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# A#20 - K so that of the closed-loop system has a time...

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Assignment #20 – p.1 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/10/09 1(30). Find the closed loop transfer function, ( ) () s X s Y , in terms of the shown. s H ' (a) - - + + () s X ( ) s H 2 ( ) s H 1 ( ) s Y ( ) s H 3 ( ) s H 4 (b) + - + + () s X ( ) s H 2 () s H 1 ( ) s Y () s H 4 ( ) s H 3 2(20). (a) Leaving K unspecified, find ) ( ) ( s X s Y . + - K () () ( ) 2 1 1 + + = s s s G () s X () s Y (b) Find the value of K so that the closed-loop system is critically damped. 3(10). For the system shown, find the value of K and 0 ω so that two of the closed-loop poles (poles of () () s X s Y ) are at 0 j s ± = (i.e., they lie on the j -axis). + - K () () 2 1 1 + = s s s G () s X () s Y

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Assignment #20 – p.2 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 04/10/09 4(25). Given + () s E () 1 1 + = s s G K - () s X ( ) s Y (a). Leaving K unspecified, find the closed-loop transfer function, ( ) () s X s Y . (b). For unspecified K , find () ( ) t y t y step = , i.e. , when ( ) ( ) t u t x = . (c). Find
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Unformatted text preview: K so that of the closed-loop system has a time constant, ( ) t y step 4 1 = τ . (d). For 2 = K , find the transfer function, ( ) ( ) s X s E (Note, you need to eliminate from the equation.) ( ) s Y (e). For 2 = K , find when ( ) t e ( ) ( ) t u t x = . 5(15). Consider the RLC circuit shown. R L C x ( t ) +-+-y ( t) (a). Find in terms of . ) ( s H C L R and , (b). Evaluate the exact |H ( ω ) | at LC n 1 = = ωω . Express answer in terms of some or all of R, L , C . (c). Suppose that R= 1000ohms and rad/sec 10 = n . |H ( ) | dB 3 dB 10 -40 dB /decade 1 For the Bode magnitude plot shown, find the values of L and C. Note that the value of |H ( ) | is exactly 3 dB at =10 rad/sec....
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A#20 - K so that of the closed-loop system has a time...

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