Fuzzy Logic Speed Control Algorithm of Induction Motor Fed by Direct ...

International Journal of Research and Reviews in Computing Engineering Vol. 1, No. 1, March 2011 Copyright © Science Academy Publisher, United Kingdom www.sciacademypublisher.com Science Academy Publisher

Fuzzy Logic Speed Control Algorithm of Induction Motor Fed by Direct Matrix Converter F. Tazerart1, A. Azib1, B. Metidji1, N. Taib1, T. Rekioua1 and P. Le Moigne2 1

Department of Electrical Engineering, University of Bejaia, Algeria Laboratoire d'Electrotechnique et Electronique de Puissance (L2EP) of University of Lille, French

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Correspondence should be addressed to F. Tazerart, [email protected]

Abstract – In this paper, the speed control of an induction motor fed by matrix converter using fuzzy logic controller is proposed. In order to achieve high performance control of matrix converter fed the induction motor drive system, a combined controller Venturini and direct field oriented control (FOC) algorithms is proposed. The present paper focuses about the artificial intelligence technique particularly fuzzy logic speed control of induction motor.

1.

Introduction

The induction motor drives fed by matrix converter have been developed for last two decade. The matrix converter drive has recently attracted the industry application and the technical development has been accelerated because of increasing importance of power quality and energy efficiency issues [1]–[2]–[3]. The ac-ac matrix converter topology was first investigated in 1976 [4]. Then Venturini and Alesina [5] developed the theory by applying the principle of low modulation matrix in high frequency signal synthesis in 1980‘s. They proposed that a multi-phase output could be high frequency-synthesized from a multi-phase input by the direct connection of input to output. The original theory limited the output/input voltage transfer ratio to 0.5 in order to maintain a good quality of sinusoidal input and output. The same researchers later showed [6] that the maximum voltage transfer ratio could be raised to maximum at 0.866 by the use of third harmonic injection techniques. The matrix converter therefore possesses the advantages of both the cycloconverter and the PWM (Pulse Width Modulation) drive, as summarized below [7]:  It can operate in all four quadrants of the torquespeed plane because of its regeneration capability.  Its input current waveform is sinusoidal and the input power factor is unity.  The input power factor may be controlled across the whole speed range.  There is no dc link and therefore no requirement for energy storage devices.  The output voltage and input current waveforms can be controlled such that they are near sinusoidal in form.  The harmonic distortion that is incurred is at

high frequencies  It may be used as direct frequency changer, converting a fixed ac or dc source into a variable ac or dc supply.  Compact converter design.  No dc-link components. Many researchers have studied the matrix converters that drive induction motors. Some researchers investigated the clamp (snubber) circuit design for a matrix converter based on an induction drive system [7]. This research, however, only focused on clamp circuit design. Recently combining the principle of sliding mode, direct torque control (DTC), and space vector modulation (SVM) in high performance sensorless AC drive has been investigated. Efforts towards applying intelligent techniques in resolving matrix converter problems are scarce in the literature. The present paper focuses about the artificial intelligence technique particularly fuzzy logic in the speed control of induction motor. Fuzzy logic is a technique to embody human-like thinking into a control system. The paper is organised in four paragraphs. The Second paragraph describes the matrix converter model, controlled by Venturini Algorithm. In the Third paragraph, the voltage fed induction machine model associated to the field oriented control is presented. In the four paragraph, the proposed technique fuzzy logic for the speed control of induction motor is deduced, and the system performances compared to those of the classic FOC.

2.

Matrix converter model

Figure 1 describes a synoptic scheme of a three-phase to three-phase matrix converter. It includes nine bidirectional switches Sij with turn-off capability that allows the construction of each output phase one from the three input

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cos( t   )  o o   [ I 0 (t )]  I om .cos( o t   o  2. ) 3   cos( t    4. ) o o  3 

phases.

