EEEB443 Control - PowerPoint PPT Presentation

Loading...

PPT – EEEB443 Control PowerPoint presentation | free to download - id: 43c1bc-Y2YzM



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

EEEB443 Control

Description:

Induction Motor Direct Torque Control By Dr. Ungku Anisa Ungku Amirulddin Department of Electrical Power Engineering College of Engineering Dr. Ungku Anisa, July 2008 – PowerPoint PPT presentation

Number of Views:703
Avg rating:3.0/5.0
Slides: 43
Provided by: itms6
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: EEEB443 Control


1
EEEB443 Control Drives
  • Induction Motor Direct Torque Control
  • By
  • Dr. Ungku Anisa Ungku Amirulddin
  • Department of Electrical Power Engineering
  • College of Engineering

2
Outline
  • Introduction
  • Switching Control
  • Space Vector Pulse Width Modulation (PWM)
  • Principles of Direct Torque Control (DTC)
  • Direct Torque Control (DTC) Rules
  • Direct Torque Control (DTC) Implementation
  • References

3
Introduction
  • High performance Induction Motor drives consists
    of
  • Field Orientation Control (FOC)
  • Direct Torque Control (DTC)
  • Direct Torque Control is IM control achieved
    through direct selection of consecutive inverter
    states
  • This requires understanding the concepts of
  • Switching control (Bang-bang or Hysteresis
    control)
  • Space Vector PWM for Voltage Source Inverters
    (VSI)

4
Switching Control
  • A subset of sliding mode control
  • Advantages
  • Robust since knowledge of plant G(s) is not
    necessary
  • Very good transient performance (maximum
    actuation even for small errors)
  • Disadvantage Noisy, unless switching frequency
    is very high
  • Feeding bang-bang (PWM) signal into a linear
    amplifier is not advisable. But it is OK if the
    amplifier contains switches (eg. inverters)

5
Switching Control
Continuous Control
Switching Control
6
PWM Voltage Source Inverter single phase
  • Reference current compared with actual current
  • Current error is fed to a PI controller
  • Output of PI controller (vc) compared with
    triangular waveform (vtri) to determine duty
    ratio of switches

Pulse width modulator
PI Controller
iref
7
Sinusoidal PWM Voltage Source Inverter
  • Same concept is extended to three-phase VSI
  • va, vb and vc are the
  • outputs from closed-loop
  • current controllers
  • In each leg, only 1 switch is on
  • at a certain time
  • Leads to 3 switching variables

Sa
Sb
Sc
8
Sinusoidal PWM Voltage Source Inverter
S1
S3
S5
S2
S4
S6
Switching signals for the SPWM VSI
va
Pulse Width Modulation
vb
S1, S2, .S6
vc
9
Sinusoidal PWM Voltage Source Inverter
  • Three switching variables are Sa, Sb and Sc
    (i.e. one per phase)
  • One switch is on in each inverter leg at a time
  • If both on at same time dc supply will be
    shorted
  • If both off at same time - voltage at output is
    undetermined
  • Each inverter leg can assume two states only,
    eg
  • Sa 1 if S1 ON and S4 OFF
  • Sa 0 if S1 OFF and S4 ON
  • Total number of states 8
  • An inverter state is denoted as SaSbSc2, eg
  • If Sa 1, Sb 0 and Sc 1, inverter is in
    State 5 since 1012 5

10
Space Vector PWM
  • Space vector representation of a three-phase
    quantities xa(t), xb(t) and xc(t) with space
    distribution of 120o apart is given by
  • where
  • a ej2?/3 cos(2?/3) jsin(2?/3)
  • a2 ej4?/3 cos(4?/3) jsin(4?/3)
  • x can be a voltage, current or flux and does
    not necessarily has to be sinusoidal

(1)
11
Space Vector PWM
  • Space vector of the three-phase stator voltage
    is
  • where va, vb and vc are the phase voltages.
  • If va, vb and vc are balanced 3-phase sinusoidal
    voltage with frequency f, then the locus of ?vs
  • circular with radius equal to the peak amplitude
    of the phase voltage
  • rotates with a speed of 2?f

