Comparison of Field-Oriented Control and Direct Torque Control for Permanent Magnet

Synchronous Motor Using Two Level InverterS.Ashok Subramanian1 , M.Murugan2 ,

1, PG Scholar, Francis Xavier Engineering College, Tirunelveli.

2, Assistant Professor, Francis Xavier Engineering College, Tirunelveli.

Abstract- This paper presents a comparative study on two most popular control strategies for permanent magnet synchronous motor (PMSM) drives. The comparison is based on various criteria including basic control characteristics, dynamic performance and implementation complexity. The study is done by simulation using the simulink power system block set allows a complete representation of the power section and the control system. The simulation and evaluation of DTC control strategy is performed using actual parameter of PMSM fed by space vector modulation and FOC control strategy fed the PMSM by an IGBT PWM inverter.

I. INTRODUCTION

Permanent magnet synchronous motors are used in many application that required rapid torque response and high performance operation. The PMSM is very similar to the standard wound rotor synchronous machine expect that the PMSM has no damper windings and excitation is provided by a permanent instead of a field winding. The high efficiency, high steady state torque density and simple controller of the permanent magnet motor drives compare with the induction motor drives make them a good alternative. The permanent magnet synchronous machine(PMSM) is basically an ordinary AC machine with windings distributed in stator slots. So that the flux created by stator current is sinusoidal and permanent magnet produce magnetic field in the air gab.

The PMSM has two high performance control strategies that is FOC and DTC. They have been invented in the 70’s and in the 80’s. These control strategies are lift on the operation principle by their objective are the

same. These control strategies are effectively control the motor torque and flux in order to force the motor to accurately track the command trajectory regardless of the machine. The purpose of this paper is to present a comparative study on these two control strategies in order to clarify which control technique is best suitable for PMSM. This comparative is based on the various criteria including basic control characteristics, static and dynamic performance and implementation complexity.

II. MODELLING OF PMSM

The model of PMSM without damper winding has been developed on rotor reference frame using the following assumptions;1) Saturation is neglected.2) The induced EMF is sinusoidal.3) Eddy currents and hysteresis losses are negligible.4) There are no field current dynamics.Voltage equations are given by,

vd = Rsid – ωrλq+ dλd/dt vq = Rsiq – ωrλd +dλq/dt (1)

Flux Linkages are given by,

λd = Ldid + λf

λq= Lqiq (2)

Substituting equations 2. 9 in 2.10,

vd = Rsid – ωrLqiq+d/dt (Ldid+ λf) vq = Rsiq – ωrLqiq+ d/dt (Lqiq) (3)

Arranging the equations in matrix form,

=+ −+ + 0

The developed torque is being given by,

Te=(3/2) P (λd iq – λq id) (4)

Substituting the λd,λq values is above equation, The torque equation becomes,

Te=3/2 P [(Ld-Lq) IdIq+Iq�f)] (5)

The mechanical torque equation is,

Te=TL+Bωm+Jd ωm/dt (6)

Solving for the mechanical speed from equation,

ωm=∫(Te-TL-B ωm/J)dt (7)

and ωm=ωr(2/p)

In the above equation Wr is the rotor electric speed, where as Wm is rotor mechanical speed.

III.DESCRIPTION OFFIELD-ORIENTED CONTROLANDDIRECTTORQUE CONTROL SCHEMES

A. Field oriented control system

The primary principle in controlling a PMSM drive is based on field orientation. Since the magnetic flux generated from the PM rotor is fixed in relation to the rotor shaft position, the flux position in the coordinates can be determined by the shaft position sensor. In (2), if Id = 0 , the d-axis flux linkage �d isfixed. Since �f is constant for a PMSM, the electromagnetic torque is then proportional to Iq which is determined by closed-loop control

Te=3/2 P �f Iq (8) Hence the representation follows,

Te= Kt Iq (9) Where Kt=3/2 P �f (10)

The rotor flux is produced only in the q axis while the current vector is generated in the

axis in the field-oriented control. Since the generated motor torque is linearly proportional to the q-axis current, as the d-axis rotor flux isconstant in (2), the maximum torque per ampere can be achieved [3].

Fig:1 System configuration for field oriented PMSM

B. Direct Torque Control system

Since M. Depenbrock and I. Takahashi proposed Direct Torque Control (DTC) for induction machines in the middle of 1980’s, more than one decade has passed. It is getting more and more popular nowadays. The basic idea of DTC for induction motor is to control the torque and flux linkage by selecting the voltage space vectors properly, which is basedon the relationship between the slip frequency and torque. In the late 1990's, DTC techniques for the Permanent Magnet Synchronous Machine (PMSM) machines have appeared [4]. Figure shows the direct torque control of PMSMdrives.

