research article estimation of stator resistance and...

Research ArticleEstimation of Stator Resistance and Rotor Flux Linkage inSPMSM Using CLPSO with Opposition-Based-Learning Strategy

Jian He and Zhao-Hua Liu

School of Information and Electrical Engineering Hunan University of Science and Technology Xiangtan 411201 China

Correspondence should be addressed to Zhao-Hua Liu zhaohualiu2009hotmailcom

Received 31 March 2016 Revised 26 May 2016 Accepted 27 June 2016

Academic Editor Qiao Zhang

Copyright copy 2016 J He and Z-H Liu This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Electromagnetic parameters are important for controller design and condition monitoring of permanent magnet synchronousmachine (PMSM) system In this paper an improved comprehensive learning particle swarm optimization (CLPSO) withopposition-based-learning (OBL) strategy is proposed for estimating stator resistance and rotor flux linkage in surface-mountedPMSM the proposedmethod is referred to as CLPSO-OBL In the CLPSO-OBL framework an opposition-learning strategy is usedfor best particles reinforcement learning to improve the dynamic performance and global convergence ability of the CLPSO Theproposed parameter optimization not only retains the advantages of diversity in theCLPSObut also has inherited global explorationcapability of the OBL Then the proposed method is applied to estimate the stator resistance and rotor flux linkage of surface-mounted PMSMThe experimental results show that the CLPSO-OBL has better performance in estimating winding resistance andPM flux compared to the existing peer PSOs Furthermore the proposed parameter estimation model and optimization methodare simple and with good accuracy fast convergence and easy digital implementation

1 Introduction

In recent years permanent magnet synchronous machines(PMSM) have been widely applied in industrial servo controlsystem and renewable energy power generation system [1ndash3] as they possess superiority in high power density torqueresponse high efficiency performances and so forth It isnecessary to exactly obtain the parameters of PMSM forassisting controller design speed regulation and conditionmonitoring in reality industrial drive system [4] Particularlythe most important physical parameters such as the statorresistance and the rotor PM flux linkage are the indicatorsof system health status For example the stator resistancecan be seen as the indicator of stator temperature due tometal thermal efficiency since the machine service life willbe damaged if the temperature exceeds its critical range Thedemagnetization in PM will influence machine electromag-netic torque output performance [5] However the PMSMis a typical nonlinear time-varying dynamic system whosephysical parameters are easily sensitive to the changes of envi-ronment such as noise and temperature Thus technologiesfor estimating the winding resistance and rotor flux linkage of

PMSM have become an important task for machine control[6] Existing literaturesmainly focus on online estimation andalgorithms including extended Kalman filter (EKF) [6 7]model reference adaptive system (MRAS) [8 9] recursiveleast-square (RLS) methods [10 11] and neural network(NN) [12] arewidely employedHowever the aforementionedmethods possess some drawbacks such as error convergenceunsteadiness and high computing expense in the process ofPMSM estimation

Recently inspired by biological computing some re-searchers try to use evolutionary computation techniquesto estimate the parameters of PMSM as the evolutionaryalgorithms have the ability to obtain a suitable set of param-eter values via optimizing objective function between thesystem model and the actual ones The particle swarmoptimization (PSO) has recently been introduced as anattractive optimization technique in system identificationand successfully applied in PMSM parameter estimation [25 13ndash15] due to its simple implementation little controlparameters multidirectional search and fast convergenceSince the basic PSO easily gets trapped in local minima whensolving the complex nonlinear problem of PMSM parameter

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2016 Article ID 5781467 7 pageshttpdxdoiorg10115520165781467

2 Journal of Control Science and Engineering

identification some enhanced operators are introduced intothe PSO and produced new hybrid PSO to design theparameters estimator of PMSM For example a coevolutionbased parameter estimator by combining multiple popu-lation PSO and artificial immune algorithm was investi-gated to improve multiparameter estimation performance ofPMSM [2] In order to improve the efficiency of parameteridentification a parallel implementation using an immune-cooperative dynamic learning particle swarm optimization(PSO) algorithm with multicore computation architecturesis presented for PMSM parameter estimations [5] anothermethod of graphic processing unit (GPU) accelerated parallelcoevolutionary immune PSO was designed for parameterestimation and temperature monitoring of a PMSM [15]for which the performance of the parameter estimation wassignificantly improved by those new PSO methods

