NASA / TM--2001-211100 / REV 1

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

September 2002
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NASA/TMm2001-211100 / REV1

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 2002
Trade names or manufacturers' names are used in this report for

identification only. This usage does not constitute an official

endorsement, either expressed or implied, by the National

Aeronautics and Space Administration.

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Hanover, MD 21076

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Available electronically at http: //gltrs.grc.nasa.gov
Document Change History

This printing, numbered as NASA/TM--2001-211100/REVI, September 2002, replaces the previous version in its

entirety, NASA/TM--2001-211100, September 2001.

NASA/TM--2001-211100/REV 1 iii

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

Abstrac_--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 frame 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 estimation 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].

P_qds: Vqds- _lds ,,,

Rr

P_ldr =(-_rr+JO)r)2_qdr +(LmRr'] _ Lr_Ls) J_,qds (2)

3PLm

'_e - 4_LsLr {2kqds x 2_ldr } (3)

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

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

rotor speed," cot, changes negligibly [8,9].

jk.qds(k+ 1) - Jkqds(k) =

Rs

Vqds(k)ts _ _) 2_qds(k)ts [ RsLm ' + {_)kqdr(k)t s (4)

_qdr(k+l) - _,qdr(k) =

(_ _r + j00r))_qdr(k)t s + {LmRr _)kqds(k)ts_ (5)

3PLm {_kqds(k+l) x _ldr(k+l)} (6)

"[e(k+l) - 4_LsLr

NASA/TM----2001-21 I 100/REV 1 1
Equations (4)-(6) can be combined to form an expression

for the change in torque, ATe(k) = 1;e(k+l) - 1;e(k). If the

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

stator flux and the terms proportional to t2s are neglected, a

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

A1;e(k) 7s /'Rr Rs) + 3PLm

{-(Or _.g(k) _,g(k) + Vqs(k) _,_r(k) - Vg(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 A'Ce(k).

VoWs(k) 4°LsLr (A,Ce(k) + ,_e(k)(o_r + _Ts)tS )ts - 3PLrn_.c_r(k)

+ tor_,_s(k) ts + V2s(k ) ts £_--_ (8)

Mgk)

If (8) is plotted in a d-q plane with V_s(k)t s and Vqs(k)t s as

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

given A'i_e(k) is a straight line. This line is parallel to the

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

use the convention fqd=fq-Jfd .)

O5

4) Oa,

02

_01

_ 001

!

"_ 0 02

0134

o_

i

,,"i

i" _)

+

-0o4 -o.02 0 o02 oo4 oo_

q--axi*, volt-_¢

Fig. i. Constant A_e(k ) line

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

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

4) ̧05

-o04 Ag=Coastant

4) 03

4) 02

OOl

002

0.o.3

004

o__ -o04 'o.h2 0 oh2 o._ ooe

q-axis, voR-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

2Lqds(k+I )- _qds(k) = Vqds(k)t s. (9)

Equation (9) can also be shown graphically. Figure 3

shows the plot of I_dstk+l)l and _.a_s(k), where _,a_s(k) =

IJqds(k)l. There are multiple voltage vectors, scaled by ts,

which will move the flux magnitude from a value of _,_s(k) to

I_Lqds(k+l)l,

4) 05

4)IMr

4_.03[

-0 02 i

_4

_ 001.

003i

'_p'>'

I

-0,04 -002 0 002 O_ O_

Q-aUX.. VOlt-_

Fig. 3. Graphical representation of multiple voltage vectors

for flux magnitude increase

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

change in flux magnitude, /Xl_d,(k) I = I_.qds(k+l)l _,_s(k),

where _,_s(k) = 12_qds(k)l.This circle is centered on the present

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

magnitude 12_qds(k+l)l. This adjustment means that the

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

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

of A1;e(k) and AlJ_lds(k)l requirements, the voltage vector

which will solve both conditions simultaneously can be

determined from the intersection of the A1;e(k) line and the

AIJkqds(k)l circle. This is shown in Fig. 4.