(7)

where ωi, ωo and o are respectively: The input frequency, desired output frequency and displacement factor. 2.2. Venturini Control Algorithm A simplified version of the Venturini algorithm is presented and applied in this section. This algorithm is defined in terms of the three-phase input and output voltages at each sampling instant and is convenient for closed loop operations. For the real-time implementation of the proposed modulation algorithm, it is required to measure any two of the three input line-to-line voltages. Then, the input peak voltage Vim and position ωit are calculated by [9]: Figure 1. Topology of three-phase matrix converter

2.1. Matrix Converter Theory Fundamentals The matrix converter theory is composed of a group of algorithms. The modulation indexes (input/output) mio associated to these nine switches are usually represented as a nine-element matrix M (t) and are used to synthesize [8] : a) The output phase voltages Vo (t) = [Va (t) Vb(t) Vc(t)] T, as a function of the input voltages Vi (t)= [VA(t) VB(t) VC (t)] T b) The input currents Ii(t)=[ IA(t) IB(t) IC(t)] T as a function of the output currents Io (t)=[Ia(t) Ib(t) Ic(t)] T. where

m Aa (t ) m Ba (t ) mCa (t ) M (t )  m Ab (t ) m Bb (t ) mCb (t )  m Ac (t ) m Bc (t ) mCc (t ) 

0  mio  1

(1)

(2)

 mia   mib   mic  1

(3)

[Vo ]  [M (t )]  [Vi ]

(4)

[ I i ]  [M (t )]  [ I o ]

(5)

i  A, B , C

i  A, B , C

i  A, B ,C

The instantaneous input-output transfer matrix M is given in (1), associated to the equality constraints (3). Assuming that the matrix converter is nourished by a three-phase balanced grid, and connected to output balances load, the input voltages Vi(t) and output current vector Io(t) is given by (6),and (7).

cos( t )  i   [Vi (t )]  Vim cos( i t  2. ) 3   cos( t  4. ) i  3 

(6)

4 2 2 2 Vim  (V AB  V BC  V AB .V BC ) 9  i .t  arctan(

V BC ) 2 1 3.(( ).V AB  ( ).V BC ) 3 3

(8) (9)

The target output peak voltage and the output position are calculated by: Vom  2

2 2 2 2 (Va  Vb  Vc ) 3

 o .t  arctan (

Vb  V c 3.Va

(10)

)

(11)

where Va, Vb and Vc, are the target phase output voltages. Alternatively, in the voltage fed induction in FOC operation, the voltage magnitude and angle may be direct outputs of the control loop. Then, the desired voltage ratio is calculated by:

q

Vom Vim

2

2

(12)

In conventional Venturini algorithm, q does not exceed 0.5, but in order to enhance this factor to achieve 0.866, third harmonic terms are added through three factors [9]:

K 31 

2.q . sin( i .t ). sin(3. i .t ) 9.q m

(13)

K 32 

2.q 2. . sin( i .t  ). sin(3. i .t ) 9.q m 3

(14)

1 1 2 1 K 33   Vom .( cos(3. o .t )  . . cos(3.i .t )) 6 4 qm

(15)

where qm = 0.866 is the maximum voltage ratio. This configuration permits the improvement of the motor peak torque and then of the overload capacity. Thus, the three modulation functions for output phase are given by:

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1 2 2 1 M Aa   K31  (Va  K33 ).( .VAB  .VBC ) 2 3 3 3 2.Vim

(16)

1 2 2 1 M Ba   K32  (Va  K33).( .VBC  .VAB ) 2 3 3 3 2.Vim

(17)

M Ca  1  (M Aa  M Ba )

(18)

The modulation functions for the other two output phases, b and c are obtained by replacing Va with Vb and Vc respectively in (16), and (17). Note that the modulation functions have third harmonic components.

3.

9

Decoupling

Direct field oriented control

The field oriented control published for the first time by Blaschke in 1972 [10], consists in adjusting the flux by the stator direct current ids and the torque by the other component iqs. In direct FOC, two regulation loops must be implemented. In addition of the speed outer loop, the second one regulates the rotor flux to its reference value. This method has the advantage to be robust towards parameter variations. Equations (19) give the voltage fed induction machine FOC model, represented in synchronous frame, where the state variables: [ω  dr  qr] T, and the control inputs: [Vds Vqs ωsl] T.

 d ids M2 MR  ( Rs  2 Rr ) ids   Ls s iqs  2 r r Vds   Ls dt Lr Lr   2 V   L d iqs  ( R  M R ) i   L  i  M   s s r qs s s ds r  qs dt L2r Lr

(19)

 d Tr r  r  M ids  dt M  iqs  s1 r  Tr  M Ce  p r iqs Lr 

(20)

d dt

 f .

