This document discusses the reduction of multiple subsystems in block diagrams. It describes the components of block diagrams, including signals, subsystems, summing junctions and pickoff points. It explains the three main topologies for block diagrams: cascade, parallel and feedback forms. Equations are provided for reducing subsystems arranged in each of these forms into a single transfer function. Examples are given to demonstrate the reduction of specific block diagrams into a single subsystem.

1. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
CONTROL SYSTEMS
B Madhuri
22 February 2015 1

2. 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

3. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor Block Diagram
mmmmm TDJ   
)()()(2
sTssDsJs mmmmm  
Mechanical Equation
mm DsJ 
1Tm(s) )(
.
s
)(
.
s
s
1 )(s
22 February 2015 3

4. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
• Electromechanical equation
KT
22 February 2015 4
atm iKT  )()( sIKsT atm 
Ia(s)
Tm(s)
DC Motor Block Diagram

5. 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

6. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION

7. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Block diagram fundamentals

8. 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

9. 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

10. 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)

11. 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

12. 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 

13. 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 

14. 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



15. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201515
Reduction of Multiple Subsystems – Block
Diagram Topology
)()()()( sHsCsRsE 
)()()( sGsEsC 
)(
)()(1
)(
)(
)(
)(
)()(1
)()(
)(
1
)()(
)(
)(
)(
)()()(
)(
)(
sR
sHsG
sG
sC
sC
sG
sHsG
sCsH
sG
sHsC
sG
sC
sR
sHsCsR
sG
sC
























G(s)
H(s)
)(sR )(sE )(sC


)(sR )(sC
)()(1
)(
sHsG
sG


16. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201516
Reduction of Multiple Subsystems – Block
Rearrangement
  )()()()( sCsGsXsR 
)()()()()( sCsGsXsGsR 

17. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201517
Reduction of Multiple Subsystems – Block
Rearrangement

18. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201518
Reduction of Multiple Subsystems – Block
Rearrangement

19. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201519
Reduction of Multiple Subsystems – Example

20. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201520
Reduction of Multiple Subsystems – Example
)(sR )(sC
)()(1
)(
sHsG
sG


21. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
22 February 201521
Reduction of Multiple Subsystems – Block
Rearrangement
)()()()( sCsXsGsR 
)()()
)(
)(
)(( sCsG
sG
sX
sR 