Dr. N. Prema kumar and B. Vanajakshi Speed Control of PMSM ...iret.co.in/Docs/IJETEE/Volume...

Dr. N. Prema kumar and B. Vanajakshi 16

International Journal of Emerging Trends in Electrical and Electronics (IJETEE – ISSN: 2320-9569) Vol. 10, Issue. 2, Mar-2014.

Speed Control of PMSM Drive UsingConventional and Self Tuning Fuzzy PI

ControllerDr. N. Prema kumar and B. Vanajakshi

Abstract— This paper presents speed control for PermanentMagnet Synchronous Motors (PMSM) by using conventionalPI controller, fuzzy tuned PI controller, conventional PID andfuzzy tuned PID Advantages over other types of synchronous,Modeling of PMSM, Control Strategies, vector control,simulation details and results. Performance index forconventional PI/PID and fuzzy tuned PI/PID are calculated.

I. INTRODUCTION

Permanent Magnet Synchronous Motor (PMSM)drives are used in many applications that require rapidtorque response and high performance operation. Newdeveloped materials such as magnetic materials, conductingmaterials and insulating materials as well as several newapplications have greatly contributed to development ofsmall and special purpose machines. Using such materialsthe size of the motor would considerably reduce and highperformance motors can be built. Due to several newapplications these motors are quite popular & use in adeveloping country such as India for Automotiveapplication.

Fuzzy PID controller has superior performance than PIDcontroller. However, despite the significant improvementsmade in the fuzzy PID controllers over its classicalcounterparts. The fuzzy PID controller is not able to meetcertain optimality criteria [1].

II. Permanent MagnetMagnetism was found to be retained in the materials

and this concept was first introduced in electrical –machineresearch in 1950’s. A material that on magnetization createsits own persistent magnetic field is called a permanentmagnet. The refrigerator magnet used to hold therefrigerator door is one such example of permanent magnet.Substances like magnetite (Fe3O4) are used to makepermanent magnets. Electromagnet is a substance whichbehaves like a magnet only when an electric current isflowing through it.

The Fig.1 shows the demagnetization segment ofthe B-H curve where the permanent magnet is usuallydesigned to operate

Fig.1 Permanent Magnet machine OperatingPoints on B-H curves

If the magnet is short circuited using steel keepers (no air-gap), then maximum flux density Br corresponding topoint A’ will be available. When the magnet is installed inthe machine, the air gap will have some demagnetizationeffect and the operating point ′ will corresponds to the noload line shown in the fig. the slope of the no load linewill be smaller with higher air gap with current flowing inthe stator winding the magnetic axis, armature reactoreffect can have a further demagnetization effect, whichwill further reduce the air gap flux density. A load linecorresponding to worst case demagnetizing which may bedue to a starting, transient, or machine fast condition, isalso shown in the figure. The demagnetization affect isremoved, once the operating point reaches D. The magnetwill recover along the coil line. The stable operating pointwill be determined by the intersection of the load line andreactor line. The DC field winding of the rotor is replacedby the permanent magnet in case of permanent magnetsynchronous machine [10].

Main Advantages of PMSM are: Higher efficiency because there are no rotor losses Absence of brushes and slip rings, lower

maintenanceis required.

Lower inertia and better dynamic performance. Higher power/weight ratio. More robust construction of the rotor. Designed for high-performance servo applications. No sparks → safer in explosive environments. Cleaner, faster, more efficient. Less noisy, more reliable.



There are two windings present in the synchronousmotors, a three phase armature winding is on stator and thefield winding is on the rotor. The three phase winding on itsstator is similar to the three phase winding on the stator of athree phase Induction Motor.

Field winding is excited with dc and it produces its ownmmf called field mmf. Three-phase stator winding carryingthree-phase balanced currents creates its own rotatingarmature mmf. The two mmf s combine together to produceresultant mmf. The field mmf interacts with the resultantmmf to produce electromagnetic torque. A synchronousmotor runs always with zero slip, i.e. at synchronous speed.The various types of synchronous motors are

(i) Cylindrical rotor motors(ii) Salient-pole motors(iii) Reluctance motor(iv) Permanent-magnet motors.

