AI based Direct Torque Fuzzy Control of AC Drives.pdf

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International Journal of Electronic Engineering Research

ISSN 0975 - 6450 Volume 1 Number 3 (2009) pp. 233–244

© Research India Publications

http://www.ripublication.com/ijeer.htm

AI based Direct Torque Fuzzy

Control of AC Drives

1Jagadish H. Pujar and

2S.F. Kodad

1 Research Scholar (JNTU, Hyderabad) & Faculty, Department of EEE, BVB

College of Engg. & Tech., Hubli, India E-mail: [email protected] & Head, Department of EEE, Aurora’s Engineering College,

Hyderabad, India

E-mail: [email protected]

Abstract

Fuzzy logic is recently getting increasing emphasis in soft control

applications. This paper presents an application of fuzzy logic to control the

speed of an AC drive system is proposed for space vector pulse widthmodulated (SVPWM) voltage source inverter-fed induction motor drive. This

paper presents the results of an investigation into the suitability of a Direct

Torque Fuzzy Control (DTFC) method for an induction motor drive system.

Direct torque control is known to produce quick and robust response in AC

drive system. However during steady state, torque, flux and current ripple

occurs. An improvement of the AC electric dive speed regulation can be

obtained using a new DTFC method based on space vector modulation (SVM)

which reduces the torque and flux ripples. To validate the proposed method,

the simulation has been carried out using MATLAB-SIMULINK. Simulated

results presented in this paper shown to have low current distortion, low

torque ripple, and a fast torque and speed responses. The simulation resultsverify the superiority of the proposed method to the conventional DTC

method.

Keywords: Fuzzy logic, Direct Torque Control (DTC), Direct Torque Fuzzy

Control (DTFC), Induction Motor (IM), Space Vector Modulation (SVM),

switching table.



234 Jagadish H. Pujar and S.F. Kodad

IntroductionFuzzy logic is recently getting increasing emphasis in soft computing applications in

the recent days. The fuzzy logic control technique has been an active research topic in

automation and control theory since the work of Mamdani proposed in 1974 based on

the fuzzy sets theory of Zadeh proposed in 1965 to deal with the system control

problems which are not easy to be modeled [1]. Hence, the development of high-

performance control strategies for AC motor drives resulted in a rapid evolution. One

of the most popular methods, known as field oriented control has been proposed by F.

Blaschke[2]. In the vector control the motor equations are transformed in a field

coordinate system that rotates in synchronism with the rotor flux vector and hence

FOC controls the induction motor in a same manner as separately excited DC motor.

The disadvantage of this control scheme is inclusion of the pulse encoder, indirect

torque control and also it is quite complex due to reference frame transformations. Toovercome these disadvantages, in the middle of 1980’s, a new quick response

technique for the torque control of induction motors was proposed by Takahashi as

direct torque control (DTC) [3]. DTC provides very quick response with simple control

structure and hence, this technique is gaining popularity in industries [4]. Though DTC

has high dynamic performance, it has few drawbacks such as high ripple in torque,

flux, current and variation in switching frequency of the inverter. The effects of flux

and torque hysteresis band amplitudes in the induction motor drive performance have

been analyzed in [5]. To improve the performance of conventional DTC, modern

resources of artificial intelligence like neural networks, fuzzy logic and genetic

algorithms are implemented [6]. In the following, we will describe the application of

fuzzy logic in DTC [7] [8].The main objective of this paper was to develop the digital simulation software for

direct torque fuzzy control of SVPWM voltage source inverter-fed induction motor

drive to reduce the ripples at all modulation indices and to improve the speed

performance, under transient and steady state uncertainties caused by variation in load

torque replacing conventional DTC by fuzzy based DTC, yields a new type of

induction motor control method called as DTFC. The MATLAB SIMULINK is used

to perform the simulation. The simulated results of this method are discussed and

compared with conventional DTC.

Principle of Conventional DTCDTC principle is widely employed for induction motor drives with fast dynamics [6].

The main notion of the conventional DTC is the rate of change of torque is

proportional to the instantaneous slip between the stator flux and rotor flux under

constant stator flux linkage [5]. DTC has been widely recognized for its fast and robust

torque and flux control. The rotor flux linkage changes slowly compared to the stator

flux linkage, as the rotor time constant of a standard squirrel-cage induction machine is

very large. However, the rotor flux is almost unchanged during a short transient. Thus

rapid changes of the electromagnetic torque can be produced by rotating the stator flux

in the required direction, as directed by the torque command. On the other hand the

stator flux can instantaneously be accelerated or decelerated by applying proper stator



AI based Direct Torque Fuzzy Control of AC Drives 235

voltage phasors. Thus, the simultaneous and decoupled control of torque and flux is

achieved by direct adjustment of the stator voltage in response to the torque and flux

errors [9]. The DTC regularly applies the appropriate voltage vector in order to

maintain the torque and stator flux within two hysteresis bands which results bangbang

behavior and produces variation in witching frequency and significant ripple in flux,

torque and current [8].

