exam0sample_problems

# exam0sample_problems - 4 Name PROBLEM NO 2(50 Given the...

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March 30, 2004 Name __________________ 4 PROBLEM NO. 2 (50%) Given the transfer function , draw the Bode straight line approximation using the following steps: (a) Find the poles, zeros, and static gain of the transfer function G ( s ). (b) Write all first order terms in the form ( ! s +1) (except s or 1/ s ) and all second order complex terms in the form . (c) Provide the break frequencies for all of the terms in transfer function G ( s ). (d) Plot magnitude and phase of all elemental transfer functions separately on the graphs on the next page. Label the elemental transfer functions on the graph along with all break frequencies and slopes. (e) Plot the total transfer function made up of the elemental transfer functions in part (d).

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March 30, 2004 Name __________________ 5 0.0 1 0. 1 1 10 100 1 . 10 3 1 . 10 4 1 . 10 5 100 80 60 40 20 0 20 40 60 80 100 Bode Plot-Phase Frequency (rad/s) Phase (deg) 0.0 1 0.1 1 10 10 1 . 10 3 1 . 10 4 1 . 10 5 30 26 22 18 14 10 6 2 2 6 10 Bode Plot- Magnitude Frequency (rad/s) Magnitude (dB)
March 30, 2004 Name __________________ 6 PROBLEM NO. 2 (Continued) (f) For G ( s ) given on the previous page, write down expressions for the magnitude and phase of the frequency response as a function of ! . (g) Assume that the transfer function on the previous page represents , where u ( t ) is the input signal and y ( t ) is the output signal. Write down an expression for the steady-state response y ss ( t ) when the input is .

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April 5, 2005 Name ____________________________ " PROBLEM NO. 1 (30%) #\$%&'()* +,) &)-\$%(.\$*()* +*/%&0)* 01%-+'\$% 2'3)% 4)5\$67 8&&19) ± ² : : y /%( ±² : : y ± 7 " " " " n n n s s s K s G s F s Y Z ]Z ³ ´ ³ ´ ;/< ='3)% +,) '%>1+ ± ²± ² t Au t f ? 6,)*) ± ² t u '& +,) 1%'+ &+)> 01%-+'\$%? &\$53) 0\$* +,) (@%/9'- *)&>\$%&)? t y ? /%( -5)/*[email protected] '()%+'[email protected] +,) +*/%&')%+ /%( &+)/(@.&+/+) >\$*+'\$%& \$0 +,) *)&>\$%&)7 ;4< A&'%2 +,) *)&15+ 0*\$9 >/*+ ;/<? 0'%( +,) %19)*'-/5 3/51) \$0 +,) >*\$(1-+ n +\$ )%&1*) +,/+ :B 7 : d µ ss ss y t y y 0\$* C t t &)-\$%(7
April 5, 2005 Name ____________________________ " #\$% &'()*+,- . +*//,-,(0 *(120 0' ±² s G 3 ±² ± ² ¸ ¹ · ¨ © § ³ ´ ³ " "" 4 56 )*( 78 4 9 :9 4 ; \$') 85 4 55 6 4 " S t t t f 4 < = , ( 6 9 4 8 s K ;8> 4 ? ] 3 .(+ :9 4 ; n Z 3 /*(+ 0=, )0,[email protected])0.0, -,)1'(),3 ss y 3 0' ± ² t f 4

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April 5, 2005 Name ____________________________ " PROBLEM NO. 2 (30%) #\$%& '() %*+,-'.'/0 1.2) -3.' %--\$.4/,%'/.5 6.\$ '() '\$%5*6)\$ 6750'/.58 ±² s s s s s G ³ ´ ³ ´ ´ ³ 99:; < 9 9:=9 < 9 9:=> < 9 9>?? < 9 > : 8 7*/[email protected] '() 6.33.&/[email protected] *')-*A B%C D/52 '() -.3)*8 E)\$.*8 %52 '() *'%'/0 @%/5 .6 '() '\$%5*6)\$ 6750'/.5 ± ² s G < B1C F4'\$%0' '() )3),)5'%3 '\$%5*6)\$ 6750'/.5* &\$/'/[email protected] %33 6/\$*'G.\$2)\$ ')\$,* /5 '() 6.\$,
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exam0sample_problems - 4 Name PROBLEM NO 2(50 Given the...

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