Fuzzy Speed Regulator for Induction Motor DirectTorque Control Scheme by ides editor

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

Fuzzy Speed Regulator for Induction Motor Direct Torque Control Scheme 1

Jagadish H. Pujar 1,

S. F. Kodad 2

Research Scholar JNTU, Anantapur & Faculty Department of EEE, B V B College of Engg. & Tech., Hubli, India Email: jhpujar@bvb.edu 2 Professor, Department of EEE, Aurora’s Engineering College, Hyderabad, India Email: kodadsf@rediffmail.com the performance of conventional DTC a fuzzy logic controller is used along with conventional DTC [7]. The main objective of this paper is to simulate the fuzzy speed regulator for induction motor direct torque control scheme to improve the speed regulation performance under transient and steady state uncertainties caused by variation in load torque which in term replacing PI regulator of DTC by FLC.

Abstract—This paper presents a novel design of a control scheme for induction motor as a fuzzy logic application, incorporating fuzzy control technique with direct torque control method for induction motor drives. The direct torque control method has been optimized by using fuzzy logic controller instead of a conventional PI controller in the speed regulation loop of induction motor drive system. The presented fuzzy based control scheme combines the benefits of fuzzy logic control technique along with direct torque control technique. Compared to the conventional PI regulator, the high quality speed regulation of induction motor can be achieved by implementing a fuzzy logic controller as a PI-type fuzzy speed regulator which is designed based on the knowledge of experts without using the mathematical model. The stability of the induction motor drive during transient and steady operations is assured through the application of fuzzy speed regulator along with the direct torque control. The proposed fuzzy speed regulated direct torque control of induction motor drive system has been validated by using MATLAB simulink.

II. INDUCTON MOTOR STATE MODEL The dynamic input and out put equations of induction motor are formulated as a state model in the stator reference frame under the assumptions of linear magnetic circuits, equal mutual inductances and neglecting iron losses as follows; (1) X& (t ) = A X (t ) + B U (t ) (2) Y (t ) = C X (t ) Where A is the system, B is the control and C is the observation matrices. And X(t) is the state, U(t) is input and Y(t) is out put vectors with elements as follows;

Index Terms—Fuzzy Logic Control (FLC), Direct Torque Control (DTC), Induction Motor (IM), Space Vector Modulation (SVM), switching table.

X (t ) T = [i sd i sq φ sd φ sq ]

I. INTRODUCTION

⎡ V sd ⎤ U (t ) = ⎢ ⎥ ⎣ V sq ⎦

Fuzzy logic is recently getting increasing emphasis in drive control applications. Recent years, fuzzy logic control has found many applications in the past two decades. This is so largely increasing because fuzzy logic control has the capability to control nonlinear uncertain systems even in the case where no mathematical model is available for the control system [1]. So, the development of highperformance control strategies for AC servo system drives resulted in a rapid evolution. To overcome the disadvantages of vector control technique, 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) [2]. DTC provides very quick response with simple control structure and hence, this technique is gaining popularity in industries [2]. 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 [3]. To improve

⎡ ⎢− δ ⎢ ⎢ ⎢ 0 A=⎢ ⎢M ⎢τ ⎢ ⎢ ⎢ 0 ⎣

−

0 M

τ T

−ω

−

⎡ 1 ⎢σL B =⎢ ⎢ ⎢ 0 ⎣ ⎡1 C = ⎢ ⎣0

−δ

1 σL

0 0

⎤ 0⎥ ⎥ ⎥ 0⎥ ⎦

0 1

(4)

ω (1 − σ )⎤ σM ⎥ ⎥ ω (1 − σ ) ⎥ σM τ ⎥

1−σ σM τ ω (1 − σ ) − σM

τr =

⎡ i sd ⎤ Y (t ) = ⎢ ⎥ ⎣ i sq ⎦

(3)

0 ⎤ 0 ⎥⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦

(5)

(6)

(7)

2 ⎛ 1 1−σ ⎞ ; Lr ; L ⎟⎟ τ s = s ; σ = 1 − M ; δ = ⎜⎜ + Rr Rs Lr Ls ⎝ στ s στ r ⎠

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

Where ω represents rotor speed. Rs and Rr are the stator and rotor resistances respectively. Ls, Lr are the stator and rotor self-inductances and M is the mutual inductance respectively. The electromagnetic torque developed by the induction motor is expressed as,

T em =

3 P (i sq φ sd − i sd φ sq 4

)

dω + Bω + TL dt

(11)

2π ⎞ ⎛ V CN = V m cos ⎜ ω t + ⎟ 3 ⎠ ⎝

(12)

(

2 V AN + aV BN + a 2VCN 3 where i = 0 to 7

Vi =

(8)

Where φ sd, and φ sq, are respectively, the stator fluxes projections on the (d, q) axis reference frame. The induction motor electromagnetic torque and load torque balancing under equilibrium can be expressed as, T em = J

2π ⎞ ⎛ V BN = V m cos ⎜ ω t − ⎟ 3 ⎠ ⎝

)

(13)

These three phase voltages are applied to the three phase induction motor employing the equation (13). The three phase bridge inverter of Fig.1 has eight permissible switching states. The switching states and the corresponding phase to neutral voltage of isolated neutral induction motor are summarized in Table.I in which “0” is off state and “1” is on state indication for the switches S1 to S3.

