Dc Motor Drives Fantastic

DC MOTOR DRIVES (MEP 1422)

Dr. Nik Rumzi Nik Idris Department 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 • 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 Stator: field windings

Rotor: armature windings

•Mechanical commutator

Current in

•Large machine employs compensation windings

Current out

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 φi a

Electric torque

e a = k E φω

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 + E a Therefore speed is given by,

Vt R a Te ω= − k T φ ( k T φ) 2 Three possible methods of speed control: Field flux Armature voltage Vt Armature resistance Ra

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 ωbase → armature voltage, above ωbase → field flux reduction Armature voltage control Field flux control

Te

Maximum Torque capability

ωbase

ω

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

ω

+ 3-phase supply

Vt −

Q2

Q1

Q3

Q4

T

Modeling of Converters and DC motor

Phase-controlled rectifier

3phase supply

+ 3-phase supply

Vt −

ω Q2

Q1

Q3

Q4

T

Modeling of Converters and DC motor

Phase-controlled rectifier R1

F1 3-phase supply +

Va

F2

R2

ω 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

+ -

curren t contro ller

vc

firing circu it

α

controll Vt ed rectifier –

Modeling of Converters and DC motor

Phase-controlled rectifier (continuous current) • Firing angle control

linear firing angle control

vt vc = 180 α Va =

α=

vc 180 vt

v  Vm cos c 180  π  vt 

Cosine-wave crossing control

v c = v s cos α Va =

Vm v c π 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

Td

0.34

0.35

0.36

10 5

Cosine-wave crossing

0 ­5 ­10 0.3

Control signal

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 ω

T1

+ Vt -

Q2

Q1

Q3

Q4

T

Modeling of Converters and DC motor

Switch–mode converters ω 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 ω 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

vc

q 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 = dVdc

Modeling of Converters and DC motor

Switch–mode converters – averaged model d 1 0.5 -Vtri,p

0 Vtri,p

d = 0.5 +

vc 2Vtri,p

Vt = 0.5Vdc +

Vdc vc 2Vtri,p

vc

Modeling of Converters and DC motor

DC motor – small signal model v t = ia R a + L a

di a + ea dt

Te = kt ia

dω m Te = Tl + J dt e e = kt ω

Extract the dc and ac components by introducing small perturbations in Vt, ia, ea, Te, TL and ωm ac components ~ d i ~ ~ v t = ia R a + L a a + ~ ea dt

~ ~ Te = k E ( ia )

dc components Vt = Ia R a + E a Te = k E Ia

~ ~) e e = k E (ω

Ee = k Eω

~) d(ω ~ ~ ~ Te = TL + Bω + J dt

Te = TL + B(ω)

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)

~ ~) e e = k E (ω

Ea(s) = kEω(s)

~) d(ω ~ ~ ~ Te = TL + Bω + J dt

Te(s) = TL(s) + Bω(s) + sJω(s)

Modeling of Converters and DC motor

DC motor – small signal model

Tl (s )

Va (s ) + -

1 R a + sL a

I a (s )

kT

-

Te (s )

1 B + sJ

+

kE

ω(s )

CLOSED-LOOP SPEED CONTROL Cascade control structure θ* +

position controller ω* +

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 Ω

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,peak

Ia (s ) 1 R a + sL a

Va (s )

+

-

kT

-

Te (s )

+

kE

1 B + sJ

ω(s )

CLOSED-LOOP SPEED CONTROL

Torque controller design Open-loop gain

Bode Diagram From: Input Point  To: Output Point

Magnitude (dB)

150

kpT= 90

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

ω* + –

T* Speed controller

Torque loop

1

T

1 B + sJ

ω

CLOSED-LOOP SPEED CONTROL

Speed controller Open-loop gain

Bode Diagram From: Input Point  To: Output Point

Magnitude (dB)

150 100

kps= 0.2

50

compensated

0

­50 0

Phase (deg)

­45 ­90 ­135 ­180

compensated ­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 →ωb) and field flux (ωb↑) 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