DTFC with Voltage Source InverterThe schematic of the basic functional blocks used to implement the proposed DTFC of

induction motor drive is shown in Fig.1. A voltage source inverter supplies the motor

and instantaneous values of the stator flux and torque are calculated from stator

variable by using a closed loop estimator [3]. Stator flux and torque can be controlleddirectly and independently by properly selecting the inverter switching.

VDC

Tref

Tem

Ф S

Ф ref

AC

MOTOR

S

V

M

DTFC Switching

TablePWM

Inverter

Flux andTorque

Estimator

∆ Ф

∆ T

θ

S1

S2

S3

VS

Flux

sector

Figure 1: Direct Torque Fuzzy Control scheme for AC motor drives.

A. Vector Model of Inverter Output Voltage

The SVPWM technique is used to approximate the voltage vector by employing the

one out of eight possible combination of vectors generated by 3-Ф phase voltagesource inverter for AC motor drives is as shown in Fig.2.




VDC

A

B

C

1S 2S 3S

1S 2S 3S

Inducton

Motor

N

Figure 2: SVPWM Iverter for AC motor drives.

In a 3-Ф, voltage source inverter, the switching commands of each limb are

complementary. So, for each limb, logic state Si (where i=1 to 3) is ON (“1”) or OFF

(“0”) can be defined. As there are three independent limbs, there will be eight different

logic states, provides eight different voltages obtained applying the vector

transformation described as:

⎥⎦

⎤⎢⎣

⎡++=

3

4

33

2

213

2 π π

j j

DC s eS eS S V V (1)

Eight switching combinations can be taken according to the above expression (1).

The partitions of d-q plane in to two zero voltage vectors and six non-zero voltagevectors are show in Fig.3.

Figure 3: Partition of the d-q planes in to six angular sectors.

B. Stator Flux and Torque Estimation

The components of the current (Id, Iq) and stator voltage (Vd, Vq) are obtained by the

application of the transformation [3] given by (2) to (5). The components of the stator




flux (ϕd, ϕq) given by (6) and (7) . The stator flux linkage per phase and the

electromagnetic torque estimated are given by (8) and (9) respectively. Ad I I

3

2=

(2)

( )C Bq I I I −=

2

1 (3)

( )⎟ ⎠

⎞⎜⎝

⎛ +−= 321

2

1

3

2S S S V V DC d

(4)

( )322

1S S V V DC q −= (5)

( )dt I RV

t

d S d d ∫ −=

0

φ (6)

( )dt I RV

t

qS qq ∫ −=

0

φ (7)

22

qd s φ φ φ += (8)

d qqd em I I pT φ φ −= (9)

The stator resistance RS can be assumed constant during a large number of

converter switching periods TS. The voltage vector applied to the induction motor

remains also constant over the time period TS. Therefore, resolving first equation of

system leads to:

( )dt I RV

t

S S S S ∫ −=

0

φ (10)

( ) ( ) S S S S T V t += 0φ φ (11)

In equation (11), φS(0) stands for the initial stator flux condition. This equation

shows that when the term RS I S can be neglected in high speed operating condition of

the extremity of stator flux vector VS. Also, the instantaneous flux speed is only

governed by voltage vector amplitude [3] given in (12).

S S V

dt

d ≈

φ (12)

Therefore, by selecting adequate voltage vector one can increase or decrease the

stator flux amplitude and phase to obtain the required performances. The deviation

obtained at the end of the switching period TS can be approached by the first order

Taylor Series. By choosing a suitable sequence of the vectors of tension, one can forcethe end of the vector flux to follow a desired trajectory. To function with a module of

practically constant fluxϕS, it is enough to choose an almost circular trajectory for the

end of the vector flux [3] [5].

C. Switching Table Formation

The vectors Vi+1 or Vi-1 are selected to increase the amplitude of flux, and Vi+2 or Vi-2 to

decrease it when flux is in sector I. Which shows that the choice of the vector tension

depends on the sign of the error of flux is independent of its amplitude [3]. Obviously,

the exit of the corrector of flux must be a Boolean variable. One adds a band of

hysteresis around zero to avoid unwanted commutations when the error of flux is very




small [3] [4]. Indeed, with this type of corrector in spite of its simplicity, one can easily

control and maintain the end of the vector flux in a circular ring form. The switching

table proposed by Takahashi [3] is as given in Table I.

Table I: Switching table for DTFC basis.

Sector

Flux TorqueI II III IV V VI

T=1 V2 V3 V4 V5 V6 V1

T=0 V7 V0 V7 V0 V7 V0 F=1

T=-1 V6 V1 V2 V3 V4 V5

T=1 V3 V4 V5 V6 V1 V2 T=0 V0 V7 V0 V7 V0 V7 F=0

T=-1 V5 V6 V1 V2 V3 V4

Principle of Direct Torque Fuzzy ControlThe DTFC of induction motor drive is designed to have three fuzzy input variables and

one output control variable to achieve fuzzy logic based DTC of the induction machine

[7] [8]. Its functional block diagram is as shown in Fig.4. It requires three input

variables, the stator flux error, electro magnetic torque error and angle of stator flux.

The output is the voltage space vector. The proposed DTFC consists of fuzzification,

rule base, data base, decision making and defuzzification blocks as shown in Fig.4.The input variables ∆Ф, ∆T and θ are fuzzyfied using fuzzy functions over the

respective domains. The output of DTFC is also fuzzyfied using fuzzy singletons. The

all possible fuzzy rules are stored in fuzzy rule base. DTFC takes the decision for the

given input crisp variables by firing this rule base.

VS

θ

∆ T

∆ Ф

µ (∆ Ф )

µ (∆ T)

µ (θ )

F

U

Z

Z

IF

I

C

A

T

I

O

N

DECISION

MAKING

RULE BASE

DATA BASE

FUZZY O / P

D

E

F

U

Z

ZI

F

I

C

A

T

I

O

N

Figure 4: Proposed DTFC functional block diagram.




A. Flux Linkage Error Fuzzification

The flux linkage error is given by ∆Ф = Фref - ФS. Where Фref is the related value of

stator flux and ФS is actual stator flux. Three linguistic values, negative, zero and

positive denoted as N, Z and P respectively are used to fuzzify flux linkage error

domain [9] [10] as shown in Fig.5.

-0.05 0 0.05 ∆ Ф

PZNµ A

1

Figure 5: Flux linkage error domain fuzzification.

B. Electromagnetic Torque Error Fuzzification

The torque error given by ∆T = Tref - Tem. Where Tref is desired torque and Tem is actual

torque. Five linguistic values, negative large, negative small zero, positive small and

positive large denoted as NL,NS, ZE, PS and PL respectively are used to fuzzify

torque error domain [9] [10] as shown in Fig.6.

µ B

-0.025 -0.1 0 0.1 0.025 ∆ T

PLZENL1

NS PS

Figure 6: Electromagnetic torque error domain fuzzification.

C. Stator Flux Linkage Angle Fuzzification

The stator flux linkage angle θ is an angle between stator flux ϕS and a reference axis

is defined as ( )d q φ φ θ 1tan −

= . Twelve linguistic values, θ0 to θ12 are used to fuzzify the

domain of stator flux linkage angle [9] [10] as shown in Fig.7.




θ

θ 0 θ 1 θ 2 θ 3 θ 4 θ 5 θ 6 θ 7 θ 8 θ 9 θ 1 0 θ 11 θ 12 µ C

1

12

23

12

21

12

19

12

17

12

15

12

13

12

11

12

9

12

7

12

5

12

3

120

π π π π π π π π π π π π

Figure 7: Stator flux linkage angle domain fuzzification.

D. Space Vector Voltage Fuzzification

The space vector voltage Vi ( i=1 to 6 ) is fuzzified using six singleton linguistic

values, as V1,V2,V3,V4,V5 and V6 [9] [10] as shown in Fig.8.

µ D

1

V1 V2 V3 V4 V5 V6 V

Figure 8: Space vector voltage domain fuzzification.

E. DTFC Rule Base Design

Each fuzzy rule can be described using the three input linguistic variables ∆ϕ, ∆T and

θ and one output linguistic variable VS in the DTFC rule base. The ith

IF-THEN fuzzy

rule Ri of DTFC can be expressed as:

Ri: IF ∆ϕ is Ai, ∆T is Bi and θ is Ci THEN VS is Di

Where Ai, Bi, Ci and Di are fuzzy membership function values obtained from µA,

µB, µC and µD membership functions of inputs and output linguistic variables of

DTFC respectively for ith

rule [9] [10].