(9)

Where J is the moment of inertia of the rotor, B damping coefficient and TL is the load torque. From the above mathematical representation, we can see that the dynamic model of an induction motor is a strongly coupled nonlinear multivariable system. The control problem is to choose (Vsd , Vsq) in such a way as to force the motor electrical angular speed ω and the rotor flux magnitude φ s=[ φ 2sd + φ 2sq]1/2 to track given reference

Table 1 SVM Iverter Switching States

VAN

VBN

VCN

values by denoted ωref and φ ref respectively. Note that the choice of a reference frame rotating at the same angle and is more suitable for the control problems since in this frame the steady state signals are seems to be constant.

2VDC /3

-VDC /3

VDC /3

-2VDC /3

-VDC /3

2VDC /3

-VDC /3

-2VDC /3

VDC /3

III. DTC SCHEME FOR INDUCTON MOTOR DRIVE

-VDC /3

2VDC /3

A. Working Strategy of Conventional DTC The SVM technique is used to approximate the voltage reference vector by employing the combination of two out of eight possible vectors generated by the three phase voltage source inverter for IM drive is as shown in Fig.1.

VDC /3

-2VDC /3

VDC /3

Consider, for example state V5 space vector voltage is,

V5 =

Vi =

B N C

The three phase sinusoidal instantaneous voltage equations of three phase inverter of Fig.1 are as follows. (10)

2π 4π j j ⎡ ⎤ 2 VDC ⎢ S1 + S 2e 3 + S3e 3 ⎥ 3 ⎣⎢ ⎦⎥

(15)

Eight switching combinations can be taken according to the above expression (15). So, the partitions of d-q plane in to two zero voltage vectors and six non-zero voltage vectors are as shown in Fig.2.

Inducton Motor

Figure 1. SVM Inverter for Induction Motor Drive

V AN = V m cos ω t

(14)

As there are three independent limbs, there will be eight different logic states, provides eight different voltages obtained applying the vector transformation described as:

A VDC

− V DC 2V ⎞ 2 ⎛ − V DC +a + a 2 DC ⎟ ⎜ 3⎝ 3 3 3 ⎠

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

we can write, the expression for change in stator flux over the sampling time period TS as,

φ S (k + 1) ≈ φ S (k ) + V S TS

(24)

Δφ S ≈ φ S (k + 1) − φ S (k ) ≈ V STS

(25)

Equation (25) implies that by applying a vector of tension which is co-linear in its direction, we can increase the stator flux. Therefore, by selecting adequate voltage vector one can increase or decrease the stator flux amplitude and phase to obtain the required performances [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. If V0 or V7 is selected, then the rotation of flux is stopped and the torque decreases whereas the module of flux remains unchanged. Which shows that the choice of the vector tension depends on the sign of the error of flux is independent of its amplitude [5].

Figure 2. Partition of the d-q planes in to six angular sectors

B. Stator Flux and Torque Estimation The components of the current (Isd, Isq) and stator voltage (Vsd, Vsq) are obtained by the application of the transformation [5] given by (1) and (2). The components of the stator flux (ϕsd, ϕsq) are given by (18). The stator flux linkage per phase and the electromagnetic torque estimated are given by (19) and (21) respectively. 1 2 (16) (I B − I C ) I sd = I A & I sq = 3 2 1 2 1 ⎛ ⎞ VDC(S2 − S3 ) (17) Vsd = VDC ⎜ S1 − (S 2 + S3 )⎟ & Vsq = 3 2 2 ⎝ ⎠ φ sd =

∫ (V t

)

− R S I sd dt & φ sq =

∫ (V t

Table II Switching table for DTC basis Sector Flux F=1

)

− R S I sq dt (18)

φs =

φ sd2 + φ sq2

F=0

(19)

The angle between referential and stator flux is given by ⎛φ ⎞ (20) θ = tan − 1 ⎜⎜ sd ⎟⎟ φ ⎝ sq ⎠

Tem = P (φsd I sq − φsq I sd )

(

)

φS (t) =φS (0) +VSTS

III

T=1

T=0

T=-1

T=1

T=0

T=-1

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 [2] [5]. 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 [2] is as given in Table.II. The voltage vector switching table receives the input signals from change in flux hysteresis controller, change in torque hysteresis controller and another signal from space vector modulation block, hence develops the appropriate control voltage vector switching states for PWM inverter according to the Table II.

