NASA/TMm2001-211100

Stator and Rotor Flux Based Deadbeat Direct

Torque Control of Induction Machines

Barbara H. Kenny

Glenn Research Center, Cleveland, Ohio

Robert D. Lorenz

University of Wisconsin, Madison, Madison, Wisconsin

q

\

September 2001

https://ntrs.nasa.gov/search.jsp?R=20020006306 2018-05-15T10:45:33+00:00Z
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NASA/TM--2001-211100

Stator and Rotor Flux Based Deadbeat Direct

Torque Control of Induction Machines

Barbara H. Kenny

Glenn Research Center, Cleveland, Ohio

Robert D. Lorenz

University of Wisconsin, Madison, Madison, Wisconsin

Prepared for the

2001 Industry Applications Society Annual Meeting

sponsored by the Institute of Electrical and Electronics Engineers

Chicago, Illinois, September 30-October 5, 2001

National Aeronautics and

Space Administration

Glenn Research Center

September 2001
Trade names or manufacturers' names are used in this report for

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of changes that may be made before formal publication, this preprint is made

available with the understanding that it will not be cited or reproduced without the

permission of the author.

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Available from

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Ava_flable electronica_y affhftp:77gltr_e'rc.nasalg-0v 7GLTRS ......... _
Stator and Rotor Flux Based Deadbeat Direct Torque Control

of Induction Machines

Barbara H. Kenny

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Robert D. Lorenz

University of Wisconsin, Madison

Madison, Wisconsin 53706

Abstract- A new, deadbeat type of direct torque control is

proposed, analyzed and experimentally verified in this paper.

The control is based on stator and rotor flux as state variables.

This choice of state variables allows a graphical representation

which is transparent and insightful. The graphical solution

shows the effects of realistic considerations such as voltage and

current limits. A position and speed sensorless implementation

of the control, based on the self-sensing signal injection

technique, is also demonstrated experimentally for low speed

operation. The paper first develops the new, deadbeat DTC

methodology and graphical representation of the new algorithm.

It then evaluates feasibility via simulation and experimentally

demonstrates performance of the new method with a laboratory

prototype including the sensorless methods.

I. INTRODUCTION

Direct torque control of induction machines has

increasingly become an alternative to field orientation

methods [ 1,2]. The classical method of direct torque control

involves the use of a look-up table to select voltage vectors

based on torque and stator flux magnitude error [3]. There is

no current regulator, no pulse width modulation (PWM), nor

reference flame transformations as in field orientation. With

appropriately high sample rates this leads to fast torque

response and low ripple. In addition, at operating conditions

where the stator flux vector can be estimated accurately from

the terminal voltage and current, this technique is also

position and speed sensorless. However, at extremely low

and zero speeds, the sensorless implementation of this

technique suffers the same performance degradation as any

control technique based on the estimate of stator flux using

only fundamental voltage and current.

An alternative method of direct torque control is based

on the deadbeat (inverse) solution to the machine equations

[4-7]. The deadbeat solution is similar to the classical direct

torque control method in that it controls torque and stator flux

directly, without an intermediate current loop. It is different,

however, in the calculation of the voltage vector to be applied

to the machine. In the deadbeat solution, an inverse model is

used to calculate the theoretical voltage vector needed to

move the machine torque and stator flux to the desired values

in one sample period. This voltage vector is then synthesized

over the sample period by the use of PWM modulation

techniques. However, the calculation of the voltage vector

requires the solution of a quadratic equation with several

parameter dependent coefficients. Insight into the operation

of the control is lost with a purely algebraic approach to the

solution of the quadratic equations.

This paper presents a new direct torque control strategy

where stator and rotor flux are chosen as state variables in the

deadbeat solution [8,9]. The use of stator and rotor flux as

state variables, represented in the stator flux oriented

synchronous reference frame, allows the construction of an

intuitive graphical depiction of the necessary voltage vector

to achieve the commanded torque and stator flux magnitude

values in one time step. The graphical depiction changes as

operating conditions or parameters vary; thus the resulting

change in the necessary voltage vector can clearly be seen.

Conversely, the impact of the selection of the wrong voltage

vector on both the stator flux and torque errors can also be

seen. In addition, practical operating limits can be shown on

the same graph, thus presenting a good visualization of the

current and voltage limitations. It is further shown that the

structure of this control strategy is suitable for use with the

self-sensing position estinaation technique [10]. This enables

low and zero speed position and speed sensorless direct

torque control.

II. FORMULATION OF A STATOR-ROTOR FLUX

DEADBEAT CONTROL ALGORITHM

The state equations for the induction machine, using the

stator and rotor flux as state variables in the stationary

reference frame, are as follows [11].

R S

p d.=Vqd.

Rr

3PLm

Ze - 4OLsLr {kqds x 2ktdr }

{RsL m "_

+t J d, (l)

{LmRr_

+t j .s

(3)

A discrete time form of (1)-(3) is shown in (4)-(6) that is

valid for small values of the sample time, ts, for which the

rotor speed, 0_, changes negligibly [8,9].

_qds(k+ 1 ) - _qds(k) =

Rs RsLm

=

_ ___ + jtOr)_qdr(k)ts +{LmRr'_ t J d (k)t (5)

3PLm

17e(k+ 1) - 4CLsLr {2kids(k+ 1) x Lqdr(k+ 1) } (6)

NASA/TM--2001-211100 1
Equations (4)-(6) can be combined to form and expression

for the change in torque, ATe(k) = Te(k+l) - Te(k). If the

d-axis of the excitation reference frame is aligned with the

stator flux and the terms proportional to t_ are neglected, a

very useful relationship results as shown in (7) [8,9].

ATe(k) (_-Rr _Rc'__) + 3PLm

ts - Te(k)_o'L r v__] 4CLs--'- _

{-(Or X_s(k) X_r(k) + Vqs(k) _,_r(k) - V_s(k) _,qr(k)} (7)

Equation (7) can be rearranged as follows to show the linear

relationship between Vqs(k)t s and V_s(k)t s values which can

be used to provide a given value of ATe(k).

Rs

V_s(k) ts- 3PLm_._(k) 4_LsLr (ATe(k) + Te(k)(---_-rr + _--_-s) ts)

+ + VL(k) (8)

If (8) is plotted m" • e , e a d-q plane with Vds(k)t s and Vqs(k)t s as

the d- and q-axis variables respectively, the voltage loci for a

given ATe(k ) is a straight line. This line is parallel to the

rotor flux vector, _,qedr(k), as shown in Fig. 1 [8,9]. (Figs. 1-6

use the convention fqd=fq-Jfd .)

-0,05

-0,04  ̧

_0.08  ̧

-0,C

0.0-"

0,IN

V

......... /

/

-0 04 _.02 0 0,02 0,04 OJ_

q-axls, volt -sec

Fig. i. Constant ATe(k) line

One representation of the multiple possible voltage (voltsee) vectors [Vqs(k)t s V_s(k)t s ] that could yield the desired

change in motor torque, ATe(],:), is shown in Fig. 2.

t

-0.04 ......... A S

-0.03 " " i

-0,02

!_0:........ :....

002

0,03

004

0"0--0%6 -0,04 -0.02 0 002 0.04 0.06

q-axis, _ott-sec

Fig. 2. Graphical representation of multiple voltage vectors

for machine torque change ATe

From (4) the discrete time expression for stator flux,

neglecting stator resistance, is

_Lqds(k+ 1) - )_qds(k) = Vqds(k)t s. (9)

Equation (9) can also be shown graphically. Fig. 3 shows

the plot of t)_qds(k+l)l and _.&(k), where _,_s(k) = ILqds(k)l.

There are multiple voltage vectors, scaled by ts, which will

move the flux magnitude from a value of )_s(k) to

IJkqds(k+ 1)1.

-0.0!

-0,03

_.06 -004 -0.02 0 002 004 006

q-_xl_, vo_-sec

Fig. 3. Graphical representation of muhiple voltage vectors

for flux magnitude increase

The flux circle shown in Fig. 3 can be redrawn to show the

change in flux magnitude, Alkqds(k)l = 12_qds(k+l)l - _,L(k),

where )_c_s(k)= I_qds(k)l. This circle is centered on the present

value of stator flux, )_gs(k), with a radius equal to the

magnitude ILqds(k+l)[. This adjustment means that the

possible voltage (volt-see) vector loci shown in Figs. 2 and 3

now all begin at the origin of the plot. Thus, for a given set

of A'_e(k) and AlLqds(k)l requirements, the voltage vector

which will solve both conditions simultaneously can be

determined from the intersection of the ATe(k) line and the

A0_qds(k)[ circle. This is shown in Fig. 4.

-O.1

ZII

_.-o.o2_ / °:f

0 04L

-0.05 0 0.05

q-axis (volt-sec)

Fig. 4. Graphical representation of a voltage vector which

satisfies both ATe(k) and 12_qds(k+1)I requirements

The solution, Vq_ts(k)ts, to the intersection of the ATe(k)

line and the Al_qds(k)l circle is bounded by the available dc

bus voltage, the sample time and the inverter current limit.

The range of voltages that can be synthesized from a twolevel inverter can be represented as a hexagon in the d-q

plane [11]. Thus the bound for Vq_s(k)t s is a hexagon with

sides equal to 2/3 Vdc ts as shown in Fig. 5. The hexagon is

shown at a static position in Fig. 5 but it actually rotates at the

synchronous speed because the figure is in the synchroiaous

reference frame.

NASA/TM--2001-211100 2
--O,1

-O.0E

_-0.0(

_._> I -°04

._ -0.02

i

_ C

0.02

0.04T

-0.05 0 0.05

q-axis (volt-sec)

Fig. 5. Graphical representation of voltage and current limits

on the possible voltage vector solutions

Fig. 5 also shows the maximum and minimum values of

ATe based on a steady state solution using the inverter current

limit, liqdsmaxl and the present value of "_e(k). The maximum

torque can be calculated as a function of the stator flux

magnitude and the maximum stator current as follows. For a

stator flux oriented system, the torque can be expressed as

3P .

"[e = T )_ds lqs (10)

In terms of current magnitude, this becomes

17e = + "_ _dsqliqds 12- i2s (11)

The variables ids and )_ds can be related through the slip

frequency by using the following two relationships which are

given in [ 11].

Lm

_'qds = Losiqds + W _qdr

P)Ndr = (_-j O_e+ j O)r) (_qdr)

(12)

[-_] iqds (13)

Assuming stator flux orientation and steady state conditions,

(12) and (13) can be used to form an expression for ids in

terms of the stator current magnitude and the stator flux.

LGsLsliqd s 12+ _,2s

ids - _,_Ls(1 +c) (14)

Equation (14) can be substituted into (11) to find a condition

on the maximum torque that is possible for a specified

maximum stator current magnitude and stator flux value.

3P s_/, 2 (LGs Ls'icldsmax'2 + _2s _

'_emax = 4-T _d lqdsmax - _k _dsts(l+G) (15)

Finally, using (15) and the present value of torque, the

maximum and minimum change in torque can be calculated.

A_emax = +17emax- "_e(k) (16)

A1;emin =-17emax- _e(k) (17)

It is interesting to consider the plot for a steady state

condition (A_e(k)=0, AILqds(k)l=0 ). This is shown in Fig. 6.

-0.1

-0.0

_-0.0

-O.Oz

0.0_

0.124'

-0,05 0 0.05

q-axis (volt-sec)

Fig. 6. Graphical representation of operating regions for

steady state conditions

Any AT e lines to the right of the A'_e(k)--0 line represent an

increase in torque. Any ATe lines to the left of AaTefk)--0

represent a decrease in torque. Any Al_qds(k)l circles within

the AIj_qds(k)l--0 circle represent a decrease in stator flux

magnitude. Any Al_qds(k)l circles outside AI)_qds(k)l=0

represent an increase in flux. Thus it is seen that tlaere are

four operating regions within the hexagon as shown:

1. Increase torque, decrease flux

2. Increase torque, increase flux

3. Decrease torque, decrease flux

4. Decrease torque, increase flux

The. standard table look up method of direct torque control

allows only the voltage vectors represented by the vertices of

the hexagon (plus the two zero vectors) to be selected for the

duration of the sample period. However, if a. pulse width

modulation technique is used, an average voltage vector over

the sample period can be synthesized which lies anywhere

within the hexagon.

