional gain K= 34, find so that 1 K =0.8. (i)(15). Set =0, and draw the root locus as K varies from 1 K . (Note. Root locus refers to a plot of the roots of the closed-loop characteristic equation as a constant, say K, varies. Choosing several values of K should give you a good idea of the basic shape of this root locus plot.) (j)(15). Set K =34, and draw the root locus as varies from 1 K . 2(25). For the block diagram shown, +-+-s 1 s 1 20 ) ( s W 10 ) ( s Y +-) ( s X (a)(10). Find the transfer function ) ( ) ( ) ( s W s Y s Z = . Express the numerator and the denominator in descending powers of s . (b)(15). Find the transfer function ) ( ) ( s X s Y . Express as the ratio of two polynomials in descending powers of s . Assign#18. p.2...
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A#18-1 - (h)(7). Now use to bring down the overshoot, i.e.,...

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