In this paper, Mamdani’s fuzzy rule base model is developed to perform thefunction of proposed DTFC. Obviously the Mamdani’s implication is used to infer the

output of DTFC rule base for any crisp in put values of ∆ϕ, ∆T and θ. In the

defuzzification stage, a crisp value of the DTFC output is computed by using the center

of gravity method.

Simulation and the ResultsTo verify the proposed scheme, a numerical simulation has been carried out by using

MATLAB/SIMULINK. In the performed simulation, certain stator flux and torque

references are compared to the values calculated in flux and torque estimator and the




corresponding errors are sending to the Direct Torque Fuzzy Controller of the

induction motor drive system. The outputs of the flux and torque comparators along

with stator flux linkage angle are used in order to determine the appropriate voltage

vector and stator flux space vector. Vector locations are shown in order to validate the

control strategies as discussed above. A digital simulation studies were made by using

the S-factions and SIMULINK software of MATLAB environment for the system

described in Fig.1. The flux and torque loops of the drive were also designed and

simulated respectively using fuzzy logic control techniques. The feedback control

algorithms were iterated until best simulation results were obtained. The proposed

DTFC is simulink model is developed by using Fuzzy Toolbox.

For the simulation, a four pole, 3 KW, 1500 rpm, three phase, 220/440 volts and 50

Hz induction motor AC drive system is developed using S-functions, Fuzzy Toolbox

and SIMULINK of the MATLAB. The rated parameters of induction motor areRs=4.85Ω, Rr=3.805Ω, Ls=0.275H, Lr=0.274H, Msr=0.258H, J=0.031kgm2 and

B=0.00039. The inverter dc bus voltage is 160 volts. The proposed DTFC AC drive

system dynamic responses were obtained by simulation of the proposed AC drive

system of Fig.1 at a sampling time period of 1000 µs. The pulsating ripple in the actual

torque simulated response of DTFC shown in Fig.11 is very much reduced compare to

the actual torque simulated response of conventional DTC shown in Fig.10 for the

same corresponding estimated torque simulated response shown in Fig.9.

The Direct Torque Fuzzy Control of induction motor presents the advanced

performance to achieve tracking of the desired smooth circular trajectory of stator flux

locus shown in Fig.13. The DTFC speed response shown in Fig.12 rejects the load

disturbance rapidly with no overshoot and with a negligible steady state errorcompared to the conventional DTC. The reason for superior performance of DTFC of

AC drive system is basically adaptive in nature and is able to realize and fire

corresponding stable control fuzzy rules for each input state of inputs ∆ϕ, ∆T and θ.

Figure 9: Estimated torque simulated response.




Figure 10: Conventional DTC torque simulated response.

Figure 11: DTFC torque simulated response.

Figure 12: DTC and DTFC actual speed simulated responses.




Figure 13: DTFC stator flux locus simulated response.

ConclusionsThe paper presents a new approach for speed control of 3-Ф induction motor using

fuzzy logic technique. The paper develops a fuzzy logic based DTC methodology for

AC drive systems is intended for an efficient control of the torque and flux without

changing the motor parameters. Also the flux and torque can be directly controlled

with the inverter voltage vector using SVPWM methodology.

A complete direct torque fuzzy control of SVPWM voltage source inverter-fed

induction motor drive system has been described. The system was analyzed, designed

and performances were studied extensively by simulation to validate the theoretical

concept. The simulation results shows that the proposed DTFC method is superior toconventional DTC in robustness and in tracking precision. It appears from the response

properties that it has a high performance in presence of load disturbances.

The control of speed by DTFC gives fast dynamic response with no overshoot and

negligible steady state error. So, it is concluded that DTFC can be applied for AC

drives and is reliable in a wide speed range. Especially in AC servo motor applications,

where high dynamic performance is demanded. DTFC has a great advantage over

other control methods due to its property of fast torque response. In order to increase

the performance, control period should be selected as short as possible. When the

sampling interval is selected smaller, it is possible to keep the bandwidth smaller and

to control the stator magnetic flux more accurately.

The simulation study clearly indicates the superior performance of DTFC overconventional DTC, because it is inherently adaptive in nature. To make this DTFC AC

drive system fully adaptive, the hybridization of fuzzy with other soft computing

techniques like ANN and Rough Sets will be preferred.

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