A Comparison of Various Strategies for Direct Torque Control of Induction Motors

Lamia YOUB , Aurelian CRACIUNESCU

POLITEHNICA University of Bucharest, Electrical Engineering Faculty, 313, Splaiul Independentei, 060042 Bucharest, Romania,

youblamia@yahoo.fr

Abstract- In this paper three new direct torque control strategies are compared with the classical direct torque control scheme. The considered new strategies are the following: direct torque control strategy with fuzzy logic regulators instead of hysteresis regulators, direct torque control strategy with hysteresis regulators associated with fuzzy logic regulators, and direct torque control strategy with fuzzy, hysteresis and space vector modulation respectively. A comparison analysis among the classical direct torque control strategy and the new ones, made by simulation in MATLAB/SIMULINK, a given. Keywords— Induction machine, Direct torque control Fuzzy logic.

I. INTRODUCTION

In applications of high-performance induction motor

drives such as motion control, it is usually desirable that the motor can provide good dynamic torque response as is obtained from dc motor drives. Many control schemes have been proposed for this goal, among which the vector control or sometimes called field oriented control has been recognized as one of the most effective methods [1, 2, 3]. It is well known that vector control needs quite complicated coordinate transforms on line to decouple the interaction between flux control and torque control to provide fast torque control of induction motor. Hence the algorithm computation is time consuming and its implementation usually requires using a high performance DSP chip. In recent years an innovative control method called direct torque control (DTC) has gained the attraction of researchers, because it can also produce fast torque control of the induction motor and does not need heavy computation on-line, in contrast to vector control.

Basically direct torque control employs two hysteresis controllers to regulate stator flux and developed torque respectively, to obtain approximately decoupling of the flux and torque control. The key issue of design of the DTC is the strategy of how to select the proper stator voltage vector to force stator flux and developed torque into their prescribed band. The hysteresis controller is

usually a two-value bang-bang controller, which results in taking the same action for the big torque error and small torque error. Thus it may produce big torque ripple. In order to improve the performance of the DTC it is natural to divide torque error into several intervals, on which different control action is; taken. As the DTC control strategy is not based on mathematical analysis, it is not easy to give an apparent boundary to the division of torque error. Fuzzy control is a way for controlling a system without the need of knowing the plant mathematic model. It uses the experience of people's knowledge to form its control rule base. There have appeared many applications of fuzzy control on power electronic and motion control in the past few years [9, 10]. A fuzzy logic controller was reported being used with DTC [7]. However there arises the problem that the rule numbers it used is too many which would affect the speed of the fuzzy reasoning. In this paper a comparison of various strategy of direct torque control of induction motors is used to improve the performance of DTC scheme. The control algorithm is based on the SVM technique to provide a constant inverter switching frequency and reduced flux and torque ripple and current distortion. A space vector is generated by two fuzzy logic controllers associated with hysteresis regulators. The first one is to control flux and the other to control torque. The use of fuzzy controllers permits a faster response and more robustness.

II. DIRECT TORQUE CONTROL PRINCIPLE

The basic functional blocks used to implement the DTC scheme are represented in Figure 1. The instantaneous values of the stator flux and torque are calculated from stator variable by using a closed loop estimator [1]. Stator flux and torque can be controlled directly and independently by properly selecting the inverter switching configuration. This method is based on maintaining the amplitude and the phase of the stator current constants, avoiding electromagnetic transients It

is possible to control directly the stator flux and torque by selecting the appropriate inverter state [1], [5].

An induction machine can be modeled with stator current and flux in reference (α, β) as state variable by the following equations

..

.. sVBXAX +=

Where:

,..

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

s

isX

φ ⎥

⎦

⎤⎢⎣

⎡=

s

siXφ

(1)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

+−

−−

−−+

−

=ω

σσ

σσ

σσ

σ

.1.

1.

1.

1.

jTT

MM

jMTL

R

A

rr

rr

s

(2)

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡=

00.

1..

1σσ rrs LLLB (3)

⎥⎦

⎤⎢⎣

⎡ −=

0110

j ,s

ss R

LT = , r

rr R

LT = (4)

The induction stator flux and torque are given by: ( )dtiRv ssss ∫ −=φ (5)

( )αββα φφ sssse iipT −= . (6)

The estimated values of the stator flux and torque are compared to their command values Φsref,, Tref respectively. Switching states are selected according to

switching table selector. ST is the stator flux modulus after the hysteresis block; SФ is the torque error after the hysteresis block.

