Steering DTC Algorithm for IPMSM Used in

Electrical Vehicle (EV)- with Fast Response and

Minimum Torque Ripple

Ali Ahmed Adam, Fatih University, Electrical & Electronic Eng. Dept.

Kayhan Gulez*, Ibrahim Aliskan, Yusuf Altun, Yildiz Technical University, Electrical Eng. Dept.

Rahmi Guclu, Muzaffer Metin, Yildiz Technical University, Mechanical Eng. Dept.

aliadam@fatih.edu.tr, gulez@yildiz.edu.tr, ialiskan@yildiz.edu.tr, yaltun@yildiz.edu.tr, guclu@yildiz.edu.tr,

mmetin@yildiz.edu.tr

Abstract- This work focuses on providing sensorless DTC

for IPMSM with minimum torque ripple and at the same

time with a simple algorithm to be implemented with

hardware. The developed algorithm method follows the

principle of steering that corrects the direction of vehicle

from deviation.

The algorithm uses the output of two hysteresis controllers

used in the traditional HDTC to determine two adjacent

active vectors. It also uses the magnitude of the torque

error and stator flux linkage position to select the switching

time required for the two selected vectors. The selection of

the switching time for the selected vector consider the

system inertia and control time delay utilizes a new

suggested table structure, which reduces the complexity of

calculation. The simulation and experimental results of this

proposed algorithm show adequate dynamic torque

performance and considerable torque ripples reduction as

well as lower harmonic current as compared to traditional

HDTC.

Index Terms—Direct torque control, vector motor control

drives, permanent-magnet motors, torque control,

electrical vehicle.

I. INTRODUCTION

Among the electric machine available for vehicle propulsion

applications, Permanent Magnet Synchronous Motors (PMSM)

attract special attention primarily due to its higher power

density, higher efficiency as compared to the other available

machines, however torque ripple and the associated mechanical

vibration play a challenge to be widely used, so many control

algorithms have been developed to deal with the problem.

Generally, the controlling algorithm of the torque of PMSM

follows either Field Oriented Control (FOC) or HDTC. The

HDTC [1-3] involves direct control of stator flux linkages and

generated electromagnetic torque by applying optimum voltage

switching vectors to the inverter supplying the motor.

However, the switching of the power inverter, which updated

only once when the outputs of the hysteresis controllers change

states, constitutes the major source of harmonics in PMSM.

These harmonics cause many unwanted phenomena such as

torque pulsation and the associated mechanical vibration and

acoustic noise.

Recently, many research efforts have been carried out [4-7] to

reduce some of these drawbacks with different degrees of

success. However, due to the problem of rotor position, many

research efforts in using sensorless DTC of PMSM for

electrical vehicle propulsion systems has been considered.

While many sensorless algorithm methods such HDTC and

space vector DTC have been developed, but their practical

application suffer either of high torque ripple as the case in

HDTC or the algorithm method is difficult to be practically

applied as the case in space vector DTC [7]. This work focuses

on the two problems, that is, to provide both sensorless DTC

with minimum torque ripple and at the same time simplify the

algorithm to be implemented with hardware.

II. MODELING AND BAND LIMITATIONS

In HDTC the motor torque control is achieved through two

hysteresis controllers, one for stator flux magnitude error

control and the other for torque error control. The selection of

one active switching vector depends on the sign of these two

errors without inspections of their magnitude with respect to

the sampling time and without considering the system inertia

and delay time. In this section, short analysis concerning this

issue will be discussed based on motor equations in rotor

reference frame given in [8].

A. Flux Band

Consider the motor voltage space vector equation (1),

dtdiRV ssss /Ψ+= .(1)

Where, Vs, is and Ψs are stator space vector voltage, current and

flux linkage respectively.

Equation (1) can be written as: )(/ ssss iRVddt −Ψ= .

