1. EEEB443 Control & Drives Induction Motor – Direct Torque Control By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

5. Switching Control Continuous Control Switching Control Amplifier Plant
G(s) PI
Continuous
Controller
Limiter
Switching Control
Amplifier
Plant
G(s)
Switching
Controller

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
vtri
Vdc q vc
Pulse width
modulator
PI Controller
iref
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
Pulse width
modulator
Va* Sa
Pulse width
modulator
Vb*
Pulse width
modulator
Vc* Sb Sc
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

8. Sinusoidal PWM Voltage Source Inverter
+ vc -
+ vb -
+ va - n N
Vdc a b c S1 S3 S5 S4 S6 S2
Switching signals
for the
SPWM VSI
va*
vb*
Pulse Width Modulation
S1, S2, ….S6
vc*
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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 [SaSbSc]2, eg:
If Sa = 1, Sb = 0 and Sc = 1, inverter is in State 5 since [101]2 = 5
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

12. will be the voltages applied to the terminals of the induction motor
Space Vector PWM
These voltages
will be the voltages applied to the terminals of the induction motor
+ vc -
+ vb -
+ va - n N
Vdc a b c S1 S3 S5 S4 S6 S2
We want va, vb and vc to follow va*, vb* and vc*
va*
vb*
vc*
S1, S2, ….S6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

15. Space Vector PWM
Example: For State 6, i.e. [110]2 (Sa = 1, Sb = 1 and Sc = 0) qs
vs ds
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

16. Inverter state [SaSbSc]2
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
(1/3)Vdc
Voltage Vector
Inverter state [SaSbSc]2 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
[010] V3
[110] V2
[000] V0 = 0
[111] V7 = 0
[011] V4
[100] V1
(2/3)Vdc ds
[001] V5
[101] V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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 S4
[011] V4
[100] V1 S1 ds
[001] V5
[101] V6 S5 S6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

19. Space Vector PWM = vy = vx 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*
[011] V4 
= vx
[100] V1 ds
Note:
[000] V0 = 0
[111] V7 = 0
[001] V5
[101] V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

20. Space Vector PWM In general: Total sampling time:
If  close to 0 : Tx > Ty
If  close to 60 : Tx < Ty
If vs* is large: more time
spent at Vx, Vy compared
to Vz i.e. Tx + Ty > Tz
If vs* is small: more time
spent at Vz compared
to Vx, Vy , i.e. . Tx + Ty < Tz
T= Tx + Ty + Tz
(9) qs
[010] V3
= vy
[110] V2
vs*
[011] V4 
[100] V1
= vx ds
Note:
[000] V0 = 0
[111] V7 = 0
[001] V5
[101] V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

21. Space Vector PWM Tz = T  Tx Ty Vector Vx to the right of vs*
In general, if  is the angle between the reference voltage vs* and Vx (vector to it’s right), then:
where qs
[010] V3
vs*
[110] V2 
(10)
[100] V1
[011] V4 ds
(11)
Note:
[000] V0 = 0
[111] V7 = 0
[001] V5
[101] V6
Tz = T  Tx Ty
(12)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

22. Space Vector PWM Example: vs* is in sector S1 = vy vs*qs
[010] V3
= vy
[110] V2
Vx = V1 is applied for time Tx
vs*
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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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 [100]2 is applied for Tx
V2 [110]2 is applied for Ty
Zero voltage V0 [000]2 and V7 [111]2 is applied for the rest of the time, i.e. Tz
Vref is sampled
T= Tx + Ty + Tz
Tz/2 V0 V1 Tx V2 Ty
Tz/2 V7 V7 V2 V1 V0 va vb vc T T
Vref is sampled
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

24. Space Vector PWM Since  = ______, Vx = ____ is applied for time Tx
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
Vx = ____ is applied for time Tx S3 S2
[011] V4 S1
[100] V1 S4 ds
Vy = ___ is applied for time Ty
Note:
[000] V0 = 0
[111] V7 = 0 S5 S6
Vz is applied for time Tz
[001] V5
[101] V6
Tz = T  Tx Ty
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

25. Space Vector Equations of IM
The two-phase dynamic model of IM in the stationary dsqs frame:
(13)
(14)
(15)
(16)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

29. Direct Torque Control (DTC) – Basic Principles (example)
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
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 s=V1(t))
Position (reduced by sr)
Assumption: Negligible change in rotor flux vector r within t
Stator flux and torque changed by voltage qs
s=V1(t)
s(t+t)
s(t)
sr
sr
r ds
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
s(t)
sr
r ds
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
s(t)
sr
r ds
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
k+1 voltage vector (Vk+1) increases s
k+2 voltage vector (Vk+2) decreases s
Example: heres is in sector 2 (S2)
V3 increases s
V4 decreases s S3 qs
[110] V2
[010] V3
s(t)
[011] V4
[100] V1 ds S4 S1
[001] V5
[101] V6 S5 S6
Note:
[000] V0 = 0
[111] V7 = 0
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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 VK+3 on Te is ambiguous, it depends on whether s leading or lagging the voltage vector
Zero vector Vz (i.e. V0 or V7) doesn’t affect s but reduces Te VK
VK+1
VK+2
VK+3
VK+4
VK+5
Vz (V0 or V7)
s     - Te ?
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

38. Direct Torque Control (DTC) – Implementation
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
Selection of voltage vector in DTC scheme:
Counterclockwise Rotation b 1 bT -1 S1 V2 V7 V6 V3 V0 V5 S2 V1 V4 S3 S4 S5 S6
To minimize
number of
switching:
V0 always
follows V1, V3
and V5
V7 always
follows V2, V4
and V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

39. Direct Torque Control (DTC) – Implementation
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
Selection of voltage vector in DTC scheme:
Clockwise Rotation b 1 bT -1 S1 V6 V7 V2 V5 V0 V3 S2 V1 V4 S3 S4 S5
Vv1 S6
To minimize
number of
switching:
V0 always
follows V1, V3
and V5
V7 always
follows V2, V4
and V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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])
[100]V1
[110]V2
[010]V3
[011]V4
[101]V6
[001]V5
s
sr
r ds b 1 bT -1 S2 V3 V0 V1 V4 V7 V6
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
Based on
Table in
Slides 37 or 38
Flux
control
loop
Eq. (21) &(22)
Eq. (25)
Eq. (27)
Eq. (23) , (24)
&(26)
Torque
control
loop
EEEB443 - Control & Drives

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.
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives