permanent magnet synchronous motor drive

7/28/2019 Permanent Magnet Synchronous Motor Drive

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1 C1. .Control Characteristicsand Speed ControllerDesignfor a High Perfonnance Pennanent Magnet

Synchronous Motor Drive

IEI:E TRANSACTIONS ON I'OWER ELECTRONICS. VOL. 5. NO.2. AI'RIL I 'NO 151

PRAGASEN PILLA Y, MEMBER, IEEE, AND RAMU KRISHNAN, MEMBER, IEEE

Abslracl- The Iheory uf vectur control is applied to Ihe nonlinearmodcl of a permancnt magnel synchronous motor to dcvclop a lincarmodcl fur cuntruller design. purpuses. The operation and relevantmathematics of a pseudo derivative feedback controller is then pre-sentcd. Three different speed controller designs are then consideredand a comparative evaluation made based on their largc and small sig-nal behaviur. In ordcr to test the large signal response, the detailednonline.ar model of the machine and real time model of the inverterswilches are used.

I. INTRODUCTIONTHE DC servo motor drive has many drawbacks whencompared 10ac servo mOlOrdrives. These include lackof robustness and overload capability, lower torque, andspeed bandwidths and the regular brush and commutatormaintenance required. For these reasons, ac servo drivesare preferred in spite of the fact that the controllers re-quired are more complicated and expensive than those fordc servos. The machines used for ac servos in tBe frac-tional to 30 hp range are the induction, brush less dc andpermanent magnet synchronous motors.Vector control [I] (also known as field oriented control)is needed in ac drives to transform the ac machine, per-formance wise, into an equivalent separately excited dcmachine. This gives the ac machine the highly desirableperformance capabilities of the separately excited dc ma-chine, while retaining the general advantages of ac ma-chines over dc. Vector control was first applied to the in-duction motor and a considerable amoun't of literature hasbeen devoted 10this area. Recent research [2]-[4] has in-dicated that the permanent magnet synchronous motor(PMSM) could become a serious competitor to the induc-tion motor for high performance servo applications. ThePMSM is more efficient and has a larger torque to inertiaratio and power density when compared to the 1M in thefractional to 30-hp range. In addition, for the same outputcapacity in the above range, the PMSM is smaller in size

Manuscripl received April 6. 1987: re\'ised Ocluber 23. 1989. This pa-per was presented allhe 1987 IEEE Power Electronics Specialists Confer-ence. Blacksburg. VA. June 21-26.

P. Pillay is with the Depanment of Electrical and Electronic Engineer'ing. Merz Coun. University of Newcastle Upon Tyne. Newcastle. NEI7RU. England.R. Krishnan is with Ihe Depanmem of Electrical Engineering. VirginiaPolytechnic and Slate University. Blacksburg. VA 24061.IEEE Log Number 8933771.

and lower in weight that makes it preferable for certainhigh performance applications like robotics and aerospaceactuators.A fair amount of research has been done on PM ac mo-tor drives [2]-[ 11]. Axial field designs have been exam-ined [2] as well as the possibility of replacing industrialPM motors with line start designs [3]. Extended speedoperation through flux weakening [5]-[7] has also beenexamined and key equations developed for the perfor-mance prediction. Design criteria have also been laiddown [8]. [9] while a comparison between the sinusoidal-fed and rectangular-fed motor drives has been presented[10].Crucial to the successful implementation of vector con-trol is proper control of the armature currents [1'1]-[ 14]that may be accomplished with a hysteresis, ramp com-parison, space vector, or some form of predictive currentcontroller.Efficient use of the PMSM necessitates a knowledge ofits characteristics from a control point of view. The model

of the PMSM is however nonlinear. This paper appliesthe concept of vector control that has been extensivelyapplied to induction machines to derive a linear model ofthe PMSM for controller design purposes. The speed con-troller is then designed. Although a linear model is usedfor controller design purposes, the speed controller is re-quirep to function over the entire speed range when thestate variables of the system experience large excursions.Hence the large signal behavior of the drive system isevaluated by simulating the entire nonlinear system. Thenonlinear equations of the PMSM, state space speed con-troller equations and a real time model of the inverterswitches are used in this simulation. Every instant of apower switch opening or closing is included. Key theo-retical results are verified experimentally.The paper is organized as follows. The operation of theentire drive system is described in Section II. Each of thecomponents of the drive system are described in subse-quent sections. Section III presents the nonlinear modelof the PMSM. In Section IV, the application of vectorcontrol to the PMSM is discussed from which a linearmodel for controller design purposes is developed. Sec-tion V describes the operation of current controllers usedin high performance motor drives. In Section VI, the op-eration and relevant equations of the speed controller are

