(408177384) FinalExam Solution (1)

8/10/2019 (408177384) FinalExam Solution (1)

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NAME MASTER

(PRINT)

EE105 FINAL

FALL 10

1

2

3

4

5

6

7

TOTAL

TOTAL

1.4

GRADE

Put your answers in the space provie

!appy !o"iays

PROBLEM 1


2/8

Given that Y(s) = (1s) = (s1)

!(s) (s3)(s4) s27s12

"#$%&ete the 'ieentia& e*+ati#n ,e- that e&ates (t) t# /(t)

0 (''t)4 (''t)3 1 (''t)2 7 (''t) 12 (t) =

0 (''t)4 (''t)3 (''t)2 1 (''t) 1 /(t)

Given /(t) = e/%(3t) in' (t)

t 8 (t) = t 8

Given /(t) = e/%(3t) in' (t)

t (t) =

t

Given that /(t) = e/%(3t) in' (t) # a&& t.

Y(s) = (s1) = 2 3 3

(s3)2(s4) (s3)2 (s3) (s4)

(t) = (32t)e/%(3t) 9 3e/%(4t)

:in' the 'ete$inant # the ;a%h in :i;.1.

< = 1666 = 1

:in' the tans$issi#n Y! in the ;a%h # :i;.1.

Y! = 012(16) 121 = 721 Y! = 3.7PROBLEM 2

56

1

2

1

! 56 1

4

3 Y


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:in' the tanse +n>ti#n ?(s) # the sste$ -ith the @#'e %t # :i;.1.

?(s) = 1

s2as1

?(1) = 1 ',

?(s) = 1

s21s1

See the lab experiments

?(s) =

:in' the #'e # the >haa>teisti>%#&n#$ia& # the 'ieentia& e*+ati#n

that ;#vens the sste$ in :i;.2.

O'e = 0 1 "#$%&ete the - ;a%h # :i;.3 that

'es>i,es the 'na$i>s # the sste$ in :i;.2.

The $#t# >#nstant is B$.

Cs ( 1$ ) $ ( B$ ) T1( 1 ) T2 ( 12) T3

( 1$ ) ( @ ) 10@2sF

e; ( B$ ) 1( 12) 2 ( 1s ) H2PROBLEM 3

F

@2

H2 T3$

Cs @1 E1D$ 1 E2

e; T1 T2

FIG 2

R(s) ?(s) G(s) "(s)

5

FIG 1

FIG 1


4/8

n the >#nt#& sste$ # :i;.1 G(s) = s an' ? has the #$ ? = (As @)s.

Ihat t%e # >#nt#&&e is ?(s). "i>&e #+ >h#i>e

A. J#%#ti#na& (J)

@. J#%#ti#na&nte;a& (J) !". J#%#ti#na&Deivative (JD)

D. J#%#ti#na&nte;a&Deivative (JD)

"h##se A an' @ s# that the >haa>teisti> %#&n#$ia& # the sste$ # :i;.1 is

J(s) = (s4)2

J(s) = s2As @ = s2Ks16

A = K = .KK @ = 16 = 1.7K

The %#siti#n >#nt#& sste$ # :i;.2 >#ntains ateee',a>.

The >#nt#&&e has the tanse +n>ti#n ?=(s1)s.:in' the #'e # the sste$ >haa>teisti>

%#&n#$ia&.

O'e = 3

:in' the sste$ >haa>teisti> %#&n#$ia& in te$s

# A.

= 1 2A(s1) 2(s1)

s2 s3

J(s) = s3 2As22As 2s 2 = s3 2As2 2(As1) 2

J(s) =

:in' the va&+e # A # -hi>h the sste$ #s>i&&ates.

4(A2A)= 2 A2 A .5 =

A = .5 .75.5= .366

PROBLEM 4

HR(s) ?(s) 23s 13s "(s)

5 A

FIG 2

N(s) '(s)

R(s) ?(s) G(s) "(s)

FIG 1


5/8

The +nitee',a> sste$ # :i;.1 has the %&ant G(s) = 2

s(s1)an' the >#nt#& &a- ?(s) = 5(ss1)

s

:in' the stea' state e# N(t8) # s1= 5 i (t) = 32t an' '(t) =

N(t8) =

:in' the stea' state #+t%+t >(t8) # s1= 5 i (t) = 32t an' '(t) =

>(t8) = 32t

:in' the stea' state e# N(t8) # s1= 5 i (t) = an' '(t) = 23t

sN(s) = (23s) 20s(s1) sN = (23s) 2s 11(s5)0s2(s1) s2(s1)1(s5)

sN(s) = 65 = .12s

N(t8) =

:in' the $a/i$+$ va&+e # s1# -hi>h the sste$ is sta,&e.

J(s) = s3 1s2 1s 1s1

1s1MA!= 1 s1MA!= 1

s1MA!=

PROBLEM 5

A >etain sste$ has the #%en#% tanse +n>ti#n

G? = B(s2) s(s6)2

As B vaies the ##ts # the sste$ have >i. :in' = 3

As B ten's t# ininit M >i ten' t# ininit. :in' M M = 2

L#>i e/ist #n the ea& a/is ,et-een s1an' s2. :in' s1an' s2.


6/8

s1 =

s2= 2L#>i &eave the #i;in at an;&es H1an' H2. :in' H1an' H2.

H1 =

H = P1KO

(31) = PO

. H2 =

The >i that ;# t# ininit ae as$%t#ti> t# stai;ht &ines.

These &ines intese>t the ea& a/is at s3. :in' s3

(122)(31) = 5

s3=

"ae+&& set>h the ##t >i an' thei as$%t#ti> &ines #n the ;a%h ,e-.

135

1K

225

27

PROBLEM 6


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The %t a,#ve is the @#'e %t # the #%en#% tanse +n>ti#n # a >etain >#nt#&

sste$.

Ma #n the %t the sste$ %hase $a;in. The sste$ has t-# ;ain $a;ins. the ;ain

is 'e>ease' the sste$ -i&& #s>i&&ate. Ma #n the ;a%h this ;ain $a;in.

Esti$ate the ;ain in>ease e*+ie' # #s>i&&ati#ns an' the #s>i&&ati#n e*+en> .

:e*+en> # #s>i&&ati#n = 2a'se>

the ;ain is in>ease' the sste$ -i&& #s>i&&ate. Ma #n the ;a%h this ;ain $a;in.

Esti$ate the ;ain 'e>ease e*+ie' # #s>i&&ati#ns an' the #s>i&&ati#n e*+en>.

:e*+en> # #s>i&&ati#n = 11 a'se>

PROBLEM


G? = M(1sQ)

s2(1s%)

is t# have a %hase $a;in # 6Oat a +nit ;ain e*+en> # 3a'se>.

:in' M an' Q an' %.

An;(G?) = 1K6 = 1K 2atn(a)


8/8

2atn(a) = 15O a = 3.73

Q = 33.73 = .K

% = 11.2

3.73M = 1 M = 2.41

M = 2.41

Q = .K

% = 11.2


G? = M(1sQ)

s2(1s1)

is t# have a %hase $a;in # 45Oat a +nit ;ain e*+en> # 3a'se>.

:in' M an' Q.

An;(G?) = 1K atn(31) atn(1Q) = 1K 45

atn(3Q) = 61.7 Q = 1.62

M = 1.3 = .4 = 4.4K 11.K5 2.1

M = 4.4K

Q = 1.62

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(408177384) FinalExam Solution (1)