DC MOTOR DRIVES (MEP 1523)

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

• 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: permanent magnet excitation

Stator

Rotor

PM

Introduction

DC Motors - 2 pole: wound stator excitation

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

Armature reaction

Field flux Armature flux Resultant flux

Introduction

DC Motors

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

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


Phase-controlled rectifier

Q1Q2

Q3 Q4

T

F1

F2

R1

R2+ Va -

3-phasesupply


Phase-controlled rectifier (continuous current)

• Firing circuit –firing angle control

Establish relation between vc and Vt

firingcircuit

currentcontroller

controlled rectifier

+

Vt

–

vciref+

-



• 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



•Steady state: linear gain amplifier•Cosine wave–crossing method


•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


Td

Td – Delay in average output voltage generation 0 – 10 ms for 50 Hz single phase system

Outputvoltage

Cosine-wave crossing

Control signal



• 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


Switch–mode converters

Q1Q2

Q3 Q4

T

+Vt

-

T1



+Vt

-

T1D1

T2

D2

Q1Q2

Q3 Q4

T

Q1 T1 and D2

Q2 D1 and T2



Q1Q2

Q3 Q4

T+ Vt -

T1D1

T2D2

D3

D4

T3

T4



• Switching at high frequency

Reduces current ripple

Increases control bandwidth

• Suitable for high performance applications


Switch–mode converters - modeling

+

Vdc

−

Vdc

vc

vtri

q

0

1q

when vc > vtri, upper switch ON

when vc < vtri, lower switch ON


tri

onTt

ttri Tt

dtqT1

dtri

vc

q

Ttri

d

Switch–mode converters – averaged model


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


Switch–mode converters – small signal model


)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


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


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


DC motor – small signal model: Block diagram transformation


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


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 – 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


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


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)


Torque controller design Open-loop gain

compensated

compensated

kpT= 90

kiT= 18000


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)


Speed controllerOpen-loop gain

compensated

kps= 0.2

kis= 0.14

compensated


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)

Documents

DC MOTOR DRIVES (MEP 1523)