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IEEE TRANSACTIONS ON rOWER EI.ECTRONIC!>. VOL. ~. NO.2. ArRIL 1990

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,a . CurrentController &Base Dr! veAmp1if leu

T I, T2. T3, T!., T5, T6

Fig. I. Schematic or PMSM speed servo drive system.

resented while Sections VII and VIII contain the resultsconclusions.II. DRIVESYSTEM

Fig. I is a schematic of the overall speed servo drive'stem. All reference or commanded values are siJper-ripted with a * in the diagram. The error between theferen~e and actual speeds is operated upon by the speedntroller to generate the torque reference. In the constantirgap nux mode of operation where i,} = 0, the torqueference is divided by the motor torque constant to givee reference quadrature axis current. This goes throughe inverse Park transform to generate the A, B, and Chase stator reference currents. Rotor position feedbackneeded in order to generate these currents. The currentontroller attempts to force the actual motor currents toqual the commanded valu~s at all times. Current feed-ack is required in order for the hysteresis or PWM cur~nt controllers to achieve this. Current control is imple-ented by the appropriate firing of power devices T1 to6. For a speed control system, speed feedback is alsoeded; both position and speed feedback can be obtainedom a resolver/signal processor combination.When greater than rated speed is commanded. the ma-ine then operates in the constant power or flux weak-ing mode. Here, the airgap nux is weakened by apply-g a direct axis current in opposition to the rotor magnetux. The torque speed profile of the drive is as shown ine block labeled FW. The output of the block is unity uprated speed and decreases hyperbolically with speedtween the rated and maximum speeds to ensure constanttput power. When the output of FW is unily then 1..111tifandi ,} = O. If the output of FW is less than unily thenlower T: is demanded. In addition Aliiis less than A'!fso

that a negative i,}.is commanded in order to buck the mag-net flux. The speed'controller is designed at rated speedbut is required to operate proprIyup to the maximumspeed. \ ,Each of the components shown in the overall driveblock diagram of Fig. I are described and elaborated uponin subsequent sections.

III. MACHINEMODELThe following are assumptions made in the derivation:I) saturation is neglected although it can be taken into. .account by parameter changes;2) the induced EMF is sinusoidal;

3) eddy currents and hysteresis losses are negligible;4) there are no field current dynamics;5) there is no cage on the rotor.With these assumptions, the stator d, q equations of thePMSM in the rotor reference frame are [I5]:

Uq = Riq + PAq+ CJJ"A,IVel = Riel + pAeI - CJJ.,Aq

( I)(2)

where1..'1= Lqiq (3)

and A,I= L"it! + A(/I' (4)lIeIand Uqand the d, q axis voltages, ieland iq are the d, qaxis stator currents, Lei and Lq are the d. q axis induc-tances, A" and 1..'1are the d, q axis stator nux linkages,while Rand CJJJre the stator resistance and inverter fre-quency respectively. A(/!s the nux linkage due to the rotormagnets linking the stator.


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ethod is used in the implementation, i.e.; where the air-p flux is measured, then operation around zero speed ismplicated by the necessity of integrating the voltagenal to obtain flux. In an indirect implementation, wheree position of the rotor flux is estimated, a model of theachine must be used which depends on parameters thatn experience large (excess of 50 %) variations due tomperature, saturation and operating frequency. Param-ers lIsed in the model that arc different from those in thetual machine cause a degradation in the 1M drive per-rmance; a corresponding degradation is not experiencedthe vector-controlled PMSM.Hence with the application of vector control, indepen-nt control of the torque (i,,) and flux (i,,) producingrrents are possible. The equations for controller designen are (8), (9), (10), and (IS). These equations busicallycribed a voltage source inverter Fed PMSM. The tech-ogical cfevelopment of high switching frequency, highrrent rating transistors has realized high bandw.idth cur-nt sources that has lead to improved servo performanceterms of torque and speed bandwidths. The mode oferation of the current controllers used in PMSM drivesdiscussed next.