For small given flux band ∆Ψso, the required fractional time to

reach the limit of this value from some reference flux Ψ* is

given by:

ssss iRVt −∆Ψ=∆ /0

.(2)

The 11th IEEE International Workshop on Advanced Motion Control March 21-24, 2010, Nagaoka, Japan

978-1-4244-6669-6/10/$26.00 ©2010 IEEE 279

And, if the voltage drop in stator resistance is ignored, the

maximum time for the stator flux to remain within the selected

band around the reference value is given as:

dcsss VVt3200

max // ∆Ψ=∆Ψ=∆ (3)

Thus, if the selected sampling time Ts is large than ∆tmax, the

stator flux linkage no longer remains within the selected band

which causing higher flux and torque pulsation. According to

(3), if the average voltage supplying the motor is reduced to

follow the magnitude of the flux linkage error, the problem can

be solved, i.e. the required voltage level to remain within the

selected band is:

skklevel TVtV /max∆= .(4)

Where, Vkk is the applied active vectors.

Thus, by controlling the level of the applied voltage, the

control of the flux error to remain within the selected band can

be achieved. For transient states, ∆Ψs is most properly large

which, requires large voltage level to be applied in order to

bring the machine into steady state as quickly as possible.

B. Torque Band

The time ∆ttorque for the torque ripple to remain within selected

hysteresis band can be estimated as:

∗∗∆=∆ TetTt torque /00 .(5)

Where, ∆T0; is the selected torque band, Te

* ; is the reference

torque t0; is the time required to accelerate the motor from

standstill to the reference torque Te*.

The minimum of the values given in (3) and (5) can be

considered as the maximum switching time to achieve both

flux and torque bands requirement. However, when the torque

pulsation is the only matter of concern, may be enough to

consider the maximum time as suggested in (5).

Now, due to flux change by ∆Ψs (Fig. 1), the load angle δ

will change by ∆δ. Under dynamic state, this change is

normally small and can be approximated as:

ssss Ψ∆Ψ≈Ψ∆Ψ≈∆ −

/)/(sin1δ (6)

δ

Ψs |∆Ψs|

∆δ

D

d

q

θr

ΨF

Figure 1. Stator flux linkage variation under dynamic state

The corresponding change in torque due to change ∆Ψs can be

obtained by differentiation of torque equation [8] with respect

to δ to have:

s

see TTT

Ψ

∆

∂

∂≈∆

∂

∂=∆

ψ

δδ

δ (7)

Substitute (3) in (7) and evaluate to obtain:

[ ]δδ 2cos)(cos2

3sdsqssqF

sqsd

sLLL

LL

tVPT −Ψ−Ψ

∆=∆ .(8)

Where, ∆t=minimum (∆tmax ,∆ttorque).

Equation (8) shows that ∆T can also be controlled by

controlling the level of Vs.

C. Inertia Effect

To guarantee some smoothness with less ripple and stable

operation of the motor, the energy stored by the rotating mass

of the rotor and load have to be considered in the control

switching operation. With angular velocity ω, the resulted

kinetic energy E is given as 2

2

1ωJE =

. Some of this energy is

dissipated by the damping system as 2

2

1βω=frictionE . The

resultant stored energy due to inertia prevents exact

compensation of the torque errors and result in higher ripple

when exactly the required reference voltage is applied during

complete sampling period Ts. Ignoring the friction effect, the

effect of the stored inertia energy leads additional deviation

load angle as in the following equations:

dt

dJTTT eLe

ω=∆=− (9)

Since the electrical loop constant is much smaller than the

mechanical loop constant (typically 1:100), the resultant

accelerating electromagnetic torque ∆Te due to the applied

active vector can be considered constant during the sampling

time. Integrate (9) twice to have:

00

2

2θωθ ++

∆= s

se TJ

TT .(10)

Where, ω0, θ0 the initial rotor position and angle. The first term

in (10) represent the additional angle movement due to inertia

of the system, that have to be compensated in one sampling

period by arranging the switching system with two active

vectors.

