DC MOTOR DRIVES (MEP 1422)
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Transcript of DC MOTOR DRIVES (MEP 1422)
DC MOTOR DRIVES(MEP 1422)
Dr. Nik Rumzi Nik Idris
Department of Energy Conversion
FKE, UTM
Contents• Introduction
– Trends in DC drives– Principles of DC motor drives
• Modeling of Converters and DC motor– Phase-controlled Rectifier– DC-DC converter (Switch-mode)– Modeling of DC motor
• Closed-loop speed control– Cascade Control Structure– Closed-loop speed control - an example
• Torque loop• Speed loop
• Summary
INTRODUCTION
• DC DRIVES: Electric drives that use DC motors as the prime movers
• Dominates variable speed applications before PE converters were introduced
• DC motor: industry workhorse for decades
• Will AC drive replaces DC drive ?
– Predicted 30 years ago
– AC will eventually replace DC – at a slow rate
– DC strong presence – easy control – huge numbers
Introduction
DC Motors
• Several limitations:
• Advantage: Precise torque and speed control without sophisticated electronics
• Regular Maintenance • Expensive
• Heavy • Speed limitations
• Sparking
Introduction
DC Motors - 2 pole
Stator
Rotor
Introduction
DC Motors - 2 pole
• Mechanical commutator to maintain armature current direction
X
X
X
X
X
Armature mmf produces flux which distorts main flux produce by field
Armature reaction
Introduction
Flux at one side of the pole may saturate
Zero flux region shifted
Flux saturation, effective flux per pole decreases
Large machine employs compensation windings and interpoles
• Armature mmf distorts field flux
Armature reaction
Introduction
at ikTe Electric torque
Ea ke Armature back e.m.f.
Lf Rf
if
aa
aat edtdi
LiRv
+
ea
_
LaRa
ia+
Vt
_
+
Vf
_
dtdi
LiRv ffff
Introduction
aaat EIRV In steady state,
2T
ea
T
t
k
TRkV
Therefore steady state speed is given by,
Three possible methods of speed control:
Field fluxArmature voltage Vt
Armature resistance Ra
aa
aat edtdi
LiRV
Armature circuit:
Introduction
2T
ea
T
t
k
TRkV
Te
TLT
t
kV
Vt ↓
Varying Vt
Requires variable DC supply
Introduction
2T
ea
T
t
k
TRkV
Te
TLT
t
kV
Vt ↓
Varying Vt
Requires variable DC supply
Te
Varying Vt
Requires variable DC supply
TL
T
eaTt k
TR)k(V
Introduction
Constant TL
Vt
Introduction
aaTt RI)k(V
aaRI
rated,tV
base
Varying Vt
Constant TL
T
eaTt k
TR)k(V
Introduction
2T
ea
T
t
k
TRkV
Te
Ra ↑
TL
T
t
kV
Varying Ra
Simple controlLosses in external resistor
Introduction
2T
ea
T
t
k
TRkV
Te
TL
T
t
kV
Varying
↓
Not possible for PM motorMaximum torque capability reduces
Introduction
For wide range of speed control 0 to base armature voltage, above base field flux reduction
Armature voltage control : retain maximum torque capability
Field flux control (i.e. flux reduced) : reduce maximum torque capability
Te
MaximumTorque capability
Armature voltage controlField flux control
base
Introduction
Te
MaximumTorque capability
base
Introduction
Te
Constant powerConstant torque
base
0 to base armature voltage, above base field flux reduction
P = EaIa,max = kaIa,max
Pmax
Pmax = EaIa,max = kabaseIa,max
1/
P
MODELING OF CONVERTERS AND DC MOTOR
Used to obtain variable armature voltage
POWER ELECTRONICS CONVERTERS
• Efficient Ideal : lossless