V. CURRENTCONTROLLERSCurrent regulated voltage source inverters arc usedidely in the Fractional to 30 hp range to achieve highrvo performance. Amongst the most common are thesteresis, ramp comparison, space vector, and predictive

Hysteresis Currellt COlltrollerFig. 3 shows a schematic of a hysteresis current con-ller. Sinusoidal curtents are needed in order to producenstant torque in the PMSM. Upper and lower hysteresisvels are defined relative to the reference value and theverter is used to ensure that the actual current is con-ed between the hysteresis bands. Tight control of thetual current is possible by defining small hysteresisnds; however this demands a higher switching fre-ency from the inverter. Care must be taken not to ex-ed the switching capability of the inverter power de-es, The actual current therefore contains harmoriics thatoduce high frequency torque ripples. However the mo-inel1ia effectively filters out these torque ripples sucht the speed is virtualJy ripple free. This current con-ller reacts instuntaneously (theoretically) to changes incurrent command, hence there is no delay or lag inmodel of this current controller.Ramp Comparisoll Currellt COlltrollerFig. 4 shows a schematic of a ramp comparison currenttroller. The actual current is compared to the referencean error signal generated. This is compared to u tri-ular wave and if the error is larger than the sawtooth,phase voltage is switched positively and vice versa.he advantage of the ramp comparison current control-over the hysteresis is that the invener switching fre-

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current trajectory can be predetermined. More complexityis req4ired to precalculate the probable, trajectory, whichis a disadvantag'e from an industrial application point of, ,vIew.

A detailed comparison of the different current control-lers is beyond the scope of this paper. A compromise be-tween the complexity of the space vector and predictivealgorithms with the simplicity of the hysteresis with itsattendant problems of variable switching frequency withmotor speed and parameters is the ramp comparison con-troller. Its switching frequency can be preset to lie withinthe capability of the inverter, while maintaining as gooda current fidelity as the hysteresis current controller. Thisprobably accounts for its use in several industrial driveproducts and is also the current controller used in this in-vestigation.

VI. SPEEDCONTROLLERDESIGNThe speed controller may be designed using classical

frequency-domain techniques or modern state space meth-ods. The state space method requires an accurate knowl-edge of the drive parameters for proper placement of the.poles. Frequency domain techniques display a general ro-bustness to parameter changes; indeed several techniquesexist to check for the sensitivity of the design to plantparameter changes and indeed to include parameter vari-ations from the outset, using for e.g., the Nichol's chart[16]. This probably accounts for its popularity in thedrives industry, with a different configuration from t~econventional proportional integral (PI) or proportiorpl in-tegral and differential (PID) being considered in this pa-per.

It was shown in Section IV that (8), (9), (10), and (IS)are needed for the speed controller design. The stator timeconstant of the machine in this paper is such that thepulsewidth modulated (PWM) switching delay can be ne-glected. The motor parameters of the machine are

R 1.411Ld 5.6 mHL'I 5.61 mHJ 0.00176 kgm2B 0.00038818 Nm/rud/sAuf 0.466 V/rad/s,In addition, (8) and (9) describe the stator current dy-namics. If the stator time constant is much smaller than

the mechanical time constant of the machine then it canbe assumed that the actual current assumes the com-manded value in negligible time when compared to themechanical time constant of the motor.

