control system

1. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Control Systems
DC motor

2. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Transfer Function of DC Motor
22 February 2015 2

3. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Electromechanical system?
22 February 2015 3
• System consists of electrical
and mechanical components
• System whereby power flows
between electrical and
mechanical components
• Sometimes called
mechatronic system

4. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
Examples of electromechanical systems
22 February 2015 4
• Speaker
• Motor

5. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Schematic Diagram
22 February 2015 5
Electrical
Components
Mechanical
Components
Magnetic
Field

6. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Transfer Function Objective
22 February 2015 6
Electrical
variable
Mechanical
variable
Electrical variable CONTROLS mechanical variable
Input: Electrical variable (applied voltage)
Output: mechanical variable (angular position)

7. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electrical Components
22 February 2015 7
aaR Rtiv )(
)()( tKtv mbb 
Using Kirchoff’s Voltage Law (KVL) around the loop
Electromotive
force (emf)
aaL Ltiv )(
Applied
Voltage

8. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electrical Components
22 February 2015 8
aaR Rtiv )(
)()( tKtv mbb 
Using Kirchoff’s Voltage Law (KVL) around the loop
aaL Ltiv )(
)()()()( tetKLtiRti ambaaaa  
Electrical
Equation
𝐵𝑎𝑐𝑘 𝑒𝑚𝑓 𝑣 𝑏 𝑡 = 𝑘∅𝑁

9. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Mechanical Component
22 February 2015 9
Rotor Schematic Model
Mechanical Components

10. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Mechanical Component
22 February 2015 10
Use Newton’s Second Law and
Free Body Diagram
mmJ 
mJ
mmD 
mT
mmmmm TDJ   
m
Mechanical
Equation

11. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electromechanical System
22 February 2015 11
Torque-Current
Equation
mmmmm TDJ   
Mechanical Equation
ambaaaa eKLiRi  
Electrical Equation
atm iKT 
Electromechanical
Equation

12. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electromechanical System
22 February 2015 12
Combined Equation in
order to obtain the transfer
function
mmmmm TDJ   Mechanical Equation
ambaaaa eKLiRi  Electrical Equation
atm iKT Electromechanical Equation

13. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electromechanical System
22 February 2015 13
Transform differential equations into frequency domain
mmmmm TDJ   
ambaaaa eKLiRi   )()()()( sEKssLssIRsI abmaaaa  
)()()(2
sTssDsJs mmmmm  
)()( sIKsT atm 
)()()()( sEKssLssIRsI abmaaaa  
Actual condition is that Resistor is much greater than Inductor

14. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electromechanical System
22 February 2015 14
Combine Equations
)()()()( sEKssLssIRsI abmaaaa  
)()()(2
sTssDsJs mmmmm  
)()( sIKsT atm 
  )()()(
)(
sEKsssLR
K
sT
abmaa
t
m
 
)()()(
)()(2
sEKsssLR
K
ssDsJs
abmaa
t
mmmm





15. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Electromechanical System
22 February 2015 15
Combine Equations
)()()(
)()(2
sEKsssLR
K
ssDsJs
abmaa
t
mmmm




b
t
aa
m
t
aa
m
a
m
sK
K
sLR
sD
K
sLR
JssE
s





2
1
)(
)(
)()()(
))(( 2
sEKsss
K
sLRsDJs
abmm
t
aamm




16. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Transfer Function Without Load
22 February 2015 16
b
t
aa
m
t
aa
m
a
m
sK
K
sLR
sD
K
sLR
JssE
s





2
1
)(
)(

17. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Transfer Function Without Load
))/(
)/(
)(
)(
1
)(
)(
2
2
aabtmm
aat
a
m
b
t
aa
m
t
aa
m
a
m
sLRKKDssJ
sLRK
sE
s
sK
K
sLR
sD
K
sLR
JssE
s










22 February 2015 17

18. ELECTRICAL ELECTRONICS COMMUNICATION INSTRUMENTATION
DC Motor – Transfer Function Without Load
constantmotor time/
constantgainmotor/
)1()(
)(
)(
/
)(
)(
,/If
system.theof
frictionviscoustheincreasesyeffectivelmotortheof
emfbackthat theindicates/termThe








DJ
DRKK
ss
K
sE
s
DsJs
RK
sE
s
RKKDD
RKKD
mm
atm
m
m
a
m
m
at
a
m
abtm
abtm



22 February 2015 18