A control algorithm can be developed based on (8) and (9)

and using Fig. 4 if ATe(k) is set equal to "Ce(k+l)* - _e(k) and

AILqdsfk)l--- IJktds(k+l)r - _.c_s(k). The voltage vector

calculated by the control algorithm is the intersection of the

ATe(k)* line with the Al_,qds(k)[* flux magnitude circle which

is the solution of (8) and (9). The voltage vector can be

synthesized using space vector modulation techniques to

calculate the inverter switch duty cycles [12]. Fig. 7 shows

the block diagram of the control system in which the

proposed algorithm was implemented. (The additional

voltage command, V_fss(k), is only necessary for the selfsensing position and speed estimation as explained in Section

V.)

The control sequence is as follows.

1. Is A'_e(k)* within the limits of A_emax and ATemin? If

not, ATe(k)* is set equal to the closest limit.

2. Do the A'_e(k)* line and the Al_ds(k)l* circle intersect?

If so, the voltage vector, Vq_s(k') is calculated. If not,

"_e(k+l)* is reduced until the corresponding A'_e(k)*

. line is tangential to the Al_,qds(k)l* circle. Then the

voltage vector to this point is calculated.

NASA/TM--2001-211100 3
Vdc

e. f Modo,a,o,

,wmJ

.

io

Fig. 7. Proposed deadbeat control block diagram

Is the desired voltage vector within the hexagon? If

so, space vector modulation is used to calculate the

corresponding inverter switch duty cycles. If not, the

magnitude of Vq_ts(k) is reduced until it lies on the

hexagon boundary. Then space vector modulation is

used to calculate the inverter switch duty cycles.

Alternate overmodulation strategies could also be

usedifor example the most appropriate hexagon

corner could be selected based on the desired change

in torque and flux which would be equivalent to using

standard direct torque control.

lie SIMULATION RESULTS

The experimental motor used in this paper is a specially

designed high speed (rated speed just over 23,000 rpm)

induction machine for a NASA electro-mechanical actuator

research project. The parameter values are given in the

Appendix. The simulation conditions are set to match the

experimental conditions. Experimentally, the machine was

limited to 10,000 rpm or less due to concern about the

condition of the beatings. All of the simulations neglect the

PWM switching harmonics.

The controller was analyzed in two ways. First, to

investigate its small signal stability, the operating point

model was formed using the Matlab TM LTI func_tio0. To form

the operating point model, the mechanical dynamics were

neglected (constant speed) and perfect flux estimation was

assumed (the flux observer was not included in the operating

point model). Pole-zero migration plots were then created for

a range of speeds from low speed to rated speed (180 rpm to

23,000 rpm) at the rated torque and rated flux operating point.

The second analysis was based on a time domain, nonlinear

model simulation of the complete system including the flux

observer and the mechanical dynamics. The speed, torque

and stator flux responses to a square wave torque command

are shown.

Fig. 8 shows the pole-zero migration plot from the LTI

analysis for a 100 p.sec sample time (used experimentally).

The result is seen to approximate the expected deadbeat

response but there is not exact pole-zero cancellation and the

free pole is not exactly at the origin. This improves as a

smaller and smaller sample time is used. (The NASA motor

has relatively small time constants as can be seen in the

Appendix.)

1| ! , ,

081 !

06 • _ : i

Real Axis

Fig. 8. Pole-Zero plot for 100 psec sample time and no

calculation delay

The time domain results shown in Figs. 9 and 10

demonstrate good performance. The torque response is seen

to be a square wave as expected. Fig. 10 also shows the

effect of neglecting the resistance in deriving (9). For a stator

resistance equal to'zero, the stator flux is at the commanded

value of 1 per unit. However, the stator flux magnitude is

slightly reduced from the commanded value for a stator

resistance of. 18 ohms.