-0.1

-0.08

_%(k)

_-0.06

.__ -0.02,

0.02

0.04

-0,05 0 0,05

q-axis (volt-set;)

Fig. 4. Graphical representation of a voltage vector which

satisfies both A17e(k) and Al2_tds(k)[ requirements

The equation defining the A kqds(k) [ circle is given in (10).

The voltage vector which will solve both the Al;e(k ) and the

A[J_qds(k)] requirements can be found mathematically from the

simultaneous solution of (8) and (10L or graphically as

shown in Fig. 4.

(Vqs(k)ts) 2 + (Vc_s(k)t s- £a_s(k))2 = I;_qds(k+])t2 (10)

The solution, Vqds(k)t s, to the intersection of the A'_e(k )

line and the Al_qds(k)t 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 [l l]. Thus the bound for Vqds(k)t s is a hexagon with

NASA/TM--2001-211100/REV 1 2
sidesequalto2/3VdctsasshowninFig.5. Thehexagonis

shownatastaticpositioninFig.5butit actuallyrotatesatthe

synchronous speedbecausethefigureisin thesynchronous

referenceframe.

-0.1

-o.o8:

_-o.06 i

ta

 -o0.1

-002i

0.02

0.04

• s_e_

AI_)I

A_° %(k)

v.;_%

-0,05 0 0.05

q-axis (volt-see)

Fig. 5. Graphical representation of voltage and current limits

on the possible voltage vector solutions

Figure 5 also shows the maximum and minimum values of

AIe based on a steady state solution using the inverter current

limit, liqdsmax] and the present value of Ie(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

Ie = _ _,ds iqs ( l l )

In terms of current magnitude, this becomes

'ge = _,ds4 [iqds]2 _id2s (12)

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 = Lt_siqds + L-T _,qdr (13)

P_dr = (_r r -jOe+ j0)r)(_qdr)+ (L-_rRr)iqd s (14)

Assuming stator flux orientation and steady state conditions,

(13) and (14) can be used to form an expression for ids in

terms of the stator current magnitude and the stator flux.

LosLsliqds 12+ Xds2

ids= _.dsLs( 1+t_) ( 15)

Equation (15) can be substituted into (12) to find a condition

on the maximum torque that is possible for a specified

maximum stator current magnitude and stator flux value.

3P • 2 _Lasksliqdsmaxlz -

2

q_emax= + "_ _'ds Iqdsmax - L _,dsLs( 1+_) (16)

Finally, using (16) and the present value of torque, the

maximum and minimum change in torque can be calculated.

A17emax - +'_emax - 17e(k) (17)

Alemin = -17emax- Ie(k ) (18)

It is interesting to consider the plot for a steady state

condition (A1;e(k)=0, Al_,qds(k)l=0). This is shown in Fig. 6.

-0.1

-0.08

-O.06

_ -O.04

>

.__..0.021

0.02

0.134

%1_),=0

_,_ ±%(k)=°_

qS-axis

o6-axis

-oOS 0 o.os

q-axis (volt-see)

Fig. 6. Graphical representation of operating regions for

steady state conditions

Any A_ e lines to the right of the AIe(k)=O line represent an

increase in torque. Any AI e lines to the left of AIe(k)=O

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

the Al_ds(k)l=O circle represent a decrease in stator flux

magnitude. Any AIZqdstk) I circles outside AI2,,qds(k)l=0

represent an increase in flux. Thus it is seen that there 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), (10)

and Fig. 4 if Ale(k) is set equal to l_e(k)* -Ie(k) and

Al_ds(k)l = ]kqds(k)l* - _,gs(k). The voltage vector calculated

by the control algorithm is the intersection of the A17e(k)* line

with the AI2_,qds(k)[* flux magnitude circle which is the

solution of (8) and (10). The voltage vector can be

synthesized using space vector modulation (SVM) techniques

to calculate the inverter switch duty cycles [12]. Figure 7

shows the block diagram of the control system in which the

proposed algorithm was implemented. (The additional

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

Section V.)

The control algorithm first tests if Ale(k)* is within the

limits of ATemax and AIemin. If it is not, A1;e(k)* is set equal

to the closest limit. There are then three possibilities for the

voltage vector solution: the AIe(k)* line and the _Xlkqds(k)l*

circle intersect within the allowable voltage hexagon, the

AIe(k)* line and the ±lkqds(k)l* circle intersect outside the

allowable hexagon, or the AIe(k)* line and the Alkqds(k)l*

circle do not intersect.

