[email protected]

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2019 6^th IEEE International Conference on Engineering Technologies and Applied Sciences (ICETAS)

Direct Torque Control of Inverter Fed Three Phase Induction Motor by Implementing Fuzzy Logic

Controller

Sabir Ali

Department of Electrical Engineering University of Engineering and

Technology Lahore Lahore, Pakistan [email protected]

Syed Abdul Rahman Kashif Department of Electrical

Engineering University of Engineering and

Hafiz Qasim Ali*

Department of Electrical Engineering University of Engineering and

Khushbakht Toqueer Department of Electrical

Engineering Imperial College of Business

Studies Lahore Lahore, Pakistan [email protected]

Abstract—This paper presents direct torque controlled (DTC) induction motor drive that employs SVPWM inverter and Fuzzy Logic Controller (FLC). Direct torque control technique is robust and fast responding approach used to obtain high performance torque control of induction machine drives.

Conventional DTC has certain drawbacks like variable switching frequency and high torque ripple due to hysteresis comparators. The DTC with SVPWM inverter has constant switching frequency and low torque ripples. As the conventional PI control requires continuous tuning of gain, so optimization of performance is difficult. So Fuzzy Logic Controller (FLC) technique is proposed to get high performance. The PI and fuzzy logic techniques in speed control loop are successfully implemented in MATLAB/Simulink.

Keywords—Direct Torque Control (DTC); Space Vector Modulation (SVM); Fuzzy Logic Controller (FLC)

I. INTRODUCTION

Induction motor is the most widely used machine because of its reliable operation, considerably less maintenance and low cost. Domestically, induction motor also has wide variety of uses like it is used in fans, blower or grinder etc. and high dynamic performance is not required. By using the speed control drives for induction motor, considerable amount of energy can be saved. The control of induction motor is of three types named, scalar, vector and intelligent controls.

Magnitude of the control variable is varied to achieve scalar control. Due to certain limitations, scalar control is only preferred in steady state [1]. On the other hand, vector control has relations which are valid for dynamic states. Field oriented control (FOC) is a vector control demonstrated by Hesse in 1969 (indirect FOC) and Blachke in 1972 (direct FOC). In FOC control, rotor flux vector control and rotation of transformed coordinate system are in synchronism. When flux is in the direction of d-axis, the q-axis component of stator current is used to control toque [2]. Also the FOC is used in order to get great dynamic performance. On the other hand, FOC has certain drawbacks like the requirement of current controller and two coordinate transformations, performance changing on varying dynamic parameters and rotor time constant [1-2]. To address these issues, a new strategy known as direct torque control (DTC) is employed [3].

The concept of direct torque control was proposed by Takashi and Noguchi in 1986. The major advantage of DTC over previous techniques is that it requires less computational efforts and there is no need of coordinate transformations in DTC [4]. In DTC drive, inverter switching modes are adjusted to control flux and torque independently and directly. The selection restricts the flux and torque errors within their hysteresis bands, and thus better torque response is achieved.

A torque and flux estimator, a voltage vector selection table and a pair of hysteresis comparators are used in conventional direct torque control (CDTC) as shown in Fig. 1 [5, 6]. In this technique, suitable voltage vectors are applied for decoupling of torque and flux. These suitable voltage vectors are limited to their hysteresis band [7, 8]. Because of its prominent characteristics, the DTC of induction motor drive is mostly used in industrial applications. High flux and torque ripples and variable switching frequency are some drawbacks of CDTC [9, 10].

Fig.1.Conventional DTC

The flux and torque ripples of DTC drives can be reduced by two methods. One method is multi-level inverter and the second method is space vector modulation (SVM). In the first method, the complexity and the cost is high [11].

The SVPWM technique is a decent technique as it has maximum output voltage 1.16 times larger than conventional sinusoidal modulation technique. In this technique, motor flux

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and torque are decoupled by locking a dq coordinate’s reference frame with stator flux space vector [12]. Hence stator q-axis and d-axis voltages are used to control motor torque and flux respectively. In SVPWM technique, torque ripples are reduced by calculating switching instant of different space vectors during every sampling period [13].

Fuzzy logic, neural network and neuro-fuzzy are famous intelligent controllers. The simplest controller among these intelligent controllers is fuzzy logic controller [4, 14].