< •

o4 oJ ul

Fig. 9. Torque and speed

response for a 100 lasec

sample time and no

calculation delay

°l o

Rs*O ohms

R$ = 18 mohrm

o2 04 os os

I_1e< _conds

Fig. 10. Stator flux

magnitude for 100 psec

sample time, no calculation

delay and two values of

stator resistance

: =

in the ideal 6fise_;]i_i_s_-sumed that the command values for

the manipulated variables (Vqs*(k), Vds*(k)) are calculated in

zero time based on the present sampled value of the measured

feedback variables (iqs(k), ids(k)). Realistically, however,

there will be a calculation delay between when the feedback

variables are measured and when the commanded values for

the manipulated variables are updated because the required

microprocessor calculations can not be done in zero time.

NASA/TM--2001-211100 4
ThecommandvaluesforthemanipulatedvariablesVqs(k)

S*

and Vds(k) ultimately become pulse width commands for the

gate drives in the inverter. In this implementation, the

sampling time is synchronized with the PWM generation.

Thus the PWM timers are updated at the same time as the

feedback variables are measured. This results in a one step

time delay for the control because the PWM timers are

updated based on the calculations from the feedback data of

the previous sample.

The effect of this one step time delay can be seen in the

pole-zero plot of Fig. 11. The free pole and the pole-zero

cancellation pair that were at or near the origin in Fig. 8 have

now moved to the edge of the unit circle. The time domain

simulations also show a more oscillatory response as seen in

Figs. 12 and 13.

1 ;

OA

04

-0._

-0 4

-OA

....... i

I...................... _-", \ _j !

-I -0,5 0 05 I

Real Axis

Fig. 11. Pole-Zero plot for 100 lasec sample time and one

step time delay

2s " ' i i ,o_ " ' {

o Is - :

°*o o:_ _14 oe o'e ,

_me, _¢on_ Ume, s_cc_ds

Fig. 12. Torque and speed

response for a 100 gsec

sample time and a 1 time

step calculation delay

Figure 13: Stator flux

magnitude for 100 lasec

sample time and a 1 time

step calculation delay

For a similar deadbeat type of controller, Ref [5] shows

that a modification to A'_e(k)* and AI2kqds(k)l* will move the

system poles to lie further within the unit circle and reduce

the oscillations. A similar derivation can be shown here. To

include the one-step time delay, (7) can be expressed as

follows.

-Rr R s " 3PLm

_e(k+2)-lTe(k+i)ts = 'l;e(k+l)(_"_ "- _'s { + 4OLs"--"_

{-oh._,_s(k+ 1)_,&(k+ 1) + Vqe(k)* _,_r(k+ 1)- V_s(k)* _r(k+ 1) }

(18)

From (8) an expression for the control variables is Vqs(k)*

e ,

and Vds(k) is

V;(k)*t s - V_s(k)*ts_ = Or_,gs(k)ts +

_,_r(k)

4_LsLr { {Rr Rs "_ "_

3PLm)h_r (k) tTe(k+ l )* - '_e(k) + Te(k)[ _r+ _jk ]19)

Under constant stator flux operation and assuming that

_,q_r(k+l) _ _,qedr(k), (18) and (19) can be combined to form

an approximate relationship between the commanded torque

and the actual torque as shown in (20).

- Rs

"_e(k+2)-'l;e(k+l) = "_e(k+l)(_L_- _'_:)ts+ "Ce(k+l) *

(Rr Rs_

From (20), the characteristic equation of this simplified

transfer function is

Rs

z2- z( i-(-_-_--+ _s)tS)+ (1-(--_ + _s)ts)= 0. (21)

For small values of ts, these poles can be seen to lie close

to the unit circle boundary. Ref [5] suggests modifying the

control equations as shown in (22) and (23) (0<C<1) to

reduce the oscillations and potential instability problems.