In this paper in order to estimate the stator resistanceand rotor flux linkage of surface-mounted PMSM effectivelythe parameter estimation of PMSM is converted to anoptimization problem and then a novel comprehensive learn-ing particle swarm optimization (CLPSO) with opposition-learning strategy is proposed to explore optimal parameterthe proposed parameter optimizationmethod called CLPSO-OBL The CLPSO was firstly proposed by Liang et al [16]where all the flying directions of individuals are updated byrandomly selected particle of the whole population duringthe iteration process and it is superior in diversity keptfor solving multimodal optimization problem In order toimprove the global convergence of theCLPSO an opposition-based-learning (OBL) strategy is used for Pbest particleslearning and helps it jump out of local optima OBL is a rein-forcement learning strategy using computing and countercomputing simultaneously which can be used to acceleratethe convergence performance of other evolutionary algo-rithms [17] Finally the proposed CLPSO-OBL is applied toestimate the stator resistance and rotor flux linkage of surface-mounted PMSM The tests show that the proposed methodcan simultaneously accurately estimate stator resistance androtor flux linkage performance much better than the existingimproved hybrid PSOs

The structure of this paper is as follows An estimatormodel for the identification of stator resistance and rotor fluxlinkage of a PMSM is described in Section 2 A CLPSO-OBLalgorithm is proposed in Section 3 where the optimizationprocedure and steps are described Experimental results andthe analysis are given in Section 4 Finally some conclusionsand future work are presented in Section 5

2 PMSM Model and Design of ParameterEstimation Model

21 PMSM Model In order to estimate the parameters ofa PMSM the 119889119902-axis voltage equations of the machine areused

119906119889 = 119877119894119889 + 119871119889

119889119894119889

119889119905minus 119871119902120596119894119902

119906119902 = 119877119894119902 + 119871119902

119889119894119902

119889119905+ 119871119889120596119894119889 + 120595120596

(1)

PMSM

CLPSO-OBL

Ud

Uq

y

y

minus

+

f(p)

Ld = Lq and is fixed to p

ud(k) = Rid(k) minus Lq120596(k)iq(k)

uq(k) = Riq(k) + Ld120596(k)id(k) + 120595120596(k)

the measured value

Figure 1 PMSM parameter estimation model

where 120596 119906119889 119906119902 119894119889 and 119894119902 are electrical angular velocity119889119902-axis stator voltage and current and the parameter set119877 119871119889 119871119902 120595 is winding resistance 119889119902-axis inductances androtor PM flux linkage respectively where 119871119889 = 119871119902 = 119871 forSPMSM Equation (1) can be discretized as follows when themachine is on steady state

119906119889 (119896) = 119877119894119889 (119896) minus 119871119902120596 (119896) 119894119902 (119896)

119906119902 (119896) = 119877119894119902 (119896) + 119871119889120596 (119896) 119894119889 (119896) + 120595120596 (119896)

(2)

In real application the 119889119902-axis inductance belongs to theslowly varying parameters within a certain range comparedto the stator resistance and the rotor PM flux linkage soit can be considered constant and fixed to measured valuesduring parameter estimation process The parameters vector119877 120595 is unknown and needs to be identified in this studyThe estimation of the parameters is formulated as a systemoptimization problem by optimizing the designed objectivefunction in this study The fitness function is defined as adiscrepancy between the model output and the measuredactual system output The estimation of the parameters canbe addressed as an optimization problem via optimizingobjective function The PMSM parameter estimation modelis as shown in Figure 1 From Figure 1 by comparing modeloutput and actual output the objective function (3) forestimating the winding resistance and rotor flux linkage isdesigned as follows

119891 () = 119865 (119877 120595)

=1

119899

119899

sum

119896=1

(1003816100381610038161003816119906119889 (119896) minus 119889 (119896)

1003816100381610038161003816 +10038161003816100381610038161003816119906119902 (119896) minus 119902 (119896)