(21)

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 also remains constant over the time period TS. Therefore, resolving first equation of system leads to;

φ S = ∫ V S − RS I S dt →

Torque

(22)

In equation (22), φS(0) stands for the initial stator flux condition. This equation shows that when the term RSIS 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 (23). dφ S (23) ≈V S dt The vector tension applied to the induction motor remains constant during the sampling time period TS. Thus

D. Hysteresis controllers The change in flux and change in torque are compensated by using two hysteresis controllers as represented in below Fig.3 respectively. 1 0

1 ∆φ S

0 -1

∆Tem

Figure 3. Flux and Torque Hystereses controllers respectively

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

C. PI-type Fuzzy Logic Controller as a Fuzzy Speed Regulator

The change in flux is compensated using one level hysteresis band as shown Fig.3. But, as the dynamic torque is generally faster than the flux, the use of a compensator with two level hysteresis band is used in order to adjust the change in torque and minimize the frequency switching average as shown in Fig.3 [7]. IV. STRATEGY OF

PROPOSED FUZZY SPEED FOR IM DTC SCHEME

e(k)

z-1

REGULATOR

ωre f ω

Фr FLC

Te m TL

Hysteresis Controlle r Flu x and Torque Estimator

VDC

The fuzzy logic controller is basically an input output static non-linear mapping technique. The PI-type FLC control action can be expressed as [6], (26) du(t ) = K e(t ) + K ce(t ) I

Where KP and KI are proportional and integral gains. On integrating above equation, we get (27) u (t ) = K e(t ) + K ∫ e(t )dt

PWM Inverter

The discrete form of equation (21) can be expressed as, (28) du(k ) = K e(k ) + K ce(k )

Equation (28) is a PI-type FLC with non-linear gain factors. The fuzzy associative memory (FAM) of Mamdani rule base model to develop the PI-type FLC as a fuzzy speed regulator which in term replace the PI speed regulator of conventional DTC [8] is given in Table. III.

iq Encoder Z -1

z-1

S V M

u(k)

In the DTC scheme of SVM voltage source inverter-fed induction motor drive system, simultaneous control of the torque and the flux linkage was required. So, the reference torque to DTC is fed from speed loop of the IM drive as shown in Fig.5 which is regulated using PI-type FLC shown inFig.6. In which K1, K2 and K3 are normalization factors. The input linguistic variables speed error e(k), change in speed error ce(k) and output linguistic variable du(k) membership functions will be divided into seven fuzzy sets with the linguistic values NL (negative large), NM (negative medium), NS (negative small), ZE (zero), PS (positive small), PM (positive medium), PL (positive large) respectively.

VDC Switching Table

du(k) K3

Figure 5. Basic Structure PI-type Fuzzy Logic Controller

A. The structure of Fuzzy Speed Regulator for Induction Motor DTC Scheme The DTC scheme of Induction Motor drive system includes flux and torque estimators, flux and torque hysteresis controllers, fuzzy logic controller as a fuzzy speed regulator and a switching table and a three phase PWM inverter as shown in Fig.4. In addition, we need a DC bus voltage sensor and two output current sensors for flux and torque estimation [7]. Hysteresis Controlle r

FLC

ce(k)

The proposed DTC employs an induction motor model to predict the voltage required to achieve a desired output torque [5]. By using only current and voltage measurements, it is possible to estimate the instantaneous stator flux and output torque. An induction motor model is then used to predict the voltage required to drive the flux and torque to the demanded values within a fixed time period. This calculated voltage is then synthesized using SVM.

Ф ref

Figure 4. The Structure of Fuzzy speed regulator for IM Direct Torque Control scheme

Table III

FAM of FLC as a Fuzzy Speed Regulator of IM

B. Fuzzy Logic Controller Concepts In the research work considered in this paper, fuzzy logic controller is used to coordinate between the various parameters induction motor drive system as shown in the block diagram of the Fig.5. These fuzzy controllers have got a lot of advantages compared to the the conventional PI controllers, such as the simplicity of control, low cost, high reliability, compactness of the hardware as fuzzy logic controller just makes use of fuzzy rules and the possibility to design without knowing the exact mathematical model of the process [1].

