Ele Dc Motor Drives Fantastic

DC MOTOR DRIVES(MEP 1422)

Dr. Nik Rumzi Nik IdrisDepartment of Energy Conversion

FKE, UTM

Contents Introduction

Trends in DC drives DC motors

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

Current in

Current out

Stator: field windings

Rotor: armature windings

Introduction

DC Motors

Mechanical commutator

Large machine employs compensation windings

Introduction

at ikTe = Electric torque

= Ea ke Armature back e.m.f.

Lf Rf

if

aa

aat edtdi

LiRv ++=

+

ea

_

LaRa

ia+

Vt

_

+

Vf

_

dtdiLiRv ffff +=

Introduction

aaat EIRV +=In steady state,

( ) 2Tea

T

t

kTR

kV

=

Therefore speed is given by,

Three possible methods of speed control:

Field fluxArmature voltage VtArmature resistance Ra

aa

aat edtdi

LiRV ++=

Armature circuit:

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

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 (ACDC)

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

firingcircu

it

current

controller

controlled

rectifier

+

Vt

vciref +-

Modeling of Converters and DC motor

Phase-controlled rectifier (continuous current)

Firing angle control

pi= 180

vv

cosVVt

cma

=

ct v180v

180vv

t

c=

linear firing angle control

= cosvv sc

Cosine-wave crossing control

s

cma v

vVVpi

=

Modeling of Converters and DC motor

Phase-controlled rectifier (continuous current)

Steady state: linear gain amplifierCosine wavecrossing method

Modeling of Converters and DC motor

Transient: sampler with zero order hold

TGH(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 0.36400

200

0

200

400

0.3 0.31 0.32 0.33 0.34 0.35 0.3610

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

Switchmode converters

Q1Q2

Q3 Q4

T

+Vt-

T1

Modeling of Converters and DC motor

Switchmode converters

+Vt-

T1D1

T2

D2

Q1Q2

Q3 Q4

T

Q1 T1 and D2

Q2 D1 and T2

Modeling of Converters and DC motor

Switchmode converters

Q1Q2

Q3 Q4

T+ Vt -

T1 D1

T2D2

D3

D4

T3

T4

Modeling of Converters and DC motor

Switchmode converters

Switching at high frequency

Reduces current ripple

Increases control bandwidth

Suitable for high performance applications

Modeling of Converters and DC motor

Switchmode converters - modeling

+

Vdc

Vdc

vc

vtri

q

=

01

qwhen vc > vtri, upper switch ON

when vc < vtri, lower switch ON

Modeling of Converters and DC motor

tri

onTt

ttri Tt

dtqT1d

tri

== +vc

q

Ttri

d

Switchmode converters averaged modelModeling of Converters and DC motor

dc

dT

0dc

trit dVdtVT

1Vtri

== Vdc Vt

Vtri,p-Vtri,pvc

d

1

0

0.5

p,tri

c

V2v

5.0d +=

cp,tri

dcdct vV2

VV5.0V +=

Switchmode converters averaged modelModeling of Converters and DC motor

DC motor small signal model

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

dtdJTT mle

+=

aa

aaat e~dti~d

LRi~v~ ++=

)i~(kT~ aEe =

)~(ke~ Ee =

dt)~(dJ~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~d

LRi~v~ ++=

)i~(kT~ aEe =

)~(ke~ Ee =

dt)~(dJ~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(TesJB

1+

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 modelMETHOD

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 106 kg.m2B = 1 x104 kg.m2/sec

kt = 0.1 Nm/Ake = 0.1 V/(rad/s)

Vd = 60 V Vtri = 5 V

fs = 33 kHz

Permanent magnet motors 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(TesJB

1+

Ek

)s(Ia )s()s(Va+

-

-

+Torquecontroller

Converter

peak,tri

dc

VV)s(Te

-+

DC motor

BodeDiagram

Frequency(rad/sec)

50

0

50

100

150From:InputPointTo:OutputPoint

Mag

nitud

e(dB)

102

101

100

101

102

103

104

105

90

45

0

45

90

Phas

e(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

BodeDiagram

Frequency(Hz)

50

0

50

100

150From:InputPointTo:OutputPoint

Mag

nitud

e(dB)

102

101

100

101

102

103

104

180

135

90

45

0

Phas

e(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 0.4540

20

0

20

40

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.452

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)