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KT2101 - Endocrien systeem, Modelvorming en Regeltechniek (Aantekeningen - 2) $4.81
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KT2101 - Endocrien systeem, Modelvorming en Regeltechniek (Aantekeningen - 2)
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  • Course
  • KT2101 (KT2101)
  • Institution
  • Technische Universiteit Delft (TU Delft)

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Document information

  • January 29, 2021
  • 38
  • 2020/2021
  • Class notes
  • B. van der eerden
  • Deel 2!

Subjects

  • endocrien systeem
  • modeling

Written for

  • Technische Universiteit Delft (TU Delft)
  • Klinische Technologie
  • KT2101 (KT2101)
All documents for this subject (3)

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ehemelsbuijsman

Content preview

C U 2 s .




Frequency response and Bode plots




uit ) = Sin ( w -
t ) with w in rad Is ( frequency) → dan 't confase with un and Wd !


↳ NEW kind of inputsignal we'll be working within this lectine




C- ( s) = ont ( 5) 1in ( s ) = ( often ) 415 ) 1415 ) .




25 Y (s) ( S2 -135 -12534
C- ( s ) = =
→ = 254 → ijt 3. is -1254 = 25 u

52 -135 U ( s)
-1 25




Higher frequency ( w) → smaller amplitude and Stoner response ( it is possible that the amplitude becomes

larger ,
which is a Sigh that the System is closeto instabiliteit ) .




For an LTI System with input : uit ) = A sinlwt )


Output yet ) Mln ) A Sintcut ¢ ( w ))
'

: = -
+



↳
phase charge ( or Phase lag)

→
amplitude Magnificat ion (→ 0
, SIonly de creasing or sudden Ig increasing)
-

Magnitude ( soaling factor ) : NCW) = C- ( jw )

'
ajtb Llajtb ) ( Atb )
-
'
Phase shift ( anale ) :
@ ( w) = C- ( jw) → = toen

↳
Example : C- ( s ) = 11 ( s -11 ) , w = 1 rad Is


C- (jw ) = 11 ( Jw -11 ) =
111J -11 ) → 1 C- ( j ) I = 11 2


↳
C- ( j ) = 1 -
j -1 =. 00 -
d. 50 = -
950


output : ijlt ) = 11 2 .
Sin ( t .
t 21T .
( -
45013600 ) )

↳ Gts )
Another example : = 251 ( S2 -135 -125 ) , w = 5rad Is


C- ( jw ) : 251 ( ( jw) 2-1 3in -1 25 ) = 25/1 W2 - i
3.) W -125 ) = 25/1 -
25 -115J -125 ) =
25115J
↳ megative !
↳ 1615531 = 25115 = 1213


C- ( Sj ) = 00 -
900 = - 900


Output :
↳ (t )
= 1213 Sin Ist + ZIT .
( -90013600 )) For our secand Example Wm = 5
,


↳ > 1 → amplitude increase s
( S2 + zfwn.se un
2
52 -135 -125 )

< C- ( jw ) -
j
Decomposition : C- ( jw ) = 1 C- ( jw ) te

↳ 1 Gljw ) 1 = 1 En CJW ) 1 -
. . .
-
1 Gm ( jw ) 1 → 10109 ( IGCJWII ) =
1010911 -01 ( jul ) t . . .
+
1010911 C- nljw ) 1 )

C- ( jw ) = C- 1 ( jw) t . . .
t En ( jw )


↳ With this can add plots of C- 1 Cjw ) and GZCJW ) to yet C- ( jw )
, 404




Bode plot : response plat for magnitude and Phase shift .




Any transfer function C- ( s ) can be presented as a product

of ( some of ) the following terms :




K ( constant )
'




II Zero → -
900 Phase shift , -20 magnitude
.
(g)

11
-
( TS -11 )

11
-
[ ( stun ) ? -1 29 ( stun ) -11 ]

↳ When we have the
frequency response plat for


these terms .
We can com pose the frequency response

plat for any transfer function . Bode plot example



1) raming a Bode plot

# #
( 1- 1) ( -11 )
C- ( wj ) → 90 Phase
-
-
. . .
- . . _ . .
. . .
=
ze ras -
20 mag and
-
shift


(÷ 1) ( II
JW


↳
-1 -11 ) . . .
= poles

20 1091 . . .
) dB =
Storting point of Bode plot

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