NASA/TM--2001-211100/REV 1 3
If theATe(k)*lineandtheAI2_qds(k)t* circle intersect within

the allowable voltage hexagon, the solution is the voltage

vector defined by the intersection point closest to the origin

and is implemented using space vector modulation.

If the A1;e(k)* line and the A[kqas(k)l* circle intersect

outside of the allowable voltage hexagon, the desired voltage

vector is again calculated; however, the magnitude is larger

than what is available given the DC bus voltage. The

magnitude of the voltage vector is reduced by the SVM

algorithm until it lies on the hexagon boundary. This reduced

magnitude voltage vector is then applied.

If the A_e(k)* line and the Al2kqds(k)]* circle do not

intersect, this is an indication that a large change in torque is

required, in this case, the maximum voltage vector in the

direction of maximum change in torque is applied. This is

the voltage vector perpendicular to the A'_e(k)* line with the

maximum magnitude allowed by the hexagon.

Vd¢

_* _ Vhfss" SA

[ e . -'-'1 [ Modulator

_ -[cDed_o_atdr_l_eatr_Q_, j V_lds*.to S_ I VSI

_ -- tswltcnstates_.l

-lUe ]_1--] ca cu a ,on]_ I

I

Flux Observer --

Fig. 7. Proposed deadbeat control block diagram

III. 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 bearings. 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 LTI function. 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.

Figure 8 shows the pole-zero migration plot from the LTI

analysis for a !00 lisec 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.)

osi

o41

0_

__-o21

-O4!

i

-0 B I

-Oa!

-' ±; -os 0 - 07_ ;

Real Axis

Fig. 8. Pole-Zero plot for 100 lasec 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. Figure 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 ! per unit. However, the stator flux magnitude is

slightly reduced from the commanded value for a stator

resistance of0.18 ohms.

'i

-, s i

Fig. 9. Torque and speed

response for a 100 lasec

sample time and no

calculation delay

o_si

Rs = 18_

o _ o12 o_ _6 os

Fig. 10. Stator flux

magnitude for 100 gsec

sample time, no calculation

delay and two values of

stator resistance

In the ideal case, it is assumed that the command values for

S* S*

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), iris(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.

NASAFFM---2001-211 IO0/REV I 4
S*

The _ommand values for the manipulated variables Vqs(k)

and V_s(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

o8

o6,

o4

o2i

_ o_

-02'

_4

_6

_a

-1

_ _,7  ̧

_is 0 o15

Real Axis

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

step time delay

2

':: t t

$ I

_ t I

1

Fig. 12. Torque and speed

response for a 100 lasec

sample time and a I time

step calculation delay

1

0_s! i !

o% o_2 o_ o_ o6

Imm. _,eeo,,O_

Figure 13. Stator flux

magnitude for 100 _tsec

sample time and a I time

step calculation delay

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

that a modification to ATe(k)* and AI;qds(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

shown in (19).

1;e(k+2)-l;e(k+l ) = 1;e(k+ 1)

-Rr - Rs /

+ _t_LsL 3PLm r

ts OLr _--L-s"

{-cor?_s(k+ I )L_r(k+l ) + Vqs(k)* _,_r(k+l) - Vds(k) e * _,;r(k+ 1)}

(19)

e*

From (8) the expression for the control variables Vqs(k) and

e*

Vds(k) is

e* _ eOr_.gs(k) ts +

Vqs(k)ts - V_;(k)tS_dr(k)

4_LsLr { , (Rr Rs'_ "_

/ze(k)-Ze(k)+Xelk)t - + ssJtS ) (20) 3PLm_,dr(k) k,

Under constant stator flux operation and assuming that

_,c]dr(k+l) _ _,_dr(k), (19) and (20) can be combined to form

an approximate relationship between the commanded torque

and the actual torque as shown in (21 ).