In [1,4,7], PI and fuzzy logic controllers in speed loop of conventional DTC have been used. Each input has five fuzzy sets, as there are two inputs so total number of fuzzy rules 25.

Fuzzy logic controller has certain advantages like fast dynamic response and low torque and flux ripples as compared to PI controller while its selection of gains is not difficult.

In [2, 15], the authors have used fuzzy self-adaptation PI controller block with conventional DTC of induction motor.

The main problem in use of PI controller is the selection of gain. This problem has been addressed by the use of fuzzy logic controller. Fuzzy logic controller uses speed error and change in speed error and gains of PI controller are updated.

In [3,16,17], the authors have used the SVPWM inverter in place of predefined switching tables and flux and torque hysteresis controllers. A constant frequency signal is applied to voltage source inverter by this technique and power gates operate to create a voltage vector which has any direction and magnitude. So, the magnitude of stator flux changes in any direction and change in torque is smooth. PI controllers have been applied in torque and flux control loop and the correct choice of gains of these controllers is main problem. This technique improves DTC and a better alternative to FOC.

In [15], SVM-DTC, artificial neural network speed estimator and fuzzy logic controller have been used. SVM inverter is used for constant switching frequency and to get better torque and flux response. The speed is adjusted by ANN and compared with the reference speed and error is minimized by fuzzy logic controller.

DTC-SVM and full-order speed adaptive stator flux observer is designed in [16]. This observer is designed to make a sensor-less (DTC-SVM) system for speed. This sensor-less drive system has the advantage as it can work in low speed environment with considerably smaller torque ripples and has better dynamic and steady state performance.

DTC-SVM and fuzzy logic controller is implemented in [17]. When motor speed and stator current change then amplitudes of flux and torque hysteresis bands are determined by fuzzy logic controller. This fuzzy based hysteresis band DTC system has better results as compared to fixed band based DTC system.

In [18], three level voltages SVPWM inverter is implemented in DTC of open end winding induction motor.

Calculation of angle of voltage vector and sector is eliminated.

This PWM algorithm generates similar three level voltages as generated by the diode clamped inverters. Flux and torque ripples are reduced by this method.

SVPWM-DTC topology with three level inverter is implemented in [19]. This inverter reduces switching losses and output current ripples. In this technique, flux and torque ripples are comparatively more reduced as compared to DTC- SVM with two level inverter.

In [20], the authors have used three level inverter in conventional DTC and fuzzy logic controller. Torque error, flux error, and flux position are inputs and switching state “n”

is output of fuzzy logic controller. The three level VSI is preferred for high voltage and high power applications.

Switching losses and output current ripples are reduced by this technique.

II. DIRECT TORQUE AND FLUX CONTROL OF INDUCTION MOTOR DRIVE

The stator or rotor flux linkage and the electromagnetic torque of induction motor can be directly controlled by a technique known as direct torque control (DTC). In this technique selection of the proper voltage vector switching states of the VSI is achieved by a space vector pulse width modulation (SVPWM) technique.

A. Direct Flux Control

The electromagnetic torque and stator flux estimators are measured by stator current and voltage signals. The “equation (3)” is used to estimate the stator flux. The reference stator flux ' ѱs*’and estimated stator flux ' ѱs ' are compared to get the flux error which is given as:

s*

s ψ s

ψ = ⁻ψ

Δ ⁽¹⁾

Proportional integral (PI) type flux controller is used to regulate the flux error. The output of this controller is taken as the reference stator voltage component in d-q co-ordinate system.

B. Direct Torque Control

The instantaneous electromagnetic torque and angle in term of stator flux linkage is given by following equations:

(

^*

)

3 *

2 2

s s s s

e ds qs qs ds

p i i

T = ^{ }  ψ ⁻ψ (2)

tan 1 s ds s qs

θ ψ

ψ

−  

 

=   (3) The torque error can be written as:

e*

e T e

T −T

Δ =

(4) Proportional integral (PI) type torque controller is used to regulate the torque error. The output of this controller is taken as the reference stator voltage component v in d-q coordinate system.

C. SVPWM Voltage Source Converter

SVPWM voltage source inverter is most commonly used for control of induction motor. The reason is it provides comparatively less harmonic distortion of voltage and current signals. The schematic model of DTC IMD with SVPWM inverter is shown in Fig. 2. In this technique, the switching time of space vectors is modulated to create a reference voltage.