III. THE PROPOSED STEERING DTC “SDTC” ALGORITHM

When you try practically to compensate exactly for the torque

error by applying the exact required reference voltage, the

system inertia takes the torque error into a new value before

the completion of the compensating operation. Thus, applying

a voltage of Vref ± ∆V may result in better torque error

compensation and smooth driving force. ∆V is account for the

unseen error taking the system inertia, sign of the torque error

rate, and control system delay time into consideration. The

compensated voltage Vref is composed of two adjacent active

vectors Vk1 and Vk2 applied in the same sampling period. The

vectors are selected logically according to the torque error, flux

error and flux position. The timing of the two vectors is

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selected according to the level of torque error and the rate of

torque error change. One of the two active vectors “Vk1 “ is

used to accelerate the rotor to compensate for the measured

torque error while the second active vector “Vk2” is used to

slightly decelerate the instantaneous torque being past the

reference torque as result of fast compensation of the torque

error during the role of Vk1. Fig.2 shows the process idea of

compensating the torque errors. Vk1 will be applied for a period

tk1 to compensate the torque error ∆T, the zero vector V0 will

be applied for t0/2 where, then the motor runs under inertia

effect passing the reference torque according to (10) as angle

deviation J

tT ke

2

2

1∆=′∆δ . Vk2 will now be applied for period

tk2 to compensate for this deviation, thereafter; zero vectors

will be applied for t0/2. The two active vectors keep the flux in

the same direction, but one vector has the ability to increase the

torque while the other has the ability to decrease the load. The

switching time of the active vectors will be determined from

the torque error level, flux position as well as flux error that

related to inertia effect as in (6).

Vk1

Vk1

Vk2

Vk2

V0

V0

Vk1

V0 Vk2

+∆T

-∆T

Tref

Figure 2. Torque compensation according to the suggested Steering DTC

The basic structure of the proposed algorithm is shown in

Fig. 3.

Figure 3.The proposed Steering DTC system of PMSM

A. Vector selector

In Fig.3 the vector selector block contains algorithm to

select two consecutive active vectors Vk1, and Vk2 depending

on the output of the hysteresis controllers of the flux error and

the torque error; φ and τ respectively as well as flux sector

number; n. The proposed vector selection table is shown in

Table I.

TABLE I ACTIVE VECTORS SELECTION TABLE

In the above table,

if Vk>6 then Vk =Vk-6 ; if Vk<1 then Vk =Vk+6.

B. Flux & Torque estimator

In Fig.3, the torque and flux estimator utilizes (1) to estimate

flux and torque values at m sampling period as follows:

sDsDDD TiRmVmm ))1(()1()( −−+−=ψψ (11)

sQsQQQ TiRmVmm ))1(()1()( −−+−=ψψ .(12)

With, )()( 222mm QDs ψψψ += &

)(

)(tan 1

m

m

D

Q

sψ

ψρ −=

The stationary D-Q axis voltages and currents are:

TstVtVmV kDkkDkD /)()1( 2211 +=−

TstVtVmV kQkkQkQ /)()1( 2211 +=− (13)

2/))()1(( mimii DDD +−=

2/))()1(( mimii QQQ +−= (14)

The torque can be calculated using estimated flux as:

))()()()((23 mimmimPT DQQDe Ψ−Ψ= (15)

C. The Timing Selector Structure

In Fig.3, the timing selector block contains algorithm to

select the timing pairs of vectors Vk1 and Vk2. The selection of

timing pairs depends on two axes, one is the required voltage

level and the other is the reflected flux position in the sector

between Vk1 and Vk2 given as:

60modsρα = (16)

Fig. 4 shows the proposed timing structure. In this figure, the

angle between the two vectors Vk1 and Vk2 is divided into 5

equal sections α-2, α-1, α0, α+1, and α+2. The required voltage

level is also divided into 5 levels, in addition to the level

required at transient states when the required voltage vector is

greater than 2/3 Vdc. The time pairs (tk1,tk2), define the timing

periods of Vk1 and Vk2 respectively. The remaining time

points, (t0=Ts-tk1 -tk2), is for the zero vectors V0 and V7.