A17e(k)* = C (_e(k+l)* - a;e(k)) (22)

Al)_,qds(k)l*= C ({2_qds(k+l)l* -IJ_qds(k)l) (23)

Using (18), (19) and (22), the characteristic equation of the

modified transfer function is

z2 _ z( 1_ (-_-- + _s)ts) + C ( l-tZff+ jt j: /eRr Rs_" _ o(24)

Ref [5] studies the effect of various values of C on the

response of the system. In the present work, it was found that

C=.8 yielded a fast response with no instability. The

corresponding LTI pole-zero migration plot and time domain

responses are shown in Figs 14-16.

OA

o_

-o.I - -

-0.!

-_ -0.5 0 0>$ 1

Axis

Fig. 14. Pole-Zero plot for 100 gsec sample time, one step

time delay and C=.8

NASA/TM--2001-211100 5
Fig.15.Torqueandspeed

responsefora100_tsec

sampletime,1timestep

delayandC=.8

o_

0_2 oa o6 o8

zln_, _nd_

Fig. 16. Stator flux

magnitude for a 100 lasec

sample time, I time step

delay and C=.8

IV. EXPER_NTAL RESULTS

The experimental test set up consisted of a dc power

supply, an intelligent power module, a dSpace 1103 TM digital

controller and the NASA test motor. The results were

captured using dSpace software. The data flies were then

plotted using Matlab". Two phase currents were measured

and an encoder was used for position feedback. The position

feedback was necessary because a flux observer based on the

current model was used. (In Section V, the position feedback

is provided by the self-sensing algorithm and the encoder

information was used for comparison purposes only.) The

speed was calculated in the controller using the position

information. The torque and flux were estimated in the

controller using current and position information.

Figs. 17 and 18 show the torque, stator flux and speed for

the same conditions as in Figs. 15 and 16 in simulation.

|

Fig. 17. Experimental results:

torque and speed response

for a 100 I.tsec sample time,

one time step delay and C=.8

Fig. 18: Experimental

results: stator flux magnitude

for a I00 gsec sample time,

one time step delay and C=.8

In general, the response is as predicted. In the actual

implementation, there is always a deadtime, or blanking time,

in the inverter so that the two switches across a leg do not

conduct at the same time. In addition, there is a voltage drop

across the conducting devices. Both of these effects result in

a lower voltage being applied to the machine than is actually

commanded. This "deadtime voltage" can be calculated [ 13].

4V d . ;r

ejCk-] )'_ Vdeadtime = "7 (25)

Vd is the magnitude of the voltage due to the combination

of the deadtime losses and the conduction losses and k is the

sector of the d-q plane in which the current vector is located,

k=1,2...6. This controller was found to be sensitive to

deadtime compensation as can be seen by comparing Figs. 19

and 20 (without deadtime) to Figs 17 and 18 (with deadtime).

It is seen that without deadtime compensation, both the

torque and stator flux magnitudes were reduced.

Fig. 19. Experimental results:

torque and speed response

for a 100 _tsec sample time,

one time step delay and

ts'=125 tasec, no deadtime

compensation

Fig. 20. Experimental results:

stator flux magnitude for a

100 I-tsec sample time, one

time step delay and ts'=125

lasec, no deadtime

compensation

V. LOW SPEED SENSORLESS IMPLEMENTATION

To date, the self-sensing method has been demonstrated

only with the field orientation method of control. The use of

self-sensing in a deadbeat direct torque control offers the

potential of full speed range sensorless operation with the

flux estimate based on the back emf method at higher speeds

and on the self-sensing position estimate at lower speeds.

To estimate the rotor position angle, Or, the self-sensing

technique requires a machine with a magnetic saliency related

to the rotor position [10]. The NASA motor rotor was

designed to produce a position dependent magnetic saliency

by changing the shape of the rotor bars as a function of

position as shown in Fig. 21. (The rotor is 1.3 inches in

diameter).

Fig. 21. Rotor cross-section of NASA machine

Additionally, the self-sensing technique requires a high

frequency cartier signal. The structure of a deadbeat type of

direct torque control lends itself to the use of the self-sensing

method of position estimation because the necessary high

frequency signal can be easily added to the fundamental

voltage command as shown in Fig. 7. Thus the cornn_ nded

voltage into the pwm modulator will consist of the

S *

fundamental voltage,command, Vacts(k) and the high

frequency voltage, Vhfss(k). The resulting current is filtered

as described in [14] and a signal at twice the rotor position is

NASA/TM_2001-211100 6
generateddueto thepositiondependent magneticsaliency.

