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# A#17 - Functions the command feedback to form the closed...

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Assignment #17 – p.1 ECSE-2410 Signals & Systems - Fall 2006 Fri 11/10/06 1(10). Find the closed loop system transfer functions, ) ( ) ( s X s Y , expressed in terms of the s s H i ) ( . 2(45). Given the system, D ( s ) X ( s ) H 1 ( s ) H 2 ( s ) Y ( s ) H 3 ( s ) where K s H = ) ( 1 , ) 1 ( 1 ) ( 2 + = s s s H , and 1 ) ( 3 = s H . (a) Find ) ( ) ( s X s Y when 0 ) ( = s D . (b) Find ) ( lim t e t , when ) ( ) ( ) ( t y t x t e - = and ) ( ) ( t tu t x = . (c) Find ) ( ) ( s D s Y when 0 ) ( = s X . (d) In (c) above, find ) ( lim t y t when ) ( s D is a unit step. (e) Find the characteristic equation of the closed loop system. (f) Find K so that the straight line Bode magnitude diagram of the transfer function in (c) above has the break frequency at 10 rad./sec. (g) For 3 = K , find the closed loop poles, and the corresponding values of ζ and n ϖ . (h) Find the gain K so that the closed loop system is critically damped. (i) Set 3 = K . Use MATLAB to plot the system response ( 10 0 t ) of the closed loop when ) ( t d is a unit step and 0 ) ( = t x . Use the command tf to define the individual transfer

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Unformatted text preview: Functions; the command feedback to form the closed loop system; and the command step to find the step response. See Help tf, … and the other commands shown here.-+ + + Assignment #17 – p.2 ECSE-2410 Signals & Systems - Fall 2006 Fri 11/10/06 3(10). For the system shown, (a) Find ) ( ) ( s X s Y . (b) Find the value of K so that the closed-loop system is critically damped. 4(15) Consider the feedback system shown below: (a) Find the transfer function ) ( ) ( s X s Y . (b) If ) ( ) ( t tu t x = , a ramp input, find ) ( lim t y t ∞ → . (c) If ) ( ) ( t u t x = , a step input, find ) ( lim t e t ∞ → , where ) ( ) ( ) ( t y t x t e-= . 5(10). Text 11.4 6(10). Text 11.49-2 1 ( 4 8) s s s + + K + X(s) Y(s) E(s)- ) 2 )( 1 ( 1 + + s s + X(s) Y(s) K...
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