10038161003816100381610038161003816)

(3)

where the symbol ldquordquo means that they are computed voltagesby the estimated parameters and measured value The actualmachine parameter values can be obtained if the designedobjective function is minimized by the proposed CLPSO-OBL Actually the objective function (3) is a nonlinearmultidimensional function optimization problem and hasmany local points as it relates to the actual motor systemwhose system variables are easy to change

3 The Proposed Improved CLPSO Using OBL

31 Principle of Basic PSO Algorithm Inspired by the intel-ligent behavior of birds a swarm of particles are to find

Journal of Control Science and Engineering 3

a better solution Assuming in a 119889-dimensional solutionspace each particle 119894 is composed of the velocity vector 119881119894 =1198811198941 1198811198942 119881119894119889 and position vector119883119894 = 1198831198941 1198831198942 119883119894119889the velocity and position of 119894th particle are modified as givenin

119881119894119889 (119905 + 1) = 120601119881119894119889 + 1205821

lowast rand1 ( ) (119875119887119890119904119905119894119889 (119905) minus 119883119894119889 (119905))

+ 1205822


119883119894119889 (119905 + 1) = 119883119894119889 (119905) + 119881119894119889 (119905 + 1)

(4)

where 119875119887119890119904119905119894119889 represents the best position found by the 119894thparticle up to now and 119866119887119890119904119905119889 is the best particle among theentire population 1205821 and 1205822 are acceleration coefficients 120601is inertia weight factor and rand1 and rand2 are uniformlydistributed numbers generated randomly on [0 1]

32 Principle of Basic CLPSO Algorithm The CLPSO wasfirst introduced by Liang et al to solve multimodel problems[16]The searchingmechanism of CLPSO is that any particlersquosvelocity vector could be selected to update the velocity of theparticle that needs to be modified according to the designedlearning probability among the swarm This modificationstrategy can effectively avoid diversity losses of convergencefor population during the search process The modificationsof the velocity and position of 119894th particle in CLPSO are asgiven in

V119896+1119894119889

= 119908 times V119896119894119889+ 119888 times rand ( ) times (119875119887119890119904119905119891119894(119889) minus 119909

119896

119894119889)

V119896119894119889= min (V119896maxmax (V119889min V

119896

119894119889))

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(5)

where 119891119894 = [119891119894(1) 119891119894(2) 119891119894(119889)] defined which particlethe 119894th particle should learn from and 119875119887119890119904119905119891119894(119889) could be anyparticlersquos dimension corresponding value or could be its self-corresponding value which is determined by the learningprobabilities 119901119888 the details as in [16] The basic ideas areas given if the random number is greater than 119901119888119894 thisdimension will be learning from the particlersquos own Pbestotherwise it learns from other particlesrsquo Pbest There is onedrawback for existing CLPSO algorithm that is once thegroup falls into local optimum the search behavior of wholeswarmwill easily get similarity among the total population asthere is no effective mechanism to guarantee the escape fromlocal optima

33 OBL for Pbestrsquos Learning The Pbestrsquos positions are used asthe exemplars to lead the flying direction of thewhole popula-tion so the search status of Pbest particles is important for theCLPSO In order to enhance global convergence performanceof the Pbest particles an OBL strategy is introduced intoCLPSO The OBL was a machine learning method describedin detail by Rahnamayan et al [17] which is a simpletechnique that allows the population-based algorithms to

Measurementdata

M M

SPMSMDC motor

(load)

DSP drive

Rotor rotation speed and position

Current signals

DC voltage

CLPSO-OBL Host PCEstimatormodel

minus +

Figure 2The hardware and software platform for the identificationof stator resistance and rotor flux linkage in SPMSM

search for an optimal point in the counter direction and thecurrent search simultaneously The basic idea is that when asolution is being exploited in a direction it executes a searchin the opposite direction simultaneously as given in

= 119886 + 119887 minus 119909 (6)

where 119909 is real number in the interval [119886 119887] and is theopposite number of 119909 This definition can also be extendedto multidimensional space In 119863-dimensional space where1199091 1199092 119909119863 isin 119877 and 119909119894 isin [119886119894 119887119894] the point 119909119894 can be definedas