Thissignalcanbetrackedinaclosedloop,saliencyimagetrackingobserverto produceposition;velocity,acceleration,

anddisturbancetorqueestimates.

Figs.22and23showtheresultsof anoloadclosedloop

low"speedsensorlesscontrolusingtheself-sensingposition

estimateasfeedbackforthecontroller.Fig.22showsthe

spectraof thenegativesequenceurrent(asdefinedin [14])

for aconstant3Hzspeed.Thecomponent duetotherotor

saliencyisclearlyvisibleat6Hz. Fig.23showsanoload

speedreversal from-3Hzto+3Hz.

rrequine¢

o 4

03

i:

Fig. 22. Negative sequence

current spectra for constant

speed 3 Hz operation

J •

Fig. 23. Sensorless speed

reversal of proposed

controller with estimated

rotor position and speed

feedback based on selfsensing method

VI. CONCLUSIONS

This paper has developed a new, deadbeat direct torque

control method based on stator and rotor flux as state

variables. This choice of state variables allows a clear

graphical visualization of the voltage vector solution and the

inverter operating limits.

The implementation of the proposed controller was

evaluated experimentally and found to produce good results.

The implementation issues which could limit performance

were also evaluated.

The controller was found to be sensitive to the one step

time delay in the experimental implementation. The

deadtime voltage drop, without appropriate compensation,

was also found to reduce the torque and flux in the machine.

The structure of the proposed controller allows the addition

of a high frequency voltage vector to the commanded

fundamental voltage vector. This allows the self-sensing

method of position and speed estimation to be used thus

demonstrating low, including zero speed, sensorless control.

REFERENCES

[1] Takahashi, Isao and Noguchi, Toshihiko; "A New

Quick-Response and High-Efficiency Control Strategy

of an Induction Motor", IEEE Transactions on Industry

Applications, Vol. IA-22, No.5, Sept/Oct 1986 pp. 820-

827.

[2] Depenbrock, M., "Direct Self-Control (DSC) of

Inverter-Fed Induction Machine", IEEE Transactions

on Power Electronics, Vol. 3, No. 4, October, 1988 pp.

420-429.

[3] Pekka Tiitinen, "The Next Generation Motor Control

Method, DTC, Direct Torque Control, Proc. 1996

h_teivlational Co1_ on Power Electronics, Drives and

Systems for h_dustrial Growth , New Delhi, India, Jan.

8-11, 1996 pp. 37-43.

[4] Habetler, Thomas, Profumo, Francesco, Pastorelli,

Michele, Tolbert, Leon, "Direct Torque Control of

Induction Machines Using Space Vector Modulation",

IEEE Trans on b2dustry Applications, Vol. 28, No. 5,

Sept/Oct 1992 pp. 1045-1053.

[5] Maes, Jehudi, Jan Melkebeek, "Discrete Time Direct

Torque Control of Induction Motors using Back-EMF

Measurement", Proc. of IEEE Industrial Applications

Society Conf, St. Louis, Mo., Oct. 12-15, 1998, pp 407-

414.

[6] Neves, Francisco, Benjamim Menezes, Selenio Silva,

"A Deadbeat Torque and Flux Field Oriented Controller

for Induction Motor Drives", Proc. of XI1 Brazilian

Automatic Control Conference, Vol. VI, Sept. 1998

pp.2243-2247.

[7] Buja, G., M. Candela, R. Menis, "A Novel Direct

Control Scheme for SVM Inverter-Fed Induction Motor

Drives", Proceedings of 1999 ISIE, Bled, Slovenia,

pp.1267-1272.

[8] Casadei, Domenico, Giovanni Serra, Angelo, Tani,

"Analytical Investigation of Torque and Flux Ripple in

DTC Schemes for Induction Motors", IECON

Proceedings of the1997 23 _ Annual hlt.ernational

Conference on Industrial Electronics, Control, and

hlstrumentation, New Orleans, Louisiana, Nov 9-14,

1997, Vol. 2, pp. 552-556.