TABLE I

SWITCHING TABLE FOR DIRECT TORQUE CONTROL

Under the basic DTC scheme, as indicated in

Figure.1, the stator flux linkage is estimated by means of integration of the terminal voltage minus the ohmic voltage drop on the stator resistance, as described in(5) [6]. The error between the estimated torque T and the reference torque T* is the input of the three level hysteresis comparator where the error between estimated stator flux magnitude Φs and the reference stator flux magnitude Φs

* is the input of a two level hysteresis comparator. In this system, the control reference frame is stationary (fixed to the stator) and space vector notation is used to represent the variables (figure.2.). The motor torque and stator flux amplitudes are controlled by two independent hysteresis controllers. The feedback signal, Te and Φr, are computed from stator voltages and currents. The stator flux space vector Φs is obtained by integrating the motor emf space vector [7]:

III. FUZZY DIRECT TORQUE CONTROL

In order to improve the DTC performances a complimentary use of fuzzy regulators are proposed. The two hysteresis controllers from figure 1. Will be complimented with two fuzzy regulators as it is shown in figure. 3

Fig. 1 Basic direct torque control scheme for ac motor drives (DTC)

Fig.2. Partition of the complex plan in six angular sectors S I = 1… 6

It follows from the previous section that the

controller adopting DTC strategy has the property of hysteresis, which only takes two value controls for the very big or small error of the torque. That means the control action will be the same in the whole error range. To get better control performance a fuzzy logic controller has been introduced to be a compliment to the hysteresis controller. The wide of hysteresis cycle will be fuzzy variables: φb for flux controller and Tb for torque controller. The fuzzy controller design is based on intuition and simulation. These values compose a training set which is used to obtain the table of rules where is given the dependence φbΔ (e1, e2) and

TbΔ (e1, e2), where e1 and e2 are the inputs. The fuzzy rules sets are shown in Table 2. In Fig. 3 it is shown the membership functions of input and output variables. The rules were formulated using analysis data obtained from the simulation of the system using different values of torque hysteresis band. PH: positive high, NH: negative high, PM: positive medium, NM: negative medium, PS: positive small, NS: negative small, ZE: zero

The linguistic rules can be expressed by the following example: • If (e1 is NH or NM and e2 is N) then ( ΔbΓ or Δbφ is N):

This case corresponds to a big overshoot in torque error, consequently high torque ripple. To reduce the torque ripple, the value ΔbΓ should be reduced [3]. In this case, the overshoot in torque error can touch the upper band which will cause a reverse voltage vector to be selected. This one will result in a torque to be reduced rapidly and causes undershoot in the torque response below the hysteresis band. Thus, ΔbΓ should not be too small; ΔbΓ is set Positive in order to avoid this situation.

TABLE. 2 FUZZY RULES OF TORQUE AND FLUX HYSTERESIS CONTROLLER

Fig. 3 The improvement of DTC performances by adding fuzzy controllers

Fig. 5 Control surface

IV. SPACE VECTOR MODULATION

The aim of SVM is to minimize harmonic distortion in the current by selecting the appropriate switching vectors and determining their corresponding dwelling widths [5]. As depicted in Fig. 6 there are eight states available for voltage space vector according to eight switching positions of the inverter. SVM is based on time averaging techniques during sampling period Ts. If the reference vector Vs (Vref = V1 + V2), is located in sector I (Fig.6), then it is composed of voltage vector V1 and V2 and zero vectors V0 and V7, one finds [6]:

All techniques SVM use to synthesize the reference

voltage standard the following equations: ( )2170 2

1 TTTTT s −−== (4)

( )

⎟⎠⎞

⎜⎝⎛−

=

3sin

sin21 π

θπaT

T s (5)

Several strategies SVM can be used for the piloting of the inverter only difference between these strategies is the choice of the null vector and the sequence of application of the vectors tension during the period of sampling.

22111 VTVTVsT += (6) ( )

⎟⎠⎞

⎜⎝⎛

=

3sin

sin21 π

θaT

T s (7)

Where: T1 and T2 are the active pulse times of voltage vectors V1 and V2.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

dc

s

V

Va

32

Vdc : d-c link voltage. T0, T7 are a null vector times.