Figure 4. Timing diagram for the suggested algorithm

φ τ Vk1 Vk2

1

1

1

0

n+1

n-1

n+2

n-2

0

0

1

0

n+2

n-2

n+1

n-1

281

The switching time tk1 is determined as ∆t tk1=minimum (∆tmax

,∆ttorque), while tk2 is determined according to the inertia effect

as 02

2

T

Jtk

∆

′∆=

δ. These times can also roughly be

determined as in Fig. 4 to reduce calculations.

The implementation of the proposed algorithm may be

summarized as:

1. Define timing table (Fig.4) ; load initial values

Loop: 2. Read sensed values: currents, dc link voltage and

speed for speed control

3. Calculate iD, iQ, VD, VQ, ΨD ,ΨQ , ρs & Te

4. Calculate ∆Ψs , ∆T. Find Hysteresis controllers

output values φ and τ . Find sector number n

5. Determine tk1,tk2 & t0. Get vectors Vk1 , Vk2

6-Apply switching pattern V0, Vk1 , Vk2.

7. Loop

The switching can follow the space vector modulation as

shown below:

INVERTER SWITCHING

Send Vk1, Delay tk1/2

Send Vk2, Delay tk2/2

Send V7, Delay t0/2

Send Vk2, Delay tk2/2

Send Vk1, Delay tk2/2

Send V0, Delay t0/2

IV. SIMULATION AND EXPERIMENTAL RESULTS

To examine the performance of the proposed SDTC

algorithm, two Matlab/Simulink models, were programmed.

The torque dynamic response with HDTC and the proposed

SDTC are shown in Fig. 5. The reference torque for both

algorithms is changed from +2.0 to -2.0 and then to 3.0 Nm. As

shown in the figures, the dynamic response with the proposed

algorithm is adequately follows the reference torque with lower

torque ripples which in turn, result in reduced motor

mechanical vibration and acoustic noise, this reduction also

reflects in smoother speed response. The dynamic torque

experimental result on prototype PMSM is shown in Fig. 6. It

is cleared that the ripple is greatly reduced or some acceptable

level.

(b)

Figure 5. Motor dynamic torque response (a) HDTC, (b) SDTC

Figure 6. Experimental measured Torque dynamic for both HDTC and the

proposed SDTC

The motor performance results under steady state are shown

in Fig. 7-10. Fig.7 shows the experimental phase currents of

the motor windings under HDTC and the proposed SDTC,

observe the change of the waveform under proposed method, it

is clear that the phase currents approach sinusoidal waveform

with almost free of current pulses.

(a)

(b)

Figure 7. Line currents when the motor is loaded: (a) HDTC (b) SDTC

(a)

282

In Fig. 8, the spectrum of phase-a with HDTC shows

harmonic currents with THD. of ~20% which, reflected as

parasitic ripples components in the motor developed torque.

When the proposed algorithm is used, the THD is effectively

reduced to less than 2% as in Fig. 9, observing the change of

the waveform. Better waveform can be obtained by direct

calculation of the times tk1 and tk2 or increasing the partition of

the timing structure. Fig. 10 shows the experimental result of

the measured study state flux.

Fig. 8 Phase-a current and it is spectrum of HDTC

Fig. 9 Phase-a current and it is spectrum of the proposed SDTC

show the experimentally measured study state flux.

Figure 10. Experimentally measured study state flux

V. CONCLUSIONS

In this paper, new direct torque algorithm for IPMSM that

considering the inertia effect in the switching operation was

analysed and simulated. The algorithm uses the output of two

hysteresis controllers to determine two adjacent active vectors.

The algorithm also uses the magnitude of the torque error to

approximate the required average voltage level and then

together with the reflected stator flux position to select or

calculate the switching time required for the selected vectors.

The selection of the switching time can utilize simple table

structure which, simplify the calculation. The simulation and

experimental results of the algorithm show adequate dynamic

torque and considerable torque ripples reduction as well as

lower harmonic current on a “Quarter Electrical Vehicle

Model”.

ACKNOWLEDGMENT

Authors thank for Yildiz Technical University/ Scientific

Research Projects Coordination Department for the support of

29-04-02-02 numbered project “Control Systems Applications

on Quarter Electrical Vehicle Model”.

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