• Phase-controlled rectifiers (AC DC)
• DC-DC switch-mode converters(DC DC)
Modeling of Converters and DC motor
Phase-controlled rectifier (AC–DC)
T
Q1Q2
Q3 Q4
3-phasesupply
+
Vt
ia
Phase-controlled rectifier
Q1Q2
Q3 Q4
T
3-phasesupply
3-phasesupply
+
Vt
Modeling of Converters and DC motor
Phase-controlled rectifier
Q1Q2
Q3 Q4
T
F1
F2
R1
R2+ Va -
3-phasesupply
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
• Firing circuit –firing angle control
Establish relation between vc and Vt
firingcircuit
currentcontroller
controlled rectifier
+
Vt
–
vciref+
-
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
• Firing angle control
180vv
cosV2
Vt
cma
ct v
180v
180vv
t
c
linear firing angle control
cosvv sc
Cosine-wave crossing control
s
cma v
vV2V
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
•Steady state: linear gain amplifier•Cosine wave–crossing method
Modeling of Converters and DC motor
•Transient: sampler with zero order hold
T
GH(s)
converter
T – 10 ms for 1-phase 50 Hz system – 3.33 ms for 3-phase 50 Hz system
0.3 0.31 0.32 0.33 0.34 0.35 0.36-400
-200
0
200
400
0.3 0.31 0.32 0.33 0.34 0.35 0.36-10
-5
0
5
10
Phase-controlled rectifier (continuous current)
Td
Td – Delay in average output voltage generation 0 – 10 ms for 50 Hz single phase system
Outputvoltage
Cosine-wave crossing
Control signal
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
• Model simplified to linear gain if bandwidth (e.g. current loop) much lower than sampling frequency
Low bandwidth – limited applications
• Low frequency voltage ripple high current ripple undesirable
Modeling of Converters and DC motor
Switch–mode converters
Q1Q2
Q3 Q4
T
+Vt
-
T1
Modeling of Converters and DC motor
Switch–mode converters
+Vt
-
T1D1
T2
D2
Q1Q2
Q3 Q4
T
Q1 T1 and D2
Q2 D1 and T2
Modeling of Converters and DC motor
Switch–mode converters
Q1Q2
Q3 Q4
T+ Vt -
T1D1
T2D2
D3
D4
T3
T4
Modeling of Converters and DC motor
Switch–mode converters
• Switching at high frequency
Reduces current ripple
Increases control bandwidth
• Suitable for high performance applications
Modeling of Converters and DC motor
Switch–mode converters - modeling
+
Vdc
−
Vdc
vc
vtri
q
0
1q
when vc > vtri, upper switch ON
when vc < vtri, lower switch ON
Modeling of Converters and DC motor
tri
onTt
ttri Tt
dtqT1
dtri
vc
q
Ttri
d
Switch–mode converters – averaged model
Modeling of Converters and DC motor
dc
dT
0dc
trit dVdtV
T1
Vtri
Vdc Vt
Vtri,p-Vtri,pvc
d
1
0
0.5
p,tri
c
V2v
5.0d
cp,tri
dcdct v
V2V
V5.0V
Switch–mode converters – averaged model
Modeling of Converters and DC motor
Switch–mode converters – small signal model
Modeling of Converters and DC motor
)s(vV2V
)s(V cp,tri
dct
)s(vVV
)s(V cp,tri
dct
2-quadrant converter
4-quadrant converter
DC motor – separately excited or permanent magnet
Modeling of Converters and DC motor
Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and m
aa
aaat edtdi
LRiv
Te = kt ia ee = kt
dtd
JTT mle
aa
aaat e~dti~
dLRi
~v~
)i~(kT
~aEe
)~(ke~ Ee
dt)~(d
J~BT~
T~
Le
ac components
aaat ERIV
aEe IkT
Ee kE
)(BTT Le
dc components
DC motor – small signal model
Modeling of Converters and DC motor
Perform Laplace Transformation on ac components
aa
aaat e~dti~
dLRi
~v~
)i~(kT
~aEe