PM excitation replaces the conventional fieldexcitation in the rotor of the synchronous machine. Apermanent magnet synchronous motor (PMSM) is similar toa salient-pole synchronous motor without the field windingon the poles.In PMSM, the required field flux is produced by permanentsmounted on the rotor. In these motors, the excitationemf cannot be varied. All the equation governing theperformance of a salient-pole synchronous motor are alsoapplicable to PMSM with excitation emf taken asconstant. The absence of field winding, dc supply to fieldwinding and two slip rings leads to reduction in motorlosses. For the same frame size, PMSM has higher pull-outtorque and more efficiency as compared to salient-polemotor.Types of PM Synchronous Machine:

The PM synchronous Motors are classified on thebasis of the wave shape of their induced emf there are Oneis Sinusoidal and Trapezoidal. The sinusoidal type is knownas PM synchronous motor, the trapezoidal type goes underthe name of PM dc brushless machine [11].Applications: PMSM Drive have find the followingapplications

(1) Robots and machine tools.(2) Can be fed from rectangular current sources or

sinusoidal current sources.(3) A rectangular current fed motor has concentrated

winding on the stator and is used in low powerdrives.

(4) A sinusoidal current fed motor has distributedwinding on the stator and is used in high powerdrives.

(5) Automotive electrical power steering.(6) Traction control.(7) Data storage.

III. PMSM MODELINGIn a motor with more than one pair of magnetic

poles the electric angle differ the mechanical. Theirrelationship is = (1)

The voltage V, over each stator winding is thesum of the resistive voltage drop and the voltage inducedfrom the time varying flux linkages, ⁄ .= + a

(2)= + b(3)= + c(4)

The stator windings are wound with the samenumber of turns so the resistance is equal in all threewindings, = = = (5)In matrix form these voltage equations (2) to (4) becomes= + abc

(6) abc

= + m(7)

Where contains self and mutual inductances and isthe flux through the stator windings due to the permanentmagnet.Inductance Matrix= (8)

The diagonal elements in the inductance matrix are selfinductances and the off diagonal elements are mutualinductances. Let the self inductance be = +

where is the leakage inductances and themagnetizing inductances. The magnetizing inductance isgenerally not constant; reluctance may depends on rotorposition [3].Assume ( ) varies sinusoidally, then= + − ∆ cos(2 ) (9)Where is the average value of the magnetizing inductanceand ∆ half the amplitude of the sinusoidal varyingmagnetizing inductance. The and self inductancescan be found from equation (9) by introducing a 2 3⁄ and4 3⁄ radians space lag respectively= + − ∆ cos(2 + 2 3⁄ ) (10)= + − ∆ cos(2 − 2 3⁄ ) (11)The mutual inductances are given by= − − ∆ cos 2 − (12)= − − ∆ cos 2 + (13)= − − ∆ cos(2 ) (14)The above derivation lead to the following inductancematrix( ) =+ − ∆ cos(2 ) − – ∆ cos(2 − 2 3⁄ ) − − ∆ cos(2 + 2 3⁄ )− – ∆ cos(2 − 2 3⁄ ) + − ∆ cos(2 + 2 3⁄ ) − − ∆ cos(2 )− − ∆ cos(2 + 2 3⁄ ) − − ∆ cos(2 ) + − ∆ cos(2 + 2 3⁄ )Mechanical EquationBoth the inductance matrix and the permanent magnetic fluxlinkage depend on rotor position. Therefore, the mechanicalequations of the rotor must be included in the model to havea complete description of the motor [4].



Using Newton’s law = − − (15)Where = .

Torque is change in energy per change in angle, thus usingco energy= + m

+ (16)The torque produced by the machine is= (17)Transformation to qdo frameIf the variables are transformed into reference frame

attached to the rotor, reluctance which in the ABC framedepends on rotor position will be constant. Thetransformation used is called the park transform [11]Let be the park transform matrix then= (18)Where represents voltage, current etc in the respective

domains q , d , o stands for quadrature , direct and zerosequence variables respectively

is defined as= 2 3⁄ cos( ) sin( ) 1cos( − 2 3⁄ ) sin( − 2 3⁄ ) 1cos( + 2 3⁄ ) sin( + 2 3⁄ ) 1 (19)And it’s inverse as=2 3⁄ cos( ) cos( − 2 3⁄ ) cos( + 2 3⁄ )sin( ) sin( − 2 3⁄ ) sin( + 2 3⁄ )1 2⁄ 1 2⁄ 1 2⁄ (20)Let the power equation in the qdo reference frame is= , = + + (21)The input power in the ABC – frame is= = (22)Transform the abc variables to the qdo frame and use the

fact power must be equal in both references frames== 3 2⁄ + + 2= (23)= 3 2⁄ + + 2 (24)= + abc(25)= + qdo(26)

= + d− q0 + qdo(27)

( ) =+ 3 2⁄ ( − ∆ cos(2 − 2 )) −3 2⁄ ∆ sin(2 − 2 ) 0−3 2⁄ ∆ sin(2 − 2 ) + 3 2⁄ ( − ∆ cos(2 − 2 )) 00 0 (28)

qdo= L 0 00 L 00 0 + 0

m0 (29)stator voltage expressed in the rotor qdo frame then is

= + d− q0 + qdo(30)

Where = ⁄∴ = (31)∴ = d− q

(32)IV. CONTROL STRATEGIES

According to the electromagnetic torque of motorthe torque control can be achieved by regulation of currents

and in closed loops. The torque angle provides a widevariety of control choices in the PMSM drive system. Somekey control strategies are the following:

(i) Constant torque-angle control or zero-directaxis-current control;

(ii) Unity power factor control;(iii) Constant mutual air gap flux-linkages

control;(iv) Optimum-torque-per-ampere control;(v) Flux-weakening control.