ERRO R (e)

CHANGE IN ERRO R (ce)

PB ZE

NVB

PVB

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

V. SIMULATION AND RESULTS

Vector locations are shown in order to validate the control strategies as discussed above. The digital simulation studies were made by using MATLAB environment for the system described in Fig.4. The speed regulation loop of the induction motor drive is designed and simulated with fuzzy logic controller. The feedback control algorithms were iterated until best simulation results were obtained. The system dynamic responses obtained by simulation were shown in Fig.5 and Fig.6 for stator current, torque and speed to conclude the comparative results of conventional DTC with PI speed regulator and proposed DTC with FLC as a fuzzy speed regulator. The DTC with FLC as a fuzzy speed regulator of IM presents the high quality performances compare to the conventional DTC with PI speed regulator shown in Fig.6 and Fig.7.

To 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 the driver and errors are sending to the hysteresis comparators. The outputs of the flux and torque comparators are used in order to determine the appropriate voltage vector and stator flux space vector.

CONCLUSIONS The paper presents a new approach for speed control of three phase induction motor using fuzzy logic technique. The paper develops a DTC with FLC 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 SVM technique. Two independent hysteresis controllers are used in order to satisfy the limits of the flux and torque. The proposed system was analyzed, designed and performances were studied extensively by simulation to validate the theoretical concept. The simulation results shows that the proposed DTC with FLC as a fuzzy speed regulator is superior to conventional DTC with PI speed regulator in robustness, in tracking precision and in presence of load disturbances because FLC is inherently adaptive in nature.

Figure 6. Conventional DTC simulated responses with PI speed

regulator

REFERENCES [1] Jagadish H. Pujar, S. F. Kodad “Simulation of Fuzzy Logic Based Direct Torque Controlled Permanent Magnet Synchronous Motor Drive”, Proceedings of the International Conference on Artificial Intelligence- ICAI'09, Vol. I, pp. 254-257, July 13-16, 2009, Las Vegas Nevada, USA. [2] Takahashi I, Naguchi T. “A new quick-response and highefficiency control strategy of an induction motor”. IEEE Transactions on Industry Application [ISSN 0093-9994], 1986, IA-22(5): 820-827. [3] D. Casadei, G. Grandi, G. Serra, A. Tani ”Effectes of flux and torque hysteresis band amplitude in direct torque control of induction machines”, IEEE-IECON-94, 1994, 299–304. [4] Jia-Qiang Yang, Jin Huang, ″Direct Torque Control System for Induction Motors With Fuzzy Speed Pi Regulator″ Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Guangzhou, 18-21 August 2005. [5] R.Toufouti S .Meziane ,H. Benalla, “Direct Torque Control for Induction Motor Using Fuzzy Logic” CGST Trans. on ACSE, Vol.6, Issue 2, pp. 17-24, June, 2006. [6] Lee, C. C. “Fuzzy Logic in Control System: Fuzzy Logic Controller”, Part I/II, IEEE Trans. Systems Man. Cybernet 20 (1990), 404-435. [7] Hui-Hui Xia0, Shan Li, Pei-Lin Wan, Ming-Fu Zhao, ″Study on Fuzzy Direct Torque Control System″, Proceedings of the Fourth International Conference on Machine Learning and Cybernetics, Beijing, 4-5 August 2002.

Figure 7. Proposed DTC simulated responses with Fuzzy speed regulator

ACEEE Int. J. on Electrical and Power Engineering, Vol. 01, No. 03, Dec 2010

[8] Jagadish H. Pujar, S. F. Kodad “Digital Simulation of Direct Torque Fuzzy Control of PMSM Servo System”, International Journal of Recent Trends in EngineeringIJRTE, Vol. 2, Nov. 2009 Issue, pp. 89-93, Academy Publishers, Finland.

Dr. S. F. Kodad received the M.Tech. degree in Energy Systems Engg. from JNTU, Hyderabad, India in the year 1992. He received his Ph.D. degree in Electrical Engg. from JNTU, Hyderabad, India in the year 2004. Currently, he is working as Professor and Head in Aurora College of Engg., Hyderabad, Andhra Pradesh, India in the Dept. of Electrical & Electronics Engg. He has published a number of papers in various national & international journals & conferences & done a number of in-house & industry projects. He is also guiding a number of PhD. His area of interests is neuro-fuzzy systems, Renewable energy systems, etc.

Mr. Jagadish. H. Pujar received the M. Tech in Power and Energy Systems from NITK Surthkal, Mangalore University in the year 1999. Currently, he is working as an Asst. Professor in B V B College of Engineering & Technology, Hubli, Karnataka, India in the Dept. of Electrical & Electronics Engg. & simultaneously pursuing his Ph.D. in Electrical & Electronics Engg. from the prestigious Jawaharlal Nehru Technological University, Anatapur, Andhra Pradesh, India. His area of interests is Soft Computing techniques based systems.