(2)
12
Space Vector PWM
These voltages will be the voltages applied to
the terminals of the induction motor
S1
S3
S5
S2
S4
S6
We want va, vb and vc to follow va, vb and vc
S1, S2, .S6
13
Space Vector PWM
  • From the inverter circuit diagram
  • van vaN vNn
  • vbn vbN vNn
  • vcn vcN vNn
  • vaN VdcSa , vbN VdcSb , vcN VdcSc
  • where Sa, Sb, Sc 1 or 0 and Vdc dc link
    voltage
  • Substituting (3) (6) into (2)

(3)
(4)
(5)
(6)
(7)
14
Space Vector PWM
  • Stator voltage space vector can also be
    expressed in two-phase (dsqs frame).
  • Hence for each of the 8 inverter states, a space
    vector relative to the ds axis is produced.

(8)
15
Space Vector PWM
  • Example For State 6, i.e. 1102 (Sa 1, Sb
    1 and Sc 0)

qs
?vs
ds
16
Space Vector PWM
  • Therefore, the voltage vectors for all the 8
    inverter states can be obtained.
  • Note for states 000 and 111, voltage vector
    is equal to zero.

qs
010 V3
Voltage Vector Inverter state SaSbSc2
V0 State 0 000 2
V1 State 4 100 2
V2 State 6 110 2
V3 State 2 010 2
V4 State 3 011 2
V5 State 1 001 2
V6 State 5 101 2
V7 State 7 111 2
110 V2
000 V0 0 111 V7 0
100 V1
011 V4
ds
001 V5
101 V6
17
Space Vector PWM
  • The dsqs plane can be divided into six 60?-wide
    sectors, i.e. S1 to S6 as shown below(? 30? from
    each voltage vectors)

S2
S3
qs
110 V2
010 V3
000 V0 0 111 V7 0
100 V1
S4
011 V4
S1
ds
001 V5
101 V6
S5
S6
18
Space Vector PWM
  • Definition of Space Vector Pulse Width Modulation
    (PWM)
  • modulation technique which exploits space
    vectors to synthesize the command or reference
    voltage vs within a sampling period
  • Reference voltage vs is synthesized by selecting
    2 adjacent voltage vectors and zero voltage
    vectors

19
Space Vector PWM
  • In general
  • Within a sampling period T, to synthesize
    reference voltage vs, it is assembled from
  • vector Vx (to the right)
  • vector Vy (to the left) and
  • a zero vector Vz (either V0 or V7)
  • Since T is sampling
  • period of vs
  • Vx is applied for time Tx
  • Vy is applied for time Ty
  • Vz is applied for the rest
  • of the time, Tz

qs
vy
010 V3
110 V2
vs
vx
011 V4
?
ds
100 V1
Note 000 V0 0 111 V7 0
001 V5
101 V6
20
Space Vector PWM
  • In general
  • Total sampling time
  • If ? close to 0? Tx gt Ty
  • If ? close to 60? Tx lt Ty
  • If vs is large more time
  • spent at Vx, Vy compared
  • to Vz i.e. Tx Ty gt Tz
  • If vs is small more time
  • spent at Vz compared
  • to Vx, Vy , i.e. . Tx Ty lt Tz

T Tx Ty Tz
(9)
qs
vy
010 V3
110 V2
vs
011 V4
?
vx
ds
100 V1
Note 000 V0 0 111 V7 0
001 V5
101 V6
21
Space Vector PWM
Vector Vx to the right of vs
  • In general, if ? is the angle between the
    reference voltage vs and Vx (vector to its
    right), then
  • where

qs
vs
110 V2
010 V3
?
(10)
100 V1
011 V4
ds
(11)
Note 000 V0 0 111 V7 0
001 V5
101 V6
Tz T ? Tx? Ty
(12)
22
Space Vector PWM
Example vs is in sector S1
qs
010 V3
vy
110 V2
vs
  • Vx V1 is applied for time Tx
  • Vy V2 is applied for time Ty
  • Vz is applied for rest
  • of the time, Tz

?
vx
100 V1
ds
011 V4
Note 000 V0 0 111 V7 0
001 V5
101 V6
23
Space Vector PWM
  • Example vs in sector S1
  • Reference voltage vs is sampled at regular
    intervals T, i.e. T is sampling period
  • V1 1002 is applied for Tx
  • V2 1102 is applied for Ty
  • Zero voltage V0 0002 and V7 1112 is applied
    for the rest of the time, i.e. Tz