Hence the final equation describing the motor operationIST,. = Tl. + BWr + Jpwr (16)

T" is a controlled input while Tl. is an uncontrolled input.The type of controller that is designed for this speedervo system is known as a pseudo-derivative feedbackPDF) controller as developed in [17]. A block diagram

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IEEE TRANSACTIONS ON POWERELECTRONICS. VOL. 5. NO.2. A"'UI. 1')1}(1

Fig. 6. PDF controllcr without difi'crcntialion.

i*q ".v7F i qFig. 7. Operating regionsor a currenl sourcc inverter.

te these concepts, three designs are considered in thisThe first is such that none of the control or power levelnals are driven into saturation. In addition the systemcritically damped so that no speed overshoot occurs. Inis design the maximum capability of the inverter andotor is utilized at only one point during the entireartup. This is referred to as the critically damped designthe rest of this paper. This is compared to a secondsign where the maximum current capability of the in-rter is commanded over an extended period of time inder to improve the response. In a practical Implemen-tion this means limiting the control signal outputs byner diodes to ensure that the inverter is not commandedproduce more than its capability. This frees the controlvel signals from having to remain within the saturation

mits as in the first design. The gains can be chosen toprove the small signal dynamic performance. This sec-d design is done for a fast response application and thenal result ends up being slightly underdamped. There-re this second design is referred to as the underdampedsign. In some applications in industry, it is undesirablehave speed overshoot. Therefore a third design is doneat is similar to the second but whose final result iserdamped to prevent speed overslioot. This is referredas the overdamped design.

VII. RESULTSThe design criteria discussed in the last section wereed to obtain the derivative and integral constants in Fig.A computer program was then written to simulate thetire speed servo drive system including the ramp com-rison current controller, PDF speed controller and d, qis equations of the motor. The response of the motorive for speed reference changes only are considered inis section. Every instant of a power switch opening orosing is represented.Figs. 8-10 show the speed, electric torque and currentthe critically damped speed servo design. From Fig, 8.is clear that there is no speed overshoot that is the dc-

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0.06 0.12 TJ1il~SJ 0.25 .lg~~1 0.&0.31 0."Fig. B. Speed or critically d:lIl1pcd syslem.

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0.06 0.'2 TJ'H~~s I 0.26 .lg~~1 0.31 0."Fig. 9. Torque or critically damped syslem.

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0.06 0.12 TJ'H~1 I 0.25 .lg~1' 0.37 0."Fig. 10. Currcnl or critically damped systcm.

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fining feature of a critically damped system. The motortakes about 50 ms to reach the commanded speed. Thecurrent and hence torque limits arc taken into account inthe design process and it is ensured that the system always


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0.06 0.12 TI~~~SI 0'.25 .lg:~1 0'.31 0."Fig. II. Underdamped speed response.

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es in the linear region. Although the PWM inverterces high frequency harmonics, the actual currentthe reference closely. These current harmonics pro-high frequency torque harmonics as shown in Fig.mechanical system filters these harmonics out quiteively so that they are not reflected in the speed re-

e shown in Fig. 8. The current and torque limits areed at only one point in the transient. The speed re-e can be improved by demanding the maximum cur-and hence torque capability of the machine over ar period. This is shown in the next set of results.s. 11-13 show the speed, torque and current re-eof the speed servo systemwhen designed for a'fast 'nse application. The motor attains the referenceafter about 15 ms as opposed to the 50 ms in the

ous case. This reduction is accomplished by de-ing the maximum torque capability of the machinea period of time as shown in Fig. 12. The actual andanded phase currents are shown in Fig. 13. The fi-ime needed by the actual current to reach the com-ed is due to the stator time constant. This producesresponding rise time in the torque in Fig. 12. Sinceximum torque is demanded until the reference speedost reached, there is a speed overshoot. When thiss, the commanded torque goes negative to bring thel speed back to the commanded value as shown in12.en speed overshoot is not tolerable, then an over-ed system could be the proper choice. The speed re-e of such a system is shown in Fig. 14. The torqueurrent curves of this system look similar to the pre-ones and are therefore not shown. During the linearn the speed, the control signal output is clamped sohe inverter delivers its maximum output. The oper-of this system has been verified experimentally asn in Fig. 15. The initial linear rise in speed and sub-nt overdamped response are clearly evident in bothactical measurement and theoretical prediction.to now, large signal responses of the speed controlsystem have been considered. In the latter two de-

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permanent magnet synchronous motor drive

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