3.1. Simulation results Simulation of the matrix converter fed induction motor controlled with field oriented control is performed in a comparative way as it will be dealt in the paragraph four. The chosen commutation frequency in the simulation is 2 kHz.

Figure 3. Speed curves

The dynamic equation is given by:

Ce  C r  J

Figure 2. Block diagram of the field oriented control

(21)

Figure 2 describes the drive bloc diagram of the direct FOC used in this paper. The four controllers used are Proportional Integral units, where their values are given in appendix. In addition, the flux estimator is obtained from (20).

Figure 3 shows the motor speed curve for both the classic FOC and for the proposed approach. The motor was started with no-load then at t =2 s, a load torque of 5 Nm is applied at the motor's shaft. One can notice that for the two techniques, the tracking of the reference speed is always guaranteed regardless of the load torque variation.

Figure 4. Torque curves

Figure 4 illustrates the torque curves. It can be seen that for both the two operation modes, the electromagnetic torque

International Journal of Research and Reviews in Computing Engineering follows the load demand. In Figure 5are presented the fluxes components  dr and  qr .

Fuzzy control regulator structure

d/dt

G2

Inference Mechanism

Fuzzyfication

G1

Defuzzyfication

The fuzzy control has the same objective as classical one. However, it is possible to happen of an explicit model of the controlled process. Using linguistic variables in place of numerical variables, that approach represents a substantive departure from the conventional quantitative techniques of system analysis and control. The basic configuration of a FLC (fuzzy logic controller) with three linguistic variables (two inputs and one output) is shown in Figure 6. e

allows expressing under linguistic form the input variables of the regulator at control variables of the system. A fuzzy rule or knowledge base is in the form of two dimensional tables, which can be looked up by the fuzzy reasoning mechanism the fuzzy inference mechanism contains 49 rules. The decision-making unit uses the conditional rules of ‗IF-THEN-ELSE‘. 4.3. Defuzzyfication The Defuzzyfication consists to take a decision i.e. obtaining a real control from the obtained under fuzzy ensemble form. In the case of reasoning based on the inference of fuzzy rules, several methods exist; we have used in this paper the method of the pondered average [11]–[12]– [13].

Figure 5. Flux components

4.

10

G3

4.4. Speed regulation with fuzzy regulator The internal structure of the controller is shown in Figure 7. The necessary inputs to the decision - making unit blocks are the rule-based units and the data based block units. The Fuzzyfication unit converts the crisp data into linguistic formats. The decision making unit decides in the linguistic format with the help of logical linguistic rules supplied by the rule base unit and the relevant data supplied by the data base [11]. The error and the change in error is modeled using the (22), as: e(k )   ref   r e(k )  e(k )  e(k  1)

(22)

where  ref is the reference speed,  r is the actual rotor speed, e (k) is the error and Δe(k) is the change in error.

Rules base

NB

NS

Z

PS

PG

NB

NB

NB

NB

NP

Z

NS

NB

NS

NS

Z

PS

Z

NB

NS

Z

PS

PB

PS PG

NS Z

Z PS

PS PB

PB PB

PB PB

Estimators

Figure 6. Speed fuzzy regulation using fuzzy regulators.

4.1. Input Fuzzyfication The objective of the Fuzzyfication is to transform the determinist variables of input to fuzzy variables, in linguistic variables, with definition of appurtenance functions for these different input variables. Corresponding linguistic values are characterized by the symbols likewise: NB: Negative big; NS: Negative Small; Z: Zero; PS: Positive small; PB: Positive big. And their universe of discourses are assigned to be between [-1, 1] for the inputs, and [-1, 1] for the output variable. The Fuzzyfication maps the error, and the error changes to linguistic labels of the fuzzy sets in Figure 6. In the first stage, the crisp variables e (k) and ∆e (k) are converted into fuzzy variables [11]–[12]. 4.2. Rule Bases and Fuzzy Inference The fuzzy rules represent the center of the regulator; it

FLC

Figure 7. Simulink diagram of controller base system

We have changed the classical PI regulators by fuzzy regulators. The scheme of the decoupling (Fuzzy Field Oriented Controller) is presented on Figure 7. Input variables are normalized with a range of membership functions specified and the normalization factors are named as G1 and G2.