T Tx Ty Tz
V7
V2
V1
V0
24
Space Vector PWM
Example A Space Vector PWM VSI, having a DC
supply of 430 V and a switching frequency of
2kHz, is required to synthesize voltage vs
240?170 ? V. Calculate the time Tx, Ty and Tz
required.
  • Since ? ______,
  • vs is in sector _______

qs
010 V3
110 V2
S2
  • Vx ____ is applied for time Tx

S3
100 V1
S1
011 V4
S4
ds
  • Vy ___ is applied for time Ty

Note 000 V0 0 111 V7 0
S6
S5
  • Vz is applied for time Tz

001 V5
101 V6
Tz T ? Tx? Ty
25
Space Vector Equations of IM
  • The two-phase dynamic model of IM in the
    stationary dsqs frame

(13)
(14)
(15)
(16)
26
Direct Torque Control (DTC) Basic Principles
  • Derivative of stator flux is equal to the
    stator EMF. Therefore, stator flux magnitude
    strongly depends on stator voltage.
  • If voltage drop across Rs ignored, change in
    stator flux can be obtained from stator voltage
    applied
  • Stator voltage can be changed using
  • the space vectors of the
  • Voltage Source Inverter (VSI).

(17)
(18)
27
Direct Torque Control (DTC) Basic Principles
  • Developed torque is proportional to the sine of
    angle between stator and rotor flux vectors ?sr.
  • Angle of??s is also dependant on stator voltage.
    Hence, Te can also be controlled using the stator
    voltage through ?sr.

(19)
(20)
28
Direct Torque Control (DTC) Basic Principles
  • Reactions of rotor flux to changes in stator
    voltage is slower than that of stator flux.
  • Assume ??r remains constant within short time ?t
    that stator voltage is changed.
  • Summary DTC Basic Principles
  • Magnitude of stator flux and torque directly
    controlled by proper selection of stator voltage
    space vector (i.e. through selection of
    consecutive VSI states)

29
Direct Torque Control (DTC) Basic Principles
(example)
  • Assuming at time t,
  • Initial stator and rotor flux are denoted as
    ??s(t) and ??r
  • the VSI switches to state 100 ? stator voltage
    vector V1 generated
  • After short time interval ?t,
  • New stator flux vector ??s(t ?t) differs from
    ??s(t) in terms of
  • Magnitude (increased by ??sV1(?t))
  • Position (reduced by ??sr)
  • Assumption Negligible change in rotor flux
    vector ??r within ?t
  • Stator flux and torque changed by voltage

qs
ds
30
Direct Torque Control (DTC) Rules for Flux
Control
  • To increase flux magnitude
  • select non-zero voltage vectors with misalignment
    with ??s(t) not exceeding ? 90?
  • To decrease flux magnitude
  • select non-zero voltage vectors with misalignment
    with ??s(t) that exceeds ? 90?
  • V0 and V7 (zero states) do not affect ??s(t) ,
    i.e. stator flux stops moving

qs
ds
31
Direct Torque Control (DTC) Rules for Torque
Control
  • To increase torque
  • select non-zero voltage vectors which
    accelerates??s(t)
  • To decrease torque
  • select non-zero voltage vectors which
    decelerates??s(t)
  • To maintain torque
  • select V0 or V7 (zero states) which causes
    ??s(t) to stop moving

qs
ds
32
Direct Torque Control (DTC) Rules for Flux and
Torque Control
  • The dsqs plane can be divided into six 60?-wide
    sectors (S1 to S6)
  • If??s is in sector Sk
  • k1 voltage vector (Vk1) increases ??s
  • k2 voltage vector (Vk2) decreases ??s
  • Example here??s is in sector 2 (S2)
  • V3 increases ??s
  • V4 decreases ??s