I. Stator flux estimation method: The stator flux is estimated using the following equation

λs=∫(Vs-Rs is)dt (11)

Using the above equation, the amplitude of the flux and the region where the flux is present, can be estimated. If the resistance term in the stator flux estimation is neglected, the variation of the stator flux linkage will

only depend on the applied voltage vector as shown in Fig. 1.For a short interval of time, namely the sampling time, Ts = Δ t, the stator flux linkage, λs position and amplitude can be changed by applying the stator voltage vector, Vs. The position change of the stator flux linkage vector, λs, will affect the torque. During the sampling interval time or switching interval, one out of the six voltage vectors isapplied. The goal of controlling the flux in DTC is to keep its amplitude within a pre-defined hysteresis band. By applying a required voltage vector stator flux linkageamplitude can be controlled [3]. To select the voltage vectors for controlling the amplitude of the stator fluxlinkage the voltage plane is divided into six regions, as shown in Fig. 3. In each region two adjacent voltage vectors, which give the minimum switching frequency, are selected to increase or decrease the amplitude of stator flux linkage, respectively. For example, according to the Table I, when the voltagevector V2, is applied in Sector 1, then the amplitude of the stator flux increases when the flux vector rotates counter clockwise. If V3,is selected then the stator flux linkage amplitude is decreases.

Fig.2 Incremental stator flux linkage space vector representation in the DQ-plane.

II. Torque estimation method:

Electromagnetic torque is estimated using stator linking flux components and measured stator currents using the following equations:

Te=3p/4(λd iq-λq id) (12)

The magnitude of stator flux and electromagnetic torque are compared with their reference values using the corresponding

hysteresis controller. Hysteresis controllers are employed to maintain the torque and stator flux within a prescribed limit. The output of these controllers, in addition to the location of stator linkage flux in particular sector is fed to a switching table to select a voltage vectorproducing desired torque. To determine the proper applied voltage vectors, information from the torque and flux hysteresis outputs, as well as stator flux vector position, are used so that circular stator flux vector trajectory isdivided into six symmetrical sections according to the non zero voltage vectors as shown in Fig. 3

Fig.3 Voltage space vectors

The switching table for controlling both the amplitude and rotating direction of the stator flux linkage is given in Table I

TABLE I

SWITCHING TABLE

Ψ T ΘΘ (1) θ (2) Θ (3) Θ(4) Θ(5) Θ(6)

Ψ = 1

T=1 V2(110) V3(010) V4(011) V5(001) V6(101) V3(010)T=0 V6(101) V1(100) V2(110) V3(010) V4(011) V5(001)

Ψ =0

T=1 V3(010) V4(011) V5(001) V6(101) V1(100) V2(110)T=0 V5(001) V6(101) V1(100) V2(110) V3(010) V4(011)

The output of the torque hysteresis comparator is denoted as τ, the output of the flux hysteresis comparator as λ and the flux linkage sector is denoted as θ. The torquehysteresis comparator is a two valued comparator; τ = 0 means that the actual value of the torque is above the reference and out of the hysteresis limit and τ =1means that the actual value is below the reference and out of the hysteresis limit. The flux hysteresis comparator is a two valued comparator as well where λ = 1me a n s that the actual value of the flux linkage is below the reference and out of

the hysteresis limit and λ = 0 means that the actual value of the flux linkage is above the reference and out of the hysteresis limit. We define λ and τ to be the outputs of the hysteresis controllers for flux and torque,respectively, and �(1) -� (6) a s the sector numbers to be used in defining the stator flux linkage positions. In Table I, if λ =1, then the actual flux linkage is smaller than thereference value. On the other hand, if λ = 0, then the actual flux linkage is greater than the reference value. The same is true for the torque.

Fig.4 Typical DTC PMSM drive system

IV. SIMULATION RESULTS

In this section, static and dynamicperformances of FOC and DTC schemes are obtained by simulation using the MATLAB/ Simulink Power System Blockset. Since the objective of the work is to compare the controlstrategies, the same power section is used in both systems. It is necessary to make a comparison of static and dynamiccharacteristics of both technical command and under the same operating conditions (reference, charges disturbance… etc.), and in the same configuration simulation (step sampling, time simulation,) In this paper we will present the advantages and disadvantages of each type of command, better command will be the one that best meets the requirement to know:

Best performance static and dynamic. Best prosecution guidelines control.

Best releases disturbance. Insensitivity to changes in parameters.