Rs

1;e(k+2)- 1;e(k+l )= 1;e(k+ 1)(_Lrr - _-_"s)ts + 1;e(k)*

/' Rr Rs_

-1;e(k)+l;e(k)_r +_sJt s (21)

From (21), the characteristic equation of this simplified

transfer function is

z2_z(l_(--_r +'_s)tS)+(l-(-_r +'_ss)tS)=0. (22)

The magnitude of the poles of (22) is given in (23). For

small values oft s, these poles can be seen to lie close to the

unit circle boundary. This indicates that the deadbeat

controller is very sensitive to the one step time delay.

IPl[ = ]P2I = 1- +_ss ts (23)

One way to reduce the sensitivity of the controller to the

one step calculation delay is to relax the response required.

Instead of a deadbeat response, an exponential response with

a small time constant can be defined. The controller with the

exponential response is much less sensitive to the one step

calculation delay [ i 3].

If the commanded change in torque, A're(k)*, in (8) and the

commanded change in flux magnitude, AIZqds(k)l*, in (10) are

reduced by a factor C, as shown in (24) and (25), the result is

an exponential response. This can be seen by substituting the

commanded values given in (26) into (7). The result is

shown in (27).

A1;e(k)* = C (17e(k)* - 17e(k)) (24)

AIZqdstk)l *= C (Ikqds(k)[*- Ikqds(k)l) (25)

e k

e* e* _ = (_._,(_s(k)ts +

Vqs(k)t s - Vds(k)ts_,_r(k )

4aLsLr (" • ( Rr Rs "_ "_

1;e(k) -

3PLm_,dr(k) _ Te(k) + '_e(k)_k_rr + _ss) ts )

(26)

NASA/TM--2001-211100/REV 1 5
l:e(k+l) = C'_e(k)* + "l;e(k)(l-C) (27)

Taking the z-transform of (27) results in the expected

transfer function for an exponential response [ 14].

l:e(Z) C

_e(Z), - z-(I-C) (28)

To see the effect of the one-step calculation delay, (26) is

substituted into (18) instead of(7) The result is given in (29)

with the same assumptions given previously---that is,

_._dr(k+ I) _ _._ds(k) and k._dr(k+ l) _ k._dr(k).

Rs

l'e(k+2)-'l;e(k+l) = _e(k+l)(_Lrr- _-s)tS+ C'lTe(k)*

(Rr Rs'_

-CXe(k)+ %(k)/_-_-_ +_ssjtS (29)

N /

The z-transform of (29) results in the transfer function

shown in (30).

_e(Z) C

"IZe(Z)*- z2 -z_l ( Rr Rs "_ "_ Rs

llk_r +_s)ts)+(f-(_--_r +_sltS /

\

(30)

The magnitude of the poles of the transfer function in (30)

is shown in (31). It can be seen that for C<I the poles will

move further inside the unit circle and the response is

expected to be less oscillatory.

Rs

The simulation results show this to be the case. Figure 14

shows the LTI pole-zero migration plot for the controller with

the commanded torque and stator flux magnitude values

given by (24) and (25) respectively and C=0.8. The poles

have clearly moved further inside the unit circle. The time

domain simulation results given in Figs. 15 and 16 show

reduced overshoot and oscillation in the response.

I .....

08-

06

O4

_4

_6

m

>

_8

-' i _5 - 6 - ols ;

Real A xis

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

time delay and C=0.8

'Ti -

.I

Fig. 15. Torque and speed

response for a 100 lasec

sample time, I time step

delay and C=0.8

i 05

)

,i

0_

i !

o% o12 o_, o6 o.

Fig. 16. Stator flux

magnitude for a 100 p.sec

sample time, l time step

delay and C=0.8

IV. EXPERIMENTAL RESULTS

The experimental test set up consisted of a dc power

supply, an intelligent power module, a dSpace 11031 digital

controller and the NASA test motor. The results were

captured using dSpace software. The data files 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.

Figures 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 lasec sample time,

one time step delay and

C=0.8

i

Fig. t8. Experimental results:

stator flux magnitude for a

100 _tsec sample time, one

time step delay and C=0.8

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 [15].