S2
S3
qs
110 V2
010 V3
100 V1
011 V4
ds
S1
S4
001 V5
101 V6
S5
S6
Note 000 V0 0 111 V7 0
33
Direct Torque Control (DTC) Rules for Flux and
Torque Control
  • Stator flux vector ??s is associated with a
    voltage vector VK when it passes through sector K
    (SK)
  • Impact of all individual voltage vectors on ??s
    and Te is summarized in table below
  • Impact of VK and VK3 on Te is ambiguous, it
    depends on whether ??s leading or lagging the
    voltage vector
  • Zero vector Vz (i.e. V0 or V7) doesnt affect ??s
    but reduces Te

VK VK1 VK2 VK3 VK4 VK5 Vz (V0 or V7)
??s ?? ? ? ?? ? ? -
Te ? ? ? ? ? ? ?
34
Direct Torque Control (DTC) Implementation
  • DC voltage Vdc and three phase stator currents
    iabcs are measured
  • vsdqs and current isdqs are determined in Voltage
    and Current Vector Synthesizer by the following
    equations
  • where Sa, Sb ,Sc switching variables of VSI
    and

(21)
(22)
35
Direct Torque Control (DTC) Implementation
  • Flux vector ??s and torque Te are calculated in
    the Torque and Flux Calculator using the
    following equations

(23)
(24)
(25)
(26)
36
Direct Torque Control (DTC) Implementation
  • Magnitude of ??s is compared with ??s in the
    flux control loop.
  • Te is compared with Te in the torque control
    loop.
  • The flux and torque errors, ???s and ?Te are fed
    to respective bang-bang controllers, with
    characteristics shown below.

Note ??s???s ?Tm ?Te b? b?
37
Direct Torque Control (DTC) Implementation
  • Selection of voltage vector (i.e. inverter
    state) is based on
  • values of b? and bT (i.e. output of the flux and
    torque bang-bang controllers )
  • angle of flux vector ?s
  • direction of motor rotation (clockwise or counter
    clockwise)
  • Specifics of voltage vector selection are
    provided based on Tables in Slide 37
    (counterclockwise rotation) and Slide 38
    (clockwise rotation) and applied in the State
    Selector block.

(27)
38
Direct Torque Control (DTC) Implementation
  • Selection of voltage vector in DTC scheme
  • Counterclockwise Rotation

b? 1 1 1 0 0 0
bT 1 0 -1 1 0 -1
S1 V2 V7 V6 V3 V0 V5
S2 V3 V0 V1 V4 V7 V6
S3 V4 V7 V2 V5 V0 V1
S4 V5 V0 V3 V6 V7 V2
S5 V6 V7 V4 V1 V0 V3
S6 V1 V0 V5 V2 V7 V4
  • To minimize
  • number of
  • switching
  • V0 always
  • follows V1, V3
  • and V5
  • V7 always
  • follows V2, V4
  • and V6

39
Direct Torque Control (DTC) Implementation
  • Selection of voltage vector in DTC scheme
  • Clockwise Rotation

b? 1 1 1 0 0 0
bT 1 0 -1 1 0 -1
S1 V6 V7 V2 V5 V0 V3
S2 V5 V0 V1 V4 V7 V2
S3 V4 V7 V6 V3 V0 V1
S4 V3 V0 V5 V2 V7 V6
S5 V2 V7 V4 Vv1 V0 V5
S6 V1 V0 V3 V6 V7 V4
  • To minimize
  • number of
  • switching
  • V0 always
  • follows V1, V3
  • and V5
  • V7 always
  • follows V2, V4
  • and V6

40
Direct Torque Control (DTC) Implementation
(Example)
qs
  • ??s is in sector S2 (assuming counterclockwise
    rotation)
  • Both flux and torque to be increased (b? 1 and
    bT 1) apply V3 (State 010)
  • Flux decreased and torque increased (b? 0 and
    bT 1) apply V4 (State 011)

ds
b? 1 1 1 0 0 0
bT 1 0 -1 1 0 -1
S2 V3 V0 V1 V4 V7 V6
41
Direct Torque Control (DTC) Implementation
Note ?s??s Tm Te b? b? a Sa b Sb c Sc
vi Vdc vs vsdqs iis isdqs ?ds?sds ?qs ?sqs
Eq. (25)
42
References
  • Trzynadlowski, A. M., Control of Induction
    Motors, Academic Press, San Diego, 2001.
  • Asher, G.M, Vector Control of Induction Motor
    Course Notes, University of Nottingham, UK, 2002.
About PowerShow.com