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Fig.2. DTC with SVPWM inverter

Let us consider a balanced three phase sinusoidal set of voltages. A balanced three phase set of voltages represented in stationary frame and rotating with angular speed ω = 2πf is called space vector. The space vector can be represented as:

^V^_ ⁼^V^d⁺ ^j^V^q⁼ ²₃

(

^V^a( )^t ⁺^a^V^b( )^t ⁺^{a V}² ^c( )^t

)

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1 1

2 1 2 2

3 3 3

0 2 2

an d

bn q

cn

V V V V

V

 − −   

 

   

 

=

   

 

   

   −   

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The switching time of space vectors in each of the six sectors is modulated to create a reference voltage as shown in Fig.4. Two active vectors and two null vectors are used to produce reference voltage 1.

Fig.3. Switching vectors and sectors

Following three steps are followed in order to implement space vector PWM.

Step-1: Transform three phase quantity to two phase quantity and determine , , and angle (α) as shown in figure below:

Fig.4. and voltages

Step-2: In sector 1, is generated by combination of active vectors , and zero vector , or as shown in figure 4.

T= Sampling period For time T1, V1 is applied For time T2, V2 is applied

Switching time calculation in sector 1

Switching time in sector 1 is calculated by the following formulas:

0

1 1 2

1 2 0

1 1

z T

T T T T

ref

T T T

dt dt dt

V V ⁺ V V

+

= + +

    (7)

By integrating the equation (7), we get equation (8)

T_Z*V_ref =T₁*V₁+T₂*V_s ⁽⁸⁾ By dividing the into X and Y coordinate we get the following equations

T^Z^*Vref^cos

( )

α =^T¹²₃Vdc+T²²₃Vdc^cos^{ }  π₃ ^ (9)

( )

2

* sin 2 sin

3 3

Z ref Vdc

T V α =^T ^{ }  π ^ (10) where 0≤ ≤α 60⁰

By solving equation (10), we get:

1

sin 3

* * sin 3

z a

T T

π α π

 − 

 

 

=  

  

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T2 is obtained from equation (11)

2

( )

* * sin sin 3

z a

T T α

= π

  

 

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( )

0 z 1 2

T =T − T +T (13)

Switching time calculation in any sector

Switching time in any sector is calculated by the following formulas:

₁ 1

* * sin

3 3

z

a n

T =T ^ ^π α− + ⁻ π^^ (14) By expanding and solving the above equations, we get:

₁ * * sin cos cos sin

3 3

z

n n

T =T a ^ ^ π^ α− ^ π^ α^ (15) Simplifying the equation (15), we get equation (16)

2

1 1

* * cos *sin sin *cos

3 3

z

n n

T T a ^ α ^ π^ α ^ π^^

   

 

− −

= − + (16)

where n= 1 through 6 and 0≤ ≤α 60⁰

Step-3: Calculation of switching time of every transistor Sector No. 1:

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There are two active voltages (V1 & V2) and a null vector (V0 or V7) during a sampling time T. In a complete cycle, during first time period T, V1 and V2 are applied for time T1 and T2 respectively. During second time period T, V2 and V1 are applied for time T2 and T1 respectively as shown in Fig.6.

In this sector states of switches with respective voltages and time periods are presented in Table.1.

TABLE 1. SWITCHING TABLE IN SECTOR 1

Vector State Time

V 000 /2

V 100

V 110

V 111 /2

V 110

V 100

V 000 /2

Sector No. 2:

There are two active voltages (V2 & V3) and a null vector (V0 or V7) during a sampling time T. In a complete cycle, during first time period T, V2 and V3 are applied for time T1 and T2 respectively. During second time period T, V3 and V2 are applied for time T2 and T1 respectively.

Sector No. 3:

In this sector, the active voltages are (V3 & V4) and a null vector (V0 or V7) during a sampling time T. In a complete cycle, during first time period T, V3 and V4 are applied for time T1 and T2 respectively.

During second time period T, V4 and V3 are applied for time T2 and T1 respectively.

Sector No. 4:

The active voltages here are (V4 & V5) and a null vector (V0 or V7) during a sampling time T. In a complete cycle, during first time period T, V4 and V5 are applied for time T1 and T2 respectively. During second time period T, V5 and V4 are applied for time T2 and T1 respectively.