4Va eJ(k-l) 3 (32)

Vdeadtime - 3

NASA/TM-----2001-211100/REV 1 6
Vdisthemagnitudeofthevoltageduetothecombination

ofthedeadtimelossesandtheconductionlossesandk isthe

sectorof thed-qplaneinwhichthecurrentvectorislocated,

k=i,2...6, Thiscontrollerwasfoundto besensitiveto

deadtimecompensation ascanbeseenbycomparingFigs.19

and 20 (withoutdeadtime)to Figs. 17 and 18 (with

deadtime).It is seenthatwithoutdeadtimecompensation,

boththetorqueandstatorfluxmagnitudeswerereduced.

.... ) i

:'_, o o, °. o_,._

Fig. 19. Experimental results:

torque and speed response

for a 100 gtsec sample time,

one time step delay and

C=0.8, no deadtime

compensation

i , I

Fig. 20. Experimental results:

stator flux magnitude for a

100 _sec sample time, one

time step delay and C=0.8,

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 carrier 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 commanded

voltage into the pwm modulator will consist of the

S*

fundamental voltage, command, Vqds(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

generated due to the position dependent magnetic saliency.

This signal can be tracked in a closed loop, saliency imagetracking observer to produce position, velocity, acceleration,

and disturbance torque estimates.

Figures 22 and 23 show the results of a no load closed loop

low speed sensorless control using the self-sensing position

estimate as feedback for the controller. Figure 22 shows the

spectra of the negative sequence current (as defined in [16])

for a constant 3 Hz speed. The component due to the rotor

saliency is clearly visible at 6 Hz. Figure 23 shows a no load

speed reversal from -3 Hz to + 3 Hz.

O5

_04

o

_t_cy Hz

,

!L

Io 20

Fig. 22. Negative sequence

current spectra for constant

speed 3 Hz operation

!

° r

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.

APPENDIX

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

Lm=l.9e-3 H., Lls=l.25e-4 H., Ltr=l.25e-4 H., Rr=.105 fL,

Rs=.09 _., J=l.02e-4 kg-m 2, 1;era=1 N-m, (Or=23,030 rpm

NASA/TM--2001-211100/REV 1 7
REFERENCES

[i] 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

International Conf. on Power Electronics, Drives and

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

8-1 l, 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 Industry 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 1EEE Industrial Applications

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

pp. 407-414.

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

"A Deadbeat Torque and Flux Field Oriented Controller

for Induction Motor Drives," Proc. of XII Brazilian

Automatic Control Conference, Voi. 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 ISLE, 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 the 1997 23rd Annual International

Conference on Industrial Electronics, Control and

Instrumentation, New Orleans, Louisiana, Nov. %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 1EEE 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," IEEE Trans. on

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

1995, pp. 240-247.

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

Control and Dynamics of A C 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 h_dustrv Applications, Vol. 24, No. I, Jan/Feb.

1988, pp. (42-150.

[13] Kenny, B.H., Deadbeat Direct Torque Control of

Induction Machines Using Self-Sensing at Low and

Zero Speeds, Ph.D. thesis, UW-Madison, 2001.

[14] Bollinger, J.G. and Duffle, N.A., Computer Control of

Machines and Processes, Addison-Wesley Publishing

Company, New York, 1988.

[15] Vas, Peter Sensorless Vector and Direct Torque

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

[16] 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.

NASA/TM--2001-211100/REV I 8
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REPORT DOCUMENTATION PAGE OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

September 2002

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Stator and Rotor Flux Based Deadbeat Direct

Torque Control of Induction Machines

6. AUTHOR(S)

Barbara H. Kenny and Robert D. Lorenz

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland, Ohio 44135- 3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546-0001

3. REPORT TYPE AND DAiES COVERED

Technical Memorandum

WU-755-1A-11--00

8. PERFORMING ORGANIZATION

REPORT NUMBER

E- 12945-1

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--2001-211100-REV 1

11. SUPPLEMENTARY NOTES

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.

12a. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified - Unlimited

Subject Category: 33 Distribution: Nonstandard

Available electronically at hnp://gltrs.grc.nasa.gov

This publication is available from the NASA Center for AeroSpace Information, 301_o21-0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

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. SUBJECT TERMS

Direct torque control; Sensorless control; Induction machine; Deadbeat control

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OF REPORT OF THIS PAGE OF ABSTRACT

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