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Figure 11. Load Torque Disturbance ( ± 2Nm) Figure 8. Surface view of fuzzy controller output

4.5. Simulation results In this section, the computer simulation results for a 1.5 KW cage rotor induction machine, using the fuzzy controller described in paragraph four is compared to a conventional controller. The simulation results are effectuated with the output gain of the speed fuzzy regulator G3 = 0,725.

Figure 12. Step response with load using FLC control

The machine is fully loaded and operate at 100 Rad/s and a load disturbance torque 2 Nm is suddenly applied, first, at 0.2 s and then at 2s. When the error and change of error are of opposite linguistic sets i.e. the output of the command torque in the diagonal is zero, the fuzzy controller will reach the command speed and will be holding at this speed. Figure 9. Torque curves

Figure 10. Zoom of transient speed curves

Figure 13. Speed response with inversion sense using FLC control.

Figure 9 and 10, show that, the speed reaches its reference value at 0.15s without overtaking, the electromagnetic torque compensates the resistant torque and presents at starting a value equal to 2 N.m. Figure 10 shows that the system using fuzzy logic and PI control under no load have good performance in terms of settling time.

Figure 14. Torque response with inversion sense Using FLC control

International Journal of Research and Reviews in Computing Engineering Table 1 parameters of induction machine Parameters Symbols Values Shaft power P 1.1 Number of pole pairs p 2 Stator resistance Rs 2.4 Rotor resistance Rr 1.452 Total leakage factor 0.136  Mutual inductance M 0.1 Stator(rotor) self inductance Ls=Lr 0.121 Inertia moment J 0.013 Viscous friction coefficient f 0.002

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units Kw

  H H SI SI

References [1] Figure 15. Motor current curves

Figure 15 shows the motor current curves at steady state (Cr=5Nm). One can notice that the proposed Venturini algorithm provides good currents characteristics, since the dominant harmonics are around the commutation frequency 2 KHz.

Figure 16. Input voltage & current curves

Figure 16 presents both the input voltage and current waveforms. It can be seen that a unity input displacement factor is obtained regardless of the load power factor. This is in fact the main advantage of the matrix converter compared with voltage inverters fed by uncontrolled rectifiers.

5.

Conclusion

In this paper, the fuzzy logic of induction motor fed by a direct matrix converter is presented. The proposed FLC controller has proved its robustness in presence of load disturbances. A comparison between a FLC controller and a PI controller for direct field-oriented induction motor drive has been presented in this paper. The fuzzy regulator has a very interesting dynamic performances compared with the conventional PI-regulator. It allows having fast response without overtaking and minimizing in the case of the rotation sense change. In fact, the fuzzy regulator synthesis is realized without take in account the machine model.

Appendix The motor parameters which are used in simulation are listed in Table 1.