)~(ke~ Ee
dt)~(d
J~BT~
T~
Le
Vt(s) = Ia(s)Ra + LasIa + Ea(s)
Te(s) = kEIa(s)
Ea(s) = kE(s)
Te(s) = TL(s) + B(s) + sJ(s)
DC motor – small signal model
Modeling of Converters and DC motor
Tkaa sLR
1
)s(Tl
)s(Te
sJB1
Ek
)s(Ia )s()s(Va
+-
-
+
CLOSED-LOOP SPEED CONTROL
Cascade control structure
• It is flexible – outer loop can be readily added or removed depending on the control requirements
• The control variable of inner loop (e.g. torque) can be limited by limiting its reference value
1/s
convertertorquecontroller
speedcontroller
positioncontroller
+
-
+
-
+
-
tacho
Motor* T**
kT
CLOSED-LOOP SPEED CONTROL
Design procedure in cascade control structure
• Inner loop (current or torque loop) the fastest – largest bandwidth
• The outer most loop (position loop) the slowest – smallest bandwidth
• Design starts from torque loop proceed towards outer loops
CLOSED-LOOP SPEED CONTROL
Closed-loop speed control – an example
OBJECTIVES:
• Fast response – large bandwidth
• Minimum overshoot good phase margin (>65o)
• Zero steady state error – very large DC gain
BODE PLOTS
• Obtain linear small signal model
METHOD
• Design controllers based on linear small signal model
• Perform large signal simulation for controllers verification
CLOSED-LOOP SPEED CONTROL
Ra = 2 La = 5.2 mH
J = 152 x 10–6 kg.m2B = 1 x10–4 kg.m2/sec
kt = 0.1 Nm/Ake = 0.1 V/(rad/s)
Vd = 60 V Vtri = 5 V
fs = 33 kHz
Permanent magnet motor’s parameters
Closed-loop speed control – an example
• PI controllers • Switching signals from comparison of vc and triangular waveform
CLOSED-LOOP SPEED CONTROL
Torque controller design
Tc
vtri
+
Vdc
−
q
q
+
–
kt
Torque controller
Tkaa sLR
1
)s(Tl
)s(Te
sJB1
Ek
)s(Ia )s()s(Va
+-
-
+
Torquecontroller
Converter
peak,tri
dc
VV)s(Te
-+
DC motor
Bode Diagram
Frequency (rad/sec)
-50
0
50
100
150From: Input Point To: Output Point
Mag
nitu
de (
dB)
10-2
10-1
100
101
102
103
104
105
-90
-45
0
45
90
Pha
se (
deg)
CLOSED-LOOP SPEED CONTROL
Torque controller design Open-loop gain
compensated
compensated
kpT= 90
kiT= 18000
CLOSED-LOOP SPEED CONTROL
Speed controller design
Assume torque loop unity gain for speed bandwidth << Torque bandwidth
1Speedcontroller sJB
1
* T* T
–
+
Torque loop
Bode Diagram
Frequency (Hz)
-50
0
50
100
150From: Input Point To: Output Point
Mag
nitu
de (
dB)
10-2
10-1
100
101
102
103
104
-180
-135
-90
-45
0
Pha
se (
deg)
CLOSED-LOOP SPEED CONTROL
Speed controllerOpen-loop gain
compensated
kps= 0.2
kis= 0.14
compensated
CLOSED-LOOP SPEED CONTROL
Large Signal Simulation results
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-40
-20
0
20
40
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45-2
-1
0
1
2
Speed
Torque
CLOSED-LOOP SPEED CONTROL – DESIGN EXAMPLE
SUMMARY
Power electronics converters – to obtain variable armature voltage
Phase controlled rectifier – small bandwidth – large ripple
Switch-mode DC-DC converter – large bandwidth – small ripple
Controller design based on linear small signal model
Power converters - averaged model
DC motor – separately excited or permanent magnet
Closed-loop speed control design based on Bode plots
Verify with large signal simulation
Speed control by: armature voltage (0 b) and field flux (b)