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DC MOTOR DRIVES
(MEP 1523)
Dr. Nik Rumzi Nik Idris
Department of Energy Conversion
FKE, UTM
INTRODUCTION
• DC DRIVES: Electric drives that use DC motors as the prime
movers
• DC motor: industry workhorse for decades
• Dominates variable speed applications before PE converters were
introduced
• Will AC drive replaces DC drive ?
– Predicted 30 years ago
– DC strong presence – easy control – huge numbers
– AC will eventually replace DC – at a slow rate
Introduction
DC Motors
• Advantage: Precise torque and speed control without
sophisticated electronics
• Several limitations:
• Regular Maintenance
• Expensive
• Heavy
• Speed limitations
• Sparking
Introduction
DC Motors - 2 pole: permanent magnet excitation
Rotor
PM
Stator
Introduction
DC Motors - 2 pole: wound stator excitation
Rotor
Stator
Introduction
DC Motors - 2 pole
Armature reaction
Armature mmf produces
flux which distorts main
flux produce by field
X
X
X
X
X
• Mechanical commutator to maintain armature current direction
Introduction
Armature reaction
Flux at one side of the pole may saturate
Zero flux region shifted
Flux saturation, effective flux per pole decreases
• Armature mmf distorts field flux
 Large machine employs compensation windings and interpoles
Introduction
Armature reaction
Field flux
Armature flux
Resultant flux
Introduction
DC Motors
Introduction
Ra
+
Lf
La
ia
+
Rf
if
+
Vt
ea
Vf
_
_
_
di
v t  R a ia  L a  ea
dt
v f  R f if  L
Te  k t i a
Electric torque
ea  k E 
Armature back e.m.f.
di f
dt
Introduction
Armature circuit:
Vt  R a i a  L
di a
 ea
dt
In steady state,
Vt  R a Ia  Ea
Therefore steady state speed is given by,

Vt
R T
 a e2
k T  k T 
Three possible methods of speed control:
Field flux
Armature voltage Vt
Armature resistance Ra
Introduction

Vt
kT
Vt
R T
 a e2
k T  k T 
Varying Vt

TL
Vt ↓
Te
Requires variable DC supply
Introduction

Vt
R T
 a e2
k T  k T 
Varying Ra

Vt
kT
TL
Ra ↑
Te
Simple control
Losses in external resistor
Introduction


Vt
kT
Vt
R T
 a e2
k T  k T 
Varying 
TL
↓
Te
Not possible for PM motor
Maximum torque capability reduces
Introduction
Armature voltage control : retain maximum torque capability
Field flux control (i.e. flux reduced) : reduce maximum torque capability
For wide range of speed control
0 to base  armature voltage, above base  field flux reduction
Armature voltage control
Field flux control
Te
Maximum
Torque capability
base

Introduction
Te
Maximum
Torque capability
base

Introduction
P Te
Constant torque
Constant power
Pmax

base
0 to base  armature voltage,
P = EaIa,max = kaIa,max
above base  field flux reduction
Pmax = EaIa,max = kabaseIa,max
   1/
MODELING OF CONVERTERS
AND DC MOTOR
POWER ELECTRONICS CONVERTERS
Used to obtain variable armature voltage
• 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)
ia

+
3-phase
supply
Vt
Q2
Q1

Q3
Q4
T
Modeling of Converters and DC motor
Phase-controlled rectifier
3phase
supply
+
3-phase
supply
Vt


Q2
Q1
Q3
Q4
T
Modeling of Converters and DC motor
Phase-controlled rectifier
R1
F1
3-phase
supply
+
Va
F2
R2

Q2
Q1
Q3
Q4
-
T
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
• Firing circuit –firing angle control
 Establish relation between vc and Vt
+
iref
+
-
current
controller
vc
firing
circuit

controlled
rectifier Vt
–
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
• Firing angle control
linear firing angle control
vt
v
 c
180

Va 

vc
180
vt
v

2Vm
cos c 180 

 vt

Cosine-wave crossing control
v c  v s cos 
2Vm v c
Va 
 vs
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
•Steady state: linear gain amplifier
•Cosine wave–crossing method
•Transient: sampler with zero order hold
converter
T
GH(s)
T – 10 ms for 1-phase 50 Hz system
– 3.33 ms for 3-phase 50 Hz system
Modeling of Converters and DC motor
Phase-controlled rectifier (continuous current)
400
200
0
Output
voltage
-200
-400
0.3
0.31
0.32
0.33
0.34
0.35
0.36
Control
signal
Td
10
5
Cosine-wave
crossing
0
-5
-10
0.3
0.31
0.32
0.33
0.34
0.35
0.36
Td – Delay in average output voltage generation
0 – 10 ms for 50 Hz single phase system
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

T1
+
Vt
-
Q2
Q1
Q3
Q4
T
Modeling of Converters and DC motor
Switch–mode converters

T1
D1
T2
+
Vt
D2 -
Q2
Q1
Q3
Q4
Q1  T1 and D2
Q2  D1 and T2
T
Modeling of Converters and DC motor
Switch–mode converters