Fig.5 Simulink diagram of FOC

Fig.6 Simulink diagram of DTCA. Comparision of stator flux amplitude wave form

Fig. 7 Illustrates the simulation results of both DTC and FOC stator flux amplitude wave

form, in (a )the DTC stator flux ripple is 0.26 range. In (b) the FOC stator flux ripple is 1.25

(a)

(b)

Fig 7: Stator flux amplitude wave form for DTC and FOC

B. Comparison of speed settling

Fig. 8 illustrates the simulation results of both technical command FOC hysteresis and the DTC, in (a) the speed settling the DTC settled the PMSM speed at 4 rad/sec. In (b) FOC it is settled at 5 rad/sec.

(a)

(b)

Fig 8: Speed selling wave form for DTC and FOC.

V. COMPARISON BETWEEN THE DTC AND THE FOC

The DTC does not necessitate any mechanical measure such as the one of speed or position of the machine; of more thesensitiveness to the machine parameters clearly is lessened in the case of the DTC, since the flow estimation is done according to a single parameter to know the resistance stator. In addition, PWM is replaced, in this order by a simple table of commutation which the return, so much easier. The order DTC has for advantages:• The reduction of the time of response of the couple.• The hardiness in comparison with thevariation of the parameters of the machine and nutrition.• The direct imposition of the amplitude of the undulations of the couple and flow.• She adapts herself by nature to the absence of sensor

Mechanical connected to the tree motor. She presents major problems:

• The absence of mastery of the harmonic ones of couple.

The check vector by orientation of the flux rotorique FOC was developed to eliminate internal coupling of the machine, provoking variations of the flux linkage to the Torque.

The control vector by orientation of the flux rotorique presents a number of advantages:

• To allow a decouplage between the flux and the torque rather simple, thus a wide beach of speed.

And a number of inconveniences:

• Weak hardiness to the variations Parametric and in particular to the one of the constant one of time rotorique.

• Necessitated of a modulation one for the order come close to the inverter that provokes delays, especially down with frequency of modulation.

TABLE IIIPARAMETERS OF THE PMSM USED IN THIS PAPER

Rated output power 1500 WMagnetic flux linkage 0.175 webPoles 4Stator resistance 0.2 Ωq-axis inductance 0.0085 Hd- axis inductance 0.0085HInertia 0.089 KG.M2

Friction coefficient 0.005N.M.S/rad

VI. CONCLUSION

In this paper, main characteristics of field-oriented and direct torque control schemes for PMSM drives are studied by simulation with a view to highlighting the advantages anddisadvantages of each approach. It is difficult to clearly state on the superiority of DTC versus FOC because of the balance of the merits of the two schemes. We one conclude that the vector order it better is adapted (load variation), and the responses with the DTC are quicker.

VII. REFERENCES

[1] C.Mademlis, V.G.Agelidis, "On Considering Magnetic Saturation withMaximum Torque to Current Control in Interior Permanent Magnet Synchronous Motor Drives," IEEE Trans. Energy Conversion, vol. 16, no. 3, Sep. 2001.

[2] H.L.Huy, "Comparison of Field-Oriented Control and Direct Torque Control for Induction Motor Drives," 0-7803-5589-X/99/1999 IEEE.

[3] K.K.Shyu, C. K. Lai, Y. W. Tsai, and D. I. Yang, "A Newly Robust Controller Design for the Position Control of Permanent-Magnet

Synchronous Motor," IEEE Trans on Industrial Electronics. vol. 49, no. 3, Jun. 2002.

[4] L.Tang, L.Zhong, M.F.Rahman and Y. Hu, "A Novel Direct Torque Control for Interior Permanent Magnet Synchronous Machine Drive System with Low Ripple in Torque and Flux-A Speed Sensorless Approach" 0-7803-7420-7/02/ 2002 IEEE.

[5] M. F.Rahman, L.Zhong, E Haque, and M. A.Rahman, "A Direct Torque-Controlled Interior Permanent-Magnet Synchronous Motor Drive Without a Speed Sensor " IEEE Trans. Energy conversion, vol. 18, no. 1, Mar. 2003.

[6]J.Luukko "Direct torque control of permanent magnet synchronous machines analysis and Implementation" Lappeenranta 2000.

[7] P.Pragasan, and R. Krishnan, "Modeling of permanent magnet motor drives" IEEE Trans. Industrial electronics, vol. 35, no.4, nov. 1988.

[8] G.Grellet et G.Clerc, "Actuators electric Principe / model / control ". Eyrolles,.(2nd ed.) 2000, pp. 298-300.

[9] F.Labrique, H.buyse, G.seguier and R. Bausière, "Converters power electronics command and dynamic behavior " vol. 5, 1998, pp. 68-73.