Casadei, D.; Serra G.; Tani A.; "Implementation of a Direct Torque Control Algorithm for Induction Motors Based on Discrete Space Vector Modulation"; IEEE Trans. on Power Electronics, Vol. 15, No. 4; July 2000,PP- 769 777. [2] H.-H. Lee, H. M. Nguyen, and T.-W. Chun, ―Implementation of direct torque control method using matrix converter fed induction motor,‖ Journal of Power Electronics, vol. 8, no. 1, pp. 74-80, Jan. 2008. [3] C. Klumpner, P.Nielsen, I. Boldea, and F. Blaabjerg, ―A new matrix converter-motor (MCM) for industry applications,‖ IEEE Trans. Ind. Electron., vol. 49, no. 2, pp. 325–335, Apr. 2002. [4] M.G.B. Venturini and A. Alesina," Solid state power conversion: a Fourier analysis approach to generalized transformer synthesis," IEEE Trans. Circuit & Systems, 1981, No.4, pp.319-330. [5] M. Venturini, ―A new sine wave in sine wave out conversion technique which eliminates reactive elements,‖ in Pro POWERCON7, 1980, pp. E3-1-E3-15. [6] Alesina, A.; Venturini, M.; ―Intrinsic amplitude limits and optimum design of 9-switches direct PWM AC-AC converters‖ Power Electronics Specialists Conference, 1988. PESC '88 Record., 19th Annual IEEE , 11-14 April 1988,Pages:1284 - 1291 vol.2 [7] R. R. Joshi, R. A. Gupta, and A. K. Wadhwani ‖ Optimal Intelligent Controller for Matrix Converter Induction Motor Drive System‖ Iranian journal of electrical and computer engineering, vol. 6, no. 1, winter-spring 2007. [8] L.Gyugyi and B. Pelly,'' Static power frequency changers,» Wiley, New York, 1976. [9] L. Huber and D. Borojevic, ―Space vector modulated three-phase to three-phase matrix converter with input power factor correction,‖ IEEE Trans. IA, vol. 3 I , pp. 1234-1246, NovlDcc1995. [10] A. Kalantri, M. Mirsalim and H. Rastegar, ―Adjustable speed drive based on fuzzy logic for a dual three-phase induction machine,‖ Electrics Drives II, Electrimacs. August 18–21, 2002. [11] M. P. Veeraiah and S. M. Chitralekha Mahanta, ―Fuzzy proportional Integral–proportional derivative (PI-PD) controller,‖ Proceeding of the 2004 American control conferences, pp. 4028–4033, Boston Massachusetts June 30 – July 2, 2004. [12] W. Y. Wang, and Y. Hsum Li, ″Evolutionary Learning of BMF FuzzyNeural Networks Using a Reduced-Form Geneti Algorithm″, IEEE Transactions on Systems, Man, And Cybernetics—Part B: Cybernetics, Vol. 33, No. 6, pp. 966-976, December 2003

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Farid TAZERART: PhD student in electrical engineering at the University of Bejaia, Algeria. He has had a Bachelor in June 2001, Engineer in electrical engineering in June 2006 option: electromichanical and master in electrical option: Industrial –Electric at the University of Biskra In July 2009. His work field includes the study and control of static converters (power electronics) and their association with electrical machines.

Ahmed AZIB: PhD student in electrical engineering at the University of Bejaia, Algeria. He has had a Bachelor in June 2001, Engineer in electrical engineering in June 2006 and master in electrical option: electro-energetic at the University of Bejaia In July 2009. His work field includes the study and control of static converters (power electronics) and their association with electrical machines.

Brahim METIDJI: was born in Bouira, Algeria He received the M.S degree in electrical engineering from the University of Bejaia, Algeria. Now he is PhD student in electrical engineering at the University of Bejaia, Algeria. His research interests are in variable-speed ac motor drives,in particular, matrix converter.

Nabil TAIB (1977), received his Engineering Degree and Master Degree on Electrical Control Systems in 2001 and 2004 respectively from the University of Bejaia (Algeria). Since 2005 he is preaparing his Doctoral thesis at the same University where the focused research is on the matrix converters and their applications. From 2009, he is assistant master in the Electrical Engineering Department at the University A. Mira of Bejaia (Algeria). He is an Editor Board Member in the International Journal of Computer Science and Emerging Technologies (IJCSET). He is interrested now, by the applications of the matrix converters on the renewable energy systems.

Toufik REKIOUA (1962), received his Egineering Degree from the Polytechnical National School (Algeria) and earned the Doctoral Degree from I.N.P.L of Nancy (France) in 1991. Since 1992, he is assistant professor at the Electrical Engineering department-University A. Mira of Bejaia (Algeria). His research activities have been devoted to several topics: control of electrical drives, modeling and control of A.C machines, the renewable energy systems.

Philippe LE MOIGNE, received his Doctoral Degree in 1990. He si a Professor at central school of Lille where he is a chief of Power Electronics Team in L2EP Laboratory. His researches have been devoted to several topics: new topologies of power converters as matrix converters and there applications.

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