V. FuzzyThe idea of fuzzy logic was invented by Professor L. A.Zadeh of the University of California at Berkeley in 1965.He was a mathematician, electrical engineer, computerscientist, artificial intelligence researcher and professoremeritus .FL is a problem-solving control systemmethodology that lends itself to implementation in systemsranging from simple, small, embedded micro-controllers tolarge, networked, multi-channel PC or workstation-baseddata acquisition and control systems. It can be implementedin hardware, software, or a combination of both. FLprovides a simple way to arrive at a definite conclusionbased upon vague, ambiguous, imprecise, noisy, or missinginput information. The output of a fuzzy controller isderived from fuzzifications of both inputs and outputs usingthe associated membership functions. A crisp input will beconverted to the different members of the associatedmembership functions based on its values [6].

To implement fuzzy logic technique to a realapplication requires the following three steps:

1. Fuzzification – convert classical data or crisp datainto fuzzy data or Membership Functions (MFs)

2. Fuzzy Inference Process – combine membershipfunctions with the control rules to derive the fuzzyoutput

3. Defuzzification – use different methods tocalculate each associated output and put them into



a table: the lookup table. Pick up the output fromthe lookup table based on the current input duringan application.

Generally, fuzzification involves two processes: derive themembership functions for input and output variables anddenote them with linguistic variables.In practice, membership functions can have multipledifferent types, such as the triangular, trapezoidal, Gaussian(two-sided), generalized bell, sigmoid – right, sigmoid –left, difference- sigmoid, product – sigmoid, polynomial –Z, polynomial –PI, and polynomial - S waveform. Thisdifferent type depends on the actual applications. For thosesystems that need significant dynamic variation in a shortperiod of time, a triangular or trapezoidal waveform shouldbe utilized. For those system that need very high controlaccuracy [7].Rule Base: In This paper rule base is built on twenty fiverules, and each of the rules depends on resolving the inputsinto a number of different fuzzy linguistic sets. Before therules can be evaluated, the inputs must be fuzzifiedaccording to each of twenty five linguistic sets.

The rules of the fuzzy used is given below

For ∆e

NB NS Z PS PB

NB PB PB PB PB PB

NS PB PM PM PM PB

Z PB PM PM PM PM

PS PB PB PB PM PM

PB PB PB PB PB PB

Table1. Rule Base for

For ∆e

NB NS Z PS PB

NB Z Z Z Z Z

NS PM PM PM PM PM

Z PM PM PS PS PS

PS Z Z Z PS PS

PB Z Z Z Z Z

Table2. Rule Base forFor

∆e

NB NS Z PS PB

NB PS PS PB PS Z

NS Z PS PB PS Z

Z Z PS PM PS Z

PS PS PS PM PS PS

PB Z PS Z PS Z

Table3. Rule Base for

VI. Simulation ModelsThe parameters of the PMSM used in simulation are givenas follows:Stator resistance 1.4 ohmq-axis self inductance 0.009 Hd-axis self inductance 0.0056 HMutual flux linkage due to rotor magnets 0.1546 wb-turnMoment of inertia 0.006 kg-m2

Friction coefficient 0.0 1 N-m/(rad/sec)Number of poles 6Constant frequency 2 KHzMaximum control voltage 10 VDC link voltage 285 VGain of the current transducer 0.8 V/AGain of the speed filter 0.05 V/V

Fig.2 Simulation Model for Conventional and Fuzzy TunedPI Controller



Fig.3 Simulation Model for Conventional and Fuzzy TunedPI D Controller

VI. RESULTS

Conventional PIThe speed control of PMSM drive is done with

conventional PI controller as shown in fig. the response isobserved as follows, from this delay time, rise time, peaktime, settling time and damper ratio are calculated.

Fig.4 Response for Conventional PI Controller

Conventional PIDIn order to increase the transient response for the

output speed of PMSM drive the tuning is done with PIDcontroller as shown in fig. and the response is observed asfollows. Delay time is increased, rise time also increases,with no peak time, settling tie is reduced. And it is underdamped.