Sector No. 5:

Sector No. 6:

Table.2 shows the time of switching of all switches in all sectors. From upper switches when S1 is on for time (T1+T2+T0/2) then S4 is on for time (T0/2). When S3 is on for time (T2+T0/2) then S6 is on for (T1+T0/2). When S5 is on for time (T0/2) then S2 is on for time (T1+T2+T0/2).

Similarly, all switches operate in all sectors and we obtain the desire signal.

TABLE 2.SWITCHING TIME TABLE AT EACH SECTOR

Sector Upper Switches

( , , ) Lower Switches ( , , ) 1 S1 = T1+T2+T0/2

S3=T2+T0/2 S5=T0/2

S4 = T0/2 S6=T1+T0/2 S2=T1+T2+T0/2

2 S1 = T1+T0/2

S3=T1+T2+T0/2 S5=T0/2

S4 = T2+T0/2 S6=T0/2 S2=T1+T2+T0/2

3 S1 = T0/2

S3=T1+T2+T0/2 S5=T2+T0/2

S4 = T1+T2+T0/2 S6=T0/2 S2=T1+T0/2

4 S1 = T0/2

S3=T1+T0/2 S5=T1+T2+T0/2

S4 = T1+T2+T0/2 S6=T2+T0/2

S2=T0/2

5 S1 = T2+T0/2

S3=T0/2 S5=T1+T2+T0/2

S4 = T1+T0/2 S6=T1+T2+T0/2

S2=T0/2 6 S1 = T1+T2+T0/2

S3=T0/2 S5=T1+T0/2

S4 = T0/2 S6=T1+T2+T0/2

S2=T1+T0/2

III. PROPOSED MODEL OF FUZZY LOGIC CONTROLLER The fuzzy logic controller is one of the artificial intelligence controllers. A precise mathematical model of the system is required for DTC of induction motor with conventional PI controller. Therefore, high torque and stator flux ripples are produced due to sudden change in load. A fuzzy logic controller is designed to solve this problem, as shown in Fig. 6. The inputs of the FLC are Eωr and change in Eωr and output is reference torque.

Fig.5. Proposed fuzzy logic controller

The characteristics of fuzzy logic controller are as follows:

• Seven fuzzy sets for each input

• Nine fuzzy set for output

• For fuzzification, continuous universe of discourse

• For implication, Mamdani’s ‘min’ operator is used

• For de-fuzzification, ‘centroid’ method is used Numerical variables are converted to linguistic variables by nine fuzzy set as shown in Table.3:

TABLE.3. LINGUISTIC VARIABLES

Sr. No. Linguistic Variables

1 Z=Zero

2 PS=Positive small

3 PM=Positive medium

4 PB=Positive big

5 NS=Negative small

6 NM=Negative medium

7 NB=Negative big

8 PVS=Positive very small 9 NVS=Negative very small

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A. Design of Fuzzy Logic Controller

Below mentioned rules are considered in order to design the controller:

• Retain the present control setting = 0 if both = 0 and = 0 are zero.

• Retain the present control setting if is not zero but is going to achieve this value at an acceptable rate.

• If is increasing then depending upon the sign and magnitude of e pu( )_and , change the control signal and force towards zero.

Fuzzy rules are defined by expert knowledge and experience. Fuzzy logic control rules are shown in Table.4.

TABLE.4:FUZZY LOGIC CONTROL RULES

ce\e NB NM NS Z PS PM PB

NB NVB NVB NVB NB NM NS Z

NM NVB NVB NB NM NS Z PS

NS NVB NB NM NS Z PS PM

Z NB NM NS Z PS PM PB

PS NM NS Z PS PM PB PVB

PM NS Z PS PM PB PVB PVB

PB Z PS PM PB PVB PVB PVB

From fuzzy logic control rules table, fuzzy logic control rules are defined for FLC. 49 fuzzy rules are defined here in order to address the problem discussed in this paper.

IV. SIMULATION AND RESULTS

The MATLAB Simulink based DTC models of induction motor with PI controllers and with Fuzzy logic controllers were developed. The values of parameters of IMD are shown in Table.4.

