25
Introduction to Feedback Systems / © 1999 Önder YÜKSEL EXAMPLE EXAMPLE
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Introduction to Feedback Systems / © 1999 Önder YÜKSEL
EXAMPLEEXAMPLE
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
2
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Return to examplecombine cascaded blocks
TM
sLR1
aa ai
mKsJB
1*
mm *Mv
bKbe
+
-
M
)sJ)(BsL(R
K*
m*
maa
m
MOTOR
G1
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
3
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
valve
Ms1
KvM q0
sKv
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
4
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
+
-
q0
q1
h1-
h2
+ q1 +
-
q2
h2
1A1
s1
1R1
2A1
s1
1sA1
2sA1
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
5
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
turbine-generator
KGiF
FF sLR vL
h2
G
NTG
BG+sJG
Nq2
KG(RF+sLF)N(BG+sJG)
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
6
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
No more cascaded blocks
No parallel blocks
1 feedback configuration
comparator motor valve double tank turbine-generator
K+
-
VR
VL
VM
Kv
q0+
-
h1 -1R
1+q1
+- h2
q2
N
TGVL
bKbe
+
-
M
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
7
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
q0
h1 -
h2
+ q1 +
-
q2
h2
1R1
2sA1
1sA1
q1
+
-
1sA1
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
8
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
feedback
+1R
1 q1 +
-
q2
2sA1q0
+1sA1
-
1sA1
-
h2
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
9
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
-
+
1R1
1sA1
11
1
AsR1
sA
+q1
-
h2
1sA1
-
q2
+
2sA1q0
+
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
10
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
cascaded
11
1
AsR1
sA
q1
+
-
q2
2sA1q0
1sA1
-
h2
+
11
1
AsR1
sA
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
11
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
q1
+
-
q2
2sA1q0
-
+
11
1
AsR1sA
cascaded
11
1
AsR1sA
1sA1
11AsR11
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
12
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
feedback
++
2sA1q0
11AsR1
1
-
-
q2
11
1
AsR1
sA
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
13
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Double tank
-
q2
q0
+11AsR1
1
)RAsAAs(A
RsA1
12121
11
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
14
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
+
-
M
G1eb
Kb
K+
-
VR
VL
VMh2
N
TG VLN(BG+sJG) KG(RF+sLF)-
q2
q0
+11AsR1
1
)RAsAAs(ARsA1
12121
11
Kv/s )AAsRAs(A
)AsR)(1sJN(B
21121
11GG
cascade
G3feedback
1b
1
GK1
G
G2
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
15
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
feedback+
-
VR
VL
TG VLKG(RF+sLF)
VM q0
K11AsR1
1
Kv/sG2
+-q2
G3
N
3
3
NG1
G
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
16
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
TG
KG(RF+sLF)VM q0
K11AsR1
1
Kv/sG2
3
3
NG1
G
VL
+
-
VR VL
cascade
)AsR)(1NGs(1
)sL(RGGKKK
113
FF32Gv
G4
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
17
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
VL
VL
+VR
G4
4
4
R
L
G1
G
(s)V
(s)VT(s)
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
18
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Parameter values
• MotorRa=1La=1Km=1Kb=1JM=1BM=1
• TurbineN=1
• GeneratorJG=1BG=1LF=1RF=1KG=1
ValveKv=1Bv=1
Double tankA1=1A2=1R1=1
Comparator gain K is the control parameter
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
19
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
23ss
1
)sJ)(BsL(R
KG
2*m
*maa
m1
33ss
1
GK1
GG
21b
12
2)s(s
12ss
)AAsRAs(A
)AsR)(1sJN(BG
2
21121
11GG3
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
20
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
1))(sGs(1
1)(sGKG
)AsR)(1NGs(1
)sL(RGGKKKG
3
32
113
FF32Gv4
6)9s5s(ss
1ssK
232
2
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
21
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
KKs6)s(K9s5ss
1)sK(s
G1
G
(s)V
(s)VT(s)
2345
2
4
4
R
L
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
22
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
t=0:.1:20;for K=5:21;
n=K*[1,1,1];d=[1,5,9,K+6,K,K];step(n,d,t),text(21,0,strcat('K=',num2str(K))),pause,figure(1),
end
MATLAB simulation
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
23
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
321s34s24s8ss12ss
K(s)G 2345
2
4
1)2s(sK321s34s24s8ss12ss
KT(s) 22345
2
NKKKK where Gv
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
24
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
Time (sec.)
Am
plit
ud
e
Step Response
0 2 4 6 8 10
0
50
100
150
200
250
300
350
K=1
K=40
K=10
25.02.1999 EE 302 - Block Diagrams - O. Yuksel
25
Introduction to Feedback Systems / © 1999 Önder YÜKSEL
End of Chapter
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