Fig.5 Response for Conventional PID Controller

Fuzzy Tuned PIIn this the speed of the PMSM drive is controlled

by using Fuzzy tuned PI, with five membership functionsand (5x5) twenty five rules in the rule base. The response isas shown in Fig.6 . For this fuzzy tuned PI controller outputdelay time is reduced, rise time is increased, with no peaktime, settling time is reduced. And it is critically damped.

Fig.6 Response for Fuzzy Tuned PI Controller

Fuzzy Tuned PIDIn order to have better transient and steady state

response, speed control of PMSM drive is done with fuzzytuned PID controller. Output response is observed asfollows.



Fig.7 Response for Fuzzy Tuned PID Controller

Performance Index:From the above time responses of self tuned

PI/PID and fuzzy tuned PI/PID time response parametersdelay time, rise time, peak time, settling time, damping ratioare observed and tabulated as follows.

Parameters

TuningMethod

Delaytime( )

Risetime( )

Peaktime

Settlingtime( )

DampingRatio

PI 0.1290.21

0.36 2.43 0.774

PID 0.1410.99

1.64 1.40.1795

FuzzyTuned PI

0.0460.74

0.52 1.1 0.98

FuzzyTuned PID

0.0050.04

1 0.7 1

REFERENCES

[1] Abdullah I. Al-Odienat, Ayman A. Al-Lawama, TheAdvantages of PID Fuzzy Controllers Over TheConventional Types, American Journal of Applied Sciences5 (6) : 653-658, 2008 ISSN 1546-9239.

[2] R.G.Shriwastava,M.B.Diagavane, S.R.Vaishnav. LiteratureReview of Permanent Magnet AC Motors drive forAutomotive Application, Buletin Teknik Elektro danInformatik (Bulletin of Electrical Engineering andInformatics) Volume: 1, No.1, March 2012 ISSN: 2089-3191.

[3] Lindita Dhamo, Aida Spahiu, Simulation Based Analysis ofTwo Different Control Strategies for PMSM, InternationalJournal of Engineering Trends and Technolog (IJETT) –Volume: 4, Issue: 4 - April 2013.

[4] Arafa S. Mohamed, Mohamed S. Zaky, Ashraf S. Zein ElDin and Hussain A.Yasin Electrical Engineering Dept.,Faculty of Engineering, Minoufiya University, ComparativeStudy of Sensorless Control Methods of PMSM DrivesInnovative Systems Design and Engineering, ISSN 2222-

1727 (Paper) ISSN 2222-2871, (Online), Volume: 2, No 5,2011.

[5] Pragasen Pillay, Member IEEE, and Ramu Krishnan,Member IEEE, Application Characteristics of PermanentMagnet Synchronous and Brushless dc Motors for ServoDrives, IEEE Transaction on Industry Applications, Volume:21, Number:5 September / October 1991.

[6] Chuen Chien Lee, Fuzzy Logic in Control Systems: FuzzyLogic Controller, IEEE transaction as on systems man andCybernetics volume: 20, Number: 2, March / April 1990.

[7] Ying Bai and Dali Wang, Fundamentals of Fuzzy LogicControl – Fuzzy sets, Fuzzy Rules and Defuzzifications.

[8] Jurifa Mat Lazi, Zulkifilie Ibrahim, Marizan Sulaman,Fizatul Aini Patakor, Siti Noormiza Mat Isa, Fuzzy LogicSpeed Controller with Reduced Rule Base for Dual PMSMDrive. World academy of Science Engineering &Technology – 53 2011.

[9] Marek Stulrajter, Valeria Hrabovcova, Marek Franko,Permanent Magnets Synchronous Motor Control Theory,Journal of Electrical Engineering, Volume: 58, NO. 2, 2007,79 – 84.

[10] Bimal.K.bose Power Electronics and Variable FrequencyDrives Technology and Applications, Institute of Electricaland Electronics Engineers, Inc, New York, 1997.

[11] Krishnan R.: Electronic Motor Drives: Modeling, Analysisand Control, Upper Saddle River, New Jersey, USA: PrenticeHall, Feb. 2001.

First Author: Associate professor, Dept.of ElectricalEngineering, A.U.college of Engineering, AndhraUniversity,Visakhapatnam- 530003. A.P [email protected]

Second Author: Asst.professor, Dept.of ElectricalEngineering, Anil Neerukonda Institute of Technology &Sciences, Bheemunipatnam, [email protected]

Dr. N. Prema kumar and B. Vanajakshi Speed Control of PMSM ...iret.co.in/Docs/IJETEE/Volume...

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