a system sensitivity example friday 19 sept 2014 ee 401: control systems analysis and design example...
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A System Sensitivity Example
Friday 19 Sept 2014 EE 401: Control Systems Analysis and Design
• Example #2: Nominally, K = 5 and H = 0.05. Determine the sensitivity of the system to variations in K
and H.
0.1( )1
0.1
p
p
KKsT sK
K Hs
𝐾 𝑝𝐾
𝑠+0.1
𝐻
𝑅 (𝑠) 𝐶 (𝑠)+
-
Controller
Sensor
Plant
Input Output
The System Transfer Function
0.1
p
p
K K
s K KH
Slide 1 of 3
( )
0.1
p
p
K KT s
s K KH
Kp 10
10
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S KT
Kp 5
5
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S KT
A System Sensitivity Example
Friday 19 Sept 2014 EE 401: Control Systems Analysis and Design
1. Sensitivity of T to variations in K
o See Mathematica “sensitivity-example.nb”
reduces with increased .
( )
( )TK
K T sS
T s K
50.05
0.1
0.1 0.25TK
K Hps i
iS
K i
0.1
0.1 p
s
HKK s
Kp 1.
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S KT
TKS
Slide 2 of 3
( )
0.1
p
p
K KT s
s K KH
Kp 10
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S HT
Kp 5
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S HT
A System Sensitivity Example
Friday 19 Sept 2014 EE 401: Control Systems Analysis and Design
2. Sensitivity of T to variations in H
o See Mathematica “sensitivity-example.nb”
Due to high sensitivity of T to H , we should invest in high performance sensor block (H).
( )
( )TH
H T sS
T s H
50.05
0.25
0.1 0.25pT
KH H
ps i
KS
K i
THS
0.1p
p
HKK
HKK s
Kp 1.
0 1 2 3 4 50 . 0
0 . 2
0 . 4
0 . 6
0 . 8
1 . 0S HT
Slide 3 of 3