TABLE 4.PARAMETERS AND VALUES OF IMD

Parameters Nominal Values Nominal Power (P) 149.3×10 VA

Stator Resistance (Rs) 14.85×10 Ω Rotor Resistance (Rr) 9.295×10 Ω Stator Inductance (L1s) 0.3027×10 H Rotor Inductance (L1r) 0.3027×10 H Mutual Inductance (Lm) 10.46×10 H

Inertia (J) 3.1 Kgm

Frequency (F) 50 Hz

The PI and fuzzy logic techniques in speed control loop are successfully implemented as shown in Fig.6 and Fig.7

Fig.6. Implementation of PI controller

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Fig.7. Implementation of fuzzy logic controller A. Results using PI Controller

The results of DTC with conventional PI controller are given below:

Fig.8. Reference torque Te* vs electromagnetic torque Te

Reference torque has been set to 1200 Nm. It is clear from the Fig.10 that electromagnetic torque Te approaches to 1200 Nm and follows the same path as reference torque Te* but there are more ripples in the response. It is clear from Fig.21 that torque ripples are between 270 to 320 Nm in case of PI controller. Load has been applied at time 0.5s and 1.5s. The response of torque changes at the same set time at which load has been applied.

Fig.9. Magnified electromagnetic torque Te

Reference speed N* and rotor speed N are shown in Fig.12. It is clear that rotor is following the reference and there is some deviation from the reference path. The rotor is accelerating and de-accelerating at the rate of 900 rpm/s. The reference speed has been set between maximum value of 500 rpm and minimum value of 0 rpm. The rotor speed does not change and follow the same path as reference speed when load is applied at 0.5s and 1.5s.

Fig.10. Reference speed N* vs rotor speed N

Fig.11. Reference flux* vs flux

Machine nominal flux is has been set 0.8 wb. It is clear from Fig.23 that running condition machine flux is same as reference flux with some ripples.

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Fig.12. Stator Flux dq axis of induction motor

Stator flux trajectory in dq axis of induction motor is shown in Fig.24. Flux is following the circular trajectory and at some places it deviates from the circular trajectory. The dynamic response of PI controller is not fast so flux takes time to reach the reference value and it deviates from the circular trajectory.

B. Results using Fuzzy Logic Controller

The results of DTC with fuzzy logic controller are given below. These results show improvement in response as compared to conventional PI controller.

Fig13. Reference torque Te* vs electromagnetic torque Te

It is clear from the Fig.15 that electromagnetic torque Te approaches to 1200 Nm and follows the same path as reference torque Te* and there are less ripples in the response. It is clear from Figure 16 that torque ripples are between 280 to 310 Nm in case of fuzzy logic controller. There is 20 % improvement in torque response. Load has been applied at time 0.5s and 1.5s. The response of torque changes at the same set time at which load has been applied.

Fig. 14. Magnified electromagnetic torque Te

Reference speed N* and rotor speed N in case of fuzzy logic controller are shown in Fig.17. It is clear that rotor is following the reference speed. The rotor is accelerating and de-accelerating at the rate of 900 rpm/s. The reference speed has been set between maximum value of 500 rpm and minimum value of 0 rpm. The rotor speed does not change and follow the same path as reference speed when load is applied at 0.5s and 1.5s.

Fig.15. Reference speed N* vs rotor speed N

Fig.16. Reference flux* vs flux

Machine nominal flux is has been set 0.8 wb. In case of fuzzy logic controller, machine flux in running condition is same as reference flux as shown in figure below.

Fig.17. Stator Flux dq axis of Induction Motor

By using fuzzy logic controller, stator flux trajectory in dq axis of induction motor is shown in Fig.29. Flux is following the circular trajectory. In this case flux response is better as compared to Fig.24. The dynamic response of fuzzy logic controller is fast so flux follow the same path as the reference flux.

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V. CONCLUSION

In this paper, direct control of induction motor using SVPWM inverter and FLC has been presented. The PI and fuzzy logic techniques in speed control loop are successfully implemented in MATLAB/Simulink. The ripple contents of stator flux, torque and current are minimized. It is clear from magnified potion of torque that torque ripples are between 270 to 320 Nm in case of PI controller. But in proposed model of fuzzy logic controller, torque ripples are minimized and present between 280 to 310 Nm. This results in 20%

improvement in torque response. From the results, it is clear that performance of fuzzy logic controller is better than PI controller. The reason is fuzzy controller can easily be tuned by fuzzy rules and problem of correct choice of PI controller gain has been solved. Speed and flux responses are better in case of proposed scheme than conventional PI control scheme.

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