[9] Casadei, Domenico, Giovanni Serra, Angelo, Tani,

"Implementation of a Direct Torque Control algorithm

for Induction Motors Based on a Discrete Space Vector

Modulation", Proceedings of the 1998 IEEE Power

Electronics Specialists Conference, Fukuoka, Japan,

May 18-21, 1998, Vol. 2, pp 997-1003.

[ 10] Jansen, Patrick L. and Robert _D. Lorenz,

"Transducerless Position and Velocity Estimation in

Induction and Salient AC Machines", /EEE Trans. on

Industry Applications, Vol. 31, No. 2, March/April 1995

pp. 240-247.

[11] Novotny, Donald W. and Thomas A. Lipo; Vector

Control and Dynamics of AC Drives, Oxford University

Press, New York, 1996.

[12] van der Broeck, H. W., Skudelny, H. C. and Stanke, G.

"Analysis and Realization of a Pulse Width Modulator

Based on Voltage Space Vectors", IEEE Transactions

on bldustry Applications, Vol. 24, No. 1, Jan/Feb. 1988,

pp. 142-150.

[13] Vas, Peter Sensorless Vector and Direct Torque

Control, Oxford, U.K.; Oxford University Press, 1998.

[14] Degner, Michael and Lorenz, Robert "Using Multiple

Saliencies for the Estimation of Flux, Position, and

Velocity in AC Machines" IEEE Transactions on

Industrial Applications, Vol. 34, No. 5, Sept/Oct 1998,

pp 1097-1104.

APPENDIX

NASA Motor: 2 pole induction, 96 VLN, 400 Hz,

Lm=l.9e-3 H., L)s=l.25e-4 H., Lh=l.25e-4 H., Rr=.105 _.,

Rs=.09 f2., J=l.02e-4 kg-m2, _em=l N-m, 0_=23,030 rpm

NASA/TM--2001-211100 7
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1. AGENCY USE ONLY (Leave b/ank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

September 2001 Technical Memorandum

4. TITLE ANDSUBTITLE 5. FUNDINGNUMBERS

Stator and Rotor Flux Based Deadbeat Direct

Torque Control of Induction Machines

6. AUTHOR(S)

Barbara H. Kenny and Robert D. Lorenz

7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORINGAGENCYNAME(S)AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

WU-755-1A-I 1-00

8. PERFORMINGORGANIZATION

REPORTNUMBER

E-12945

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--2001-211100

11. SUPPLEMENTARYNOTES

Prepared for the 2001 Industry Applications Society Annual Meeting sponsored by the Institute of Electrical and Electronics Engineers, Chicago, Illinois, September 30-October 5, 2001. Barbara H. Kenny, NASA Glenn Research Center;

Robert D. Lorenz, University of Wisconsin, Madison, Department of ECE and ME, 1513 University Avenue, Madison,

Wisconsin 53706. Responsible person, Barbara H. Kenny, organization code 5450, 216--433-6289.

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Unclassified - Unlimited

Subject Category: 33 Distribution: Nonstandard

Available electronically at htto://_ltrs.zrc.nasa.gov/GLTRS

This publication is avfiilable from the NASA Center for AeroSpace Information, 301-621-0390.

13. ABSTRACT(Maximum200 words)

12b, DISTRIBUTIONCODE

A new, deadbeat type of direct torque control is proposed, analyzed, and experimentally verified in this paper. The control

is based on stator and rotor flux as state variables. This choice of state variables allows a graphical representation which

is transparent and insightful. The graphical solution shows the effects of realistic considerations such as voltage and

current limits. A position and speed sensorless implementation of the control, based on the self-sensing signal injection

technique, is also demonstrated experimentally for low speed operation. The paper first develops the new, deadbeat DTC

methodology and graphical representation of the new algorithm. It then evaluates feasibility via simulation and experimentally demonstrates performance of the new method with a laboratory prototype including the sensorless methods.

14. SUBJECTTERMS

Induction motor control; Direct torque control; Sensorless motor control

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