Speed Sensor Less Control of IM by Current Error Compensation

8/14/2019 Speed Sensor Less Control of IM by Current Error Compensation

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q-axis components Ad,= LmiA(10)

where P is the number of poles.From (7) and (81, d- and g-axis rotor currents are

(11)

(12)Substituting (11) and (12) into ( 3 ) and (4) yields

& R L+ .L Aq,- R , i + wS l I d r = 0d t L, Lr (14)If the vector control is fulfilled such that q-axisrotor flux can be zero, and d-axis rotor flux can beconstant, the electromagnetic torque is controlledonly by q-axis stator currenthave

Substituting (15) nto 113) and

from (lo), and we

(15)14)yields

(16)

(17)where T,(=L./R,.) is the time contant of rotor.In case of the constant flux control, that is&d,-/dt'o, from ( 3 ) , (121, and (15)idr= 0 (18)

If (18) and (19) are substituted into ( lo ) , (16) and(17), the flux, slip frequency and electromagnetictorque are

III. PROPOSED CONTROL SCHEME

(20)(21)

(22)

The proposed sensorless control scheme doesnot require the speed and flux estimations, but u sedirectly the stator currents. An induction motormay be considered as a multi-variable input/outputsystem shown in Fig . 1, in which the inputvariables are the stator voltages, and the outputvariables are the stator currents and rotor speed.I -0 rVos-jos INDUCTIONMOTOR 1 15

Fig. 1 Input and output variables of induction motorThe voltages and currents in Fig. 1 are thequantities in the stationary reference frame fixed tothe stator. The voltage equations in the stationaryreference frame are

Fig. 2 Input and output variables of modelFig. 2 shows a model where the input and outpuvariables are newly established. The subscript mdenotes the variable of the model. w r m is the therotor speed of the model, and becomes the speedcommand. From the induction motor of Fig. 1 andthe model of Fig. 2, the following inference ispossible. If both th e stat or curre nts of the motoand model are forced to be same in case that boththe stator voltages are same, the motor speedbecomes sam e a s the model speed, that is, thespeed command. In other words, if ias= i andiB= im in case of vas= U,, and vgs=vm , then

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u y = u rm . he above th ings can be expressed interm s of t he (quantities of the sync hronouslyrotating reference frame. If i, = i,, and ids= id,in case of uqs= U*, and = zidm , then w,= w rm .These relations can be also obtained from theequations described in the section II. The q -ax isstator voltage equations of the motor and model are

where 0 (= 1- L k l LJr 1 is th e leakage factor.

(24)

(25)

If the voltages applied to the motor and model aresame, that is, uqs= uqsm, ro m (24) nd (25)

stator voltage) is obtained a s the output of PIcontroller, and the difference between th e torqueproducing currents of the model and motor is useda s the input of PI controller. T he d-axis statorvoltage for the constant flux vector control isobtained from the output of another PI controller,and the difference between the reference currentand the flux producing current of the model is usedas the input of the PI controller.

where KitK j , KO and K, are the gains.

where B,,is the angle of the d-axis of th esynchronously rotating reference frame.Fig. 3 shows th e overall block diagram of th eproposed sensorless control scheme.

From (26) an d E r ) , it is recognized that if i,= i,,an d ib=idm then w,=u,, and w y = u r m .Therefore the motor speed is forced to be same asthe model speed if the difference between thetorque producing currents(q-axis s ta tor currentsand the difference between the flux producingcurren tdd-axis s ta tor currents) of the motor and

Fig. 3 Block diagram of the control system

IV.SIMULATIONSmodel are controlled to be zero in case that th esame voltages are applied to th e motor and model.Furthermore, if the same voltages are applied to themotor and model in the reference frame with thesam e synchronously-rotating speed (w, U em), from

Th e following simulations have been performedfor the verification of th e proposed control scheme.The nominal power and speed of induction motorare 3hp and 1735rpm. Fig. 4(a), (b) and (c) showthe speed responses in cases of the speed(26) it is recognized that the difference between the

difference between the torque producing currents iscontrolled to be zero. For the realization of theabove mentioned, the control q uanti ty( the T a x i s

commands 1500, 50 an d 25. ~ i ~ .shows the+200rpm. ~ i ~ .shows the speed response inthat the load torque 10 is applied in theof the operation of the speed command 2OOIpm. Fig.

flux producing (-l.lrrents Shuld be zero if the bidirectional operation of the speed command


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7 shows the speed response in case that the rotorresistance is decreased by 20% below the nominalvalu e, and t he load to rque 10" is applied in themiddle of the operation of the speed command200rpm.

100TIME[I seddiv]

Fig. 6 Speed response in the load variation (O-flONm)I I I I I

TIME[Sec]

( a )

( c ) .Fig. 4 Speed responses in the speed command

(a)15o rPm (b1501gm (c125mm

TIME[lseddiv]

Fig. 5 Speed response in the bidirectional operation(200rpm--200rpm)

Fig. 7 Speed response in the rotor resistance decreased by 20%with the load variation (O-tlONm)

V . EXPERIMENTS AND DISCUSSIONSThe experiments have been performed for thverification of the proposed scheme. The 8058microprocessor system is used for the digitprocessing of the proposed algorithm. Fig. 8(a), (band (c) show the speed responses in cases of thspeed commands 1500, 50 and 25rpm. Fig. 9 showthe bidirectional operation of the speed commanf200rpm. Fig. 10 shows the speed response in cathat the load torque 10" is applied in the middof the operation of the speed command 200rpm. Fi11 shows the speed response in case that the rotoresistance is decreased by 20% below the nominvalue, and the load torque 10" is applied in thmiddle of the operation of the speed comman200rpm. T h e results of simulation and experimeindicate that the proposed scheme has a gooperformance. The proposed scheme has comparable performance in the respects of thsteady state error, the low speed performance anthe parameter variation performance. Furthermothe proposed control scheme has a simple algorithwithout the speed and flux estimations.

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TIME[seo]

Fig. 8 Speed responses in the speed command(a ) 1503rpm (b ) 3 r p m (c) 25rpm

TIME[lseddiv]

Fig. 9 Speed response in the bidirectional operation(200rpm-*-200rpm)

VI. CONCLUSIONSThis paper proposed a sensorless control schemewithout the speed and flux estimations in which the

....a2iwv)

-Eia

Fig. 11

TIME[lseddivj

Fig. 10 Speed response in the load variation(0 - 10")

Speed response in the rotor resistance decreased by20% with the load variation (O@lO[Nml)

motor speed indirectly follows the model speed(command speed) by forcing the difference betweenstator currents of the mathematical model andmotor to decay to zero. The simulation andexperiment have been conducted for the verificationof the proposed schem e. T h e proposed scheme ha sbeen easily implemented through the microprocessorsystem. The simulation and experimental resultsshow the good speed responses.

W. REFERENCES[ l l Edited by K. Rajashekara, A. Kawamura and K.Matsuse, Sensorless Control of A C Motor

Drives, IEEE press, pp. 1-258, 19%[2] J. Holtz, "State of the art of controlled ACdrives without speed sensors", Int. J.Electronics, vol. 80, no. 2, pp. 249-263, 1996[31 C. Ilas, A. Bettini, L. Ferraris, and F. Profumo,

"Comparison of different schemes withoutshaft sensors for field oriented controldrives", IEEEAECON, pp. 1579-1588, 1994[4 ] Peter Vas, Vector Control of AC Machine,Clarendon press, 1990

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Speed Sensor Less Control of IM by Current Error Compensation