csl6 28 j15
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ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
CONTROL SYSTEMS
B Madhuri
22 February 2015 1
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor Block Diagram
)()(
)()()()(
tKtV
tetKLtiRti
mbb
ambaaaa
aa RsL
1Ea (s)
Vb (s)
Ia (s)
Electrical Equation
)()()()( sEKssLssIRsI abmaaaa
22 February 2015 2
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor Block Diagram
mmmmm TDJ
)()()(2 sTssDsJs mmmmm
Mechanical Equation
mm DsJ
1Tm(s) )(.
s
)(.
ss
1 )(s
22 February 2015 3
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
• Electromechanical equation
KT
22 February 2015 4
atm iKT )()( sIKsT atm
Ia (s)Tm(s)
DC Motor Block Diagram
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 2015 5
aa RsL
1Ea (s)
Vb (s)
Ia (s)KT
Tm(s)
mm DsJ
1
)(.
s
1/s
)(s
Kb
DC Motor Block Diagram
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Block diagram fundamentals
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
What is Multiple Subsystems?
22 February 20158
Feedback Control
System consists of
process and
subsystems
Our objective is to combine
multiple subsystems into single
system – thus the name
reduction of multiple
subsystems
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Components
22 February 20159
Components of block diagram:
1. Signals
2. Subsystem
3. Summing junction
4. Pickoff point
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Topology
22 February 201510
Block diagram has
three topologies (or
arrangements or
forms):
1. Cascade form
2. Parallel form
3. Feedback form
G1(s) G2(s)
G1(s)
G2(s)
G1(s)
G2(s)
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Topology
22 February 201511
How to reduce subsystems in cascade form?
G1(s) G2(s) G3(s))(sR )(1 sX )(2 sX )(sC
)()()()()()()(
)()()()()()(
)()()(
32132
21212
11
sGsGsGsRsGsXsC
sGsGsRsGsXsX
sGsRsX
Gs(s)=G1(s)G2(s)G3(s))(sR )(sC
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Topology
22 February 201512
How to reduce subsystems in parallel form?
)()()()()()()(
)()()(
)()()(
)()()(
321
32
22
11
sGsRsGsRsGsRsC
sGsRsX
sGsRsX
sGsRsX
G1(s)
G2(s)
G3(s)
)(sR )(sC
)(1 sX
)(2 sX
)(3 sX
)(sR )(sC )()()()()( 321 sGsGsGsRsC
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Topology
22 February 201513
How to reduce subsystems in parallel form?
)()()()()()()(
)()()(
)()()(
)()()(
321
32
22
11
sGsRsGsRsGsRsC
sGsRsX
sGsRsX
sGsRsX
G1(s)
G2(s)
G3(s)
)(sR )(sC
)(1 sX
)(2 sX
)(3 sX
)(sR )(sC )()()()()( 321 sGsGsGsRsC
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Reduction of Multiple Subsystems – Block Diagram Topology
22 February 201514
How to reduce subsystems in feedback form?
G1(s) G2(s)
H2(s) H1(s)
)(sR )(sE )(sC
G(s)
H(s)
)(sR )(sE )(sC
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201515
Reduction of Multiple Subsystems – Block Diagram Topology
)()()()( sHsCsRsE
)()()( sGsEsC
)()()(1
)()(
)()(
)()(1)()(
)(
1)()(
)(
)()(
)()()()(
)(
sRsHsG
sGsC
sCsG
sHsGsCsH
sGsHsC
sG
sCsR
sHsCsRsG
sC
G(s)
H(s)
)(sR )(sE )(sC
)(sR )(sC
)()(1
)(
sHsG
sG
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201516
Reduction of Multiple Subsystems – Block Rearrangement
)()()()( sCsGsXsR
)()()()()( sCsGsXsGsR
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201517
Reduction of Multiple Subsystems – Block Rearrangement
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201518
Reduction of Multiple Subsystems – Block Rearrangement
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201519
Reduction of Multiple Subsystems – Example
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201520
Reduction of Multiple Subsystems – Example
)(sR )(sC
)()(1
)(
sHsG
sG
ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION22 February 201521
Reduction of Multiple Subsystems – Block Rearrangement
)()()()( sCsXsGsR
)()())(
)()(( sCsG
sG
sXsR