T1
T4
D1
D3
+ Vt -
D4
D2
T3
T2
Q2
Q1
Q3
Q4
T
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
−
vtri
q
vc
1
q
0
when vc > vtri, upper switch ON
when vc < vtri, lower switch ON
Modeling of Converters and DC motor
Switch–mode converters – averaged model
Ttri
vc
q
d
Vdc
Vt
1
d
Ttri

1
Vt 
Ttri
t  Ttri
t

dTtri
0
t on
qdt 
Ttri
Vdc dt  dV dc
Modeling of Converters and DC motor
Switch–mode converters – averaged model
d
1
0.5
0
vc
-Vtri,p
Vtri,p
d  0.5 
vc
2Vtri,p
Vt  0.5Vdc 
Vdc
vc
2Vtri,p
Modeling of Converters and DC motor
Switch–mode converters – small signal model
Vdc
Vt ( s) 
v c (s)
2Vtri ,p
2-quadrant converter
Vdc
Vt (s) 
v c (s)
Vtri ,p
4-quadrant converter
Modeling of Converters and DC motor
DC motor – separately excited or permanent magnet
v t  ia R a  L a
di a
 ea
dt
Te = kt ia
d m
Te  Tl  J
dt
e e = kt 
Extract the dc and ac components by introducing small
perturbations in Vt, ia, ea, Te, TL and m
ac components
~
d
i
~
~
v t  ia R a  L a a  ~
ea
dt
~
~
Te  k E ( ia )
dc components
Vt  Ia R a  Ea
Te  k E Ia
~
~)
ee  k E (
Ee  k E 
~)
d(
~
~
~
Te  TL  B  J
dt
Te  TL  B()
Modeling of Converters and DC motor
DC motor – small signal model
Perform Laplace Transformation on ac components
~
d
i
~
~
v t  ia R a  L a a  ~
ea
dt
Vt(s) = Ia(s)Ra + LasIa + Ea(s)
~
~
Te  k E ( ia )
Te(s) = kEIa(s)
~
~)
ee  k E (
Ea(s) = kE(s)
~)
d(
~
~
~
Te  TL  B  J
dt
Te(s) = TL(s) + B(s) + sJ(s)
Modeling of Converters and DC motor
DC motor – small signal model
Modeling of Converters and DC motor
DC motor – small signal model: Block diagram transformation
CLOSED-LOOP SPEED CONTROL
Cascade control structure
* +
position
controller
* +
speed
controller
T* +
-
-
-
torque
controller
converter
Motor
tacho
kT
1/s
•
The control variable of inner loop (e.g. torque) can be
limited by limiting its reference value
•
It is flexible – outer loop can be readily added or removed
depending on the control requirements
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)
•
BODE PLOTS
Zero steady state error – very large DC gain
METHOD
•
Obtain linear small signal model
•
Design controllers based on linear small signal model
•
Perform large signal simulation for controllers verification
CLOSED-LOOP SPEED CONTROL
Closed-loop speed control – an example
Permanent magnet motor’s parameters
Ra = 2 
La = 5.2 mH
B = 1 x10–4 kg.m2/sec
J = 152 x 10–6 kg.m2
ke = 0.1
V/(rad/s)
kt = 0.1
Nm/A
Vd = 60 V
Vtri = 5 V
fs = 33
kHz
• PI controllers
• Switching signals from comparison
of vc and triangular waveform
CLOSED-LOOP SPEED CONTROL
Torque controller design
vtri
q
Torque
controller
Tc
+
+
Vdc
–
−
q
kt
DC motor
Tl (s )
Converter
Te (s )
Torque
controller
+
-
Vdc
Vtri,pe ak
Ia (s )
1
R a  sL a
Va (s )
+
kT
-
Te (s )
+
-
kE
1
B  sJ
(s )
CLOSED-LOOP SPEED CONTROL
Torque controller design
Open-loop gain
Bode Diagram
From: Input Point To: Output Point
150
kpT= 90
Magnitude (dB)
100
compensated
kiT= 18000
50
0
-50
90
Phase (deg)
45
0
compensated
-45
-90
-2
10
-1
10
0
10
1
10
2
10
Frequency (rad/sec)
3
10
4
10
5
10
CLOSED-LOOP SPEED CONTROL
Speed controller design
Assume torque loop unity gain for speed bandwidth << Torque bandwidth
*
+
–
T*
Speed
controller
Torque loop
1
T
1
B  sJ

CLOSED-LOOP SPEED CONTROL
Speed controller
Open-loop gain
Bode Diagram
From: Input Point To: Output Point
150
Magnitude (dB)
100
kps= 0.2
50
compensated
0
-50
0
Phase (deg)
-45
-90
-135
compensated
-180
-2
10
-1
10
0
10
1
10
Frequency (Hz)
2
10
3
10
4
10
kis= 0.14
CLOSED-LOOP SPEED CONTROL
Large Signal Simulation results
40
20
Speed
0
-20
-40
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
2
1
Torque
0
-1
-2
CLOSED-LOOP SPEED CONTROL – DESIGN EXAMPLE
SUMMARY
Speed control by: armature voltage (0 b) and field flux (b)
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