IV. SIMULATION RESULTS

To study the performance of the fuzzy logic controller with direct torque control strategy, the simulation of the system was conducted by using MATLAB /SIMULINK and fuzzy logic. The problem of how to make the flux rapidly reaching its given value when system started with direct torque control was experienced. From figure (8) one can see that torque response in steady state is very rapid especially during the starting stage due to the flux being controlled within its rated value before torque reaching its given value. This control strategy can provide full torque while the motor is at a standstill. In steady state the torque is quite stable. Figure (8, 9, 10, and 11) shows a comparison between the DTC classic and DTC with fuzzy regulators, DTFC- hysteresis and DTFC-SVM. The comparison of the steady state behavior obtained using the basic switching table and the proposed DTFC. The machine is running at 100 rad/sec. Fig. (9) and Fig. (10) shows an appreciable reduction of current, flux and torque ripple has been obtained using fuzzy regulators associated with hysteresis regulators. These results are obtained in spite of using larger sampling period for the DTFC. The simulation results given in Fig. (11) show a good tracking of electromagnetic torque using DTFC -SVM and prove that this technique allow a good dynamic performance similar to the basic DTC schemes. Also it can be noted that the effects due to the crossing of sector boundaries, typical of basic DTC schemes, are avoided using the DTFC-hysteresis scheme.

Fig. 6 Decomposition of voltage vector

Fig. 11 Response of a.4) trajectory of flux, b.4) electromagnetic torque and c.4) stator current for scheme of DTC

DTC- fuzzy hysteresis with SVM

Fig.9. Simulation results of DTC with fuzzy regulators of induction motors, a.2) Stator flux trajectory , b.2)

Electromagnetic torque, c.2) Stator current

Fig.8. Simulation results of Classical DTC of induction motor a.1) Stator flux trajectory b.1) Electromagnetic torque c.1) Stator

current

Fig. 10. a.3) Response of trajectory of flux,b.3) electromagnetic c.3)torque and stator current for scheme of DTC

Simulation results of DTC -fuzzy hysteresis regulators associated

VI. CONCLUSION

In this paper the following strategies of direct torque control of induction motors are compared with classical DTC strategy : direct torque control strategy with fuzzy logic regulators instead of hysteresis regulators, direct torque control strategy with hysteresis regulators associated with fuzzy logic regulators, and direct torque control strategy with fuzzy, hysteresis and space vector modulation. It is shown that in the case of direct torque control strategy with fuzzy regulators instead of hysteresis regulators the magnetic flux and the torque ripples are smaller as in DTC classical strategy but the current amplitude is bigger. In the case of DTC strategy with hysteresis regulators associated with fuzzy logic regulators the performances are better: the magnetic flux, the torque ripples and the current amplitude are smaller as in DTC classical strategy. The similar results have been obtained also in the case of direct torque control strategy with fuzzy, hysteresis and space vector modulation associated.

REFERENCE [1] Casadei, D., serra, G., Tani, A, «Performance Analysis of a

DTC Control Scheme for Induction Motor in the Low Speed Range», in proceeding of EPE, (1997), p.3.700-3.704, Trondheim.

[2] Depenbrok. M, «Direct self-control (DSC) of Inverter Fed Induction Machine», In: IEEE Trans. On PE (1988), Vol. PE-3, No4, October 1988, p 420-429.

[3] Youb, L, Craciunescu, A, «Study on Fuzzy Control of Induction Motors with Direct Torque Control», the 4 th Internationnal Conference on Computer, Electrical, and Systems Science, and Engineering, Prague, Republic Czech, July 27-29, 2007 (Paper Accepted). [4] Ned Gulley, J.-S. Roger Jang: «Fuzzy Logic Toolbox for Use With Matlab ». The Math Works inc, Natick, Mass, 1996. [5] H.Buhler: «Réglage par Logique floue ». Presses polytechniques et universitaires Romande, 1994. [6] Sayeed Mir, Malik E. Elbuluk, Donald S. Zinger: «PI and fuzzy Estimators for Tuning the Stator Resistance in Direct Torque Control of Induction Machines ». IEEE Trans. On Power Electronics, Vol. 13, No. 2, pp. 279-287, March 1998.

APPENDIX

INDUCTION MOTOR PARAMETRS Power rating 4 kW Stator voltage 220/380 V Stator resistance 10 Ω Stator leakage inductance 0.6550 H

Rotor resistance 6.3 Ω Rotor leakage inductance 0.6520 H Mutual inductance 0.612 H Inertia 0.03kg.m2 Number of poles 2 Torque rating 25 N.m