119894 = 119886119894 + 119887119894 minus 119909119894 (7)

The OBL machine learning technique is applied into CLPSOand executes opposite learning for Pbestrsquos particles as given in

119900119875119887119890119904119905119894119889(119895) = 119874119886119889 (119905) + 119874119887119889 (119905) minus 119875119887119890119904119905119894119889(119895)

119874119886119889 (119905) = min (119875119887119890119904119905119894119889(119895))

119874119887119889 (119905) = max (119875119887119890119904119905119894119889(119895))

(8)

After the above modification evaluate the fitness value(119865119894119905(119883119894)) of 119900119875119887119890119904119905119899 (opposition 119875119887119890119904119905119894) and update 119875119887119890119904119905119894as (119875119887119890119904119905119894 larr 119875119887119890119904119905119894 cup 119900119875119887119890119904119905119894) The proposed OBL learningoperator can help Pbest particles jump out of the local optimaand obtain a global convergence performance in the CLPSO

4 Experimental Verification

The proposed estimator is verified by experiments in thissection The Digital Signal Process (DSP) based vector con-trol system and the schematic diagram of testing processare shown in Figure 2 The offline estimation procedureusing CLPSO-OBL is as shown in Figure 3 The designparameters of the used prototype machine are detailed asfollows rated speed (400 rpm) rated current (4A) DClink voltage (36 v) nominal terminal wire resistance (0043)nominal self-inductance (291mh) nominal mutual induc-tance (minus0330mh) nominal 119889-axis inductance (324mh)


Begin

End

Parameterinitialization

CLPSO evolutionarycomputation

OBL strategy for Pbestparticles learning

Fitnesscalculation

Termination condition met

Optimal results

Best individualselection

Yes

No

Datameasurement

Parameter estimatormodeling

Objectivefunction

Figure 3 The process of parameter estimation in PMSM based onCLPSO-OBL

nominal 119902-axis inductance (324mh) nominal amplitude offlux induced by magnets (776mWb) number of pole pairs(5) nominal phase resistance (119879 = 25

∘C) (0330Ω) andinertia (08119890 minus 5 kgm2)

119871119889 = 119871119902 = 119871 is fixed to one of our prior estimated values[18] (in this research literature 119871 is set to be 397 (mWb) onnormal temperature and 119871 is set to be 376 (mWb) on theheating temperature) As is shown in Figure 3 the estimationof PMSM parameter includes data measurement parameterestimation modeling and model parameter optimizationprocedure For comparison the designed PMSM parameterestimationmodel is also tested by other existing PSOs such asa hybrid PSO with wavelet mutation (HPSOWM) operationmethod [19] comprehensive learning PSO (CLPSO) method[16] an improved comprehensive learning PSO (A-CLPSO)method [20] and adaptive particle swarm optimization(APSO) method [21] The basic settings of these PSOs are asfollows the population size is 50 the maximum generationis 300 and the number of runs is 30 All the tested PSOs areusing the same measurement data and operated on the samesoftware platform All experiments are carried out on thesame host computer with hardware configuration of Intel-core-i5-2450M and 40GB DDR3 RAM

The experiments are carried out under two different workconditions including normal temperature and temperaturevariation

Under normal temperature condition the convergenceof different PSOs is shown in Figure 4 the experimentalresults are depicted in Table 1 and the two parametersrsquoestimated results plotted curve for different PSOs is shown

Mea

n fit

ness

50 100 150 200 250 3000Iteration number

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101

100

Figure 4The convergence curve of five PSOs on PMSM parameterestimation under normal temperature condition

Table 1 Result of PMSM parameter estimation under normaltemperature condition

119879 = 300 HPSOWM CLPSO A-CLPSO APSO CLPSO-OBLParameters Results119877 (Ω) 0339 0329 0333 0346 0334120595 (mWb) 00790 7929 7920 7921 7916FitMean 1819 4224 4632 28034 886Std dev 2412 3124 2989 21209 267119905-value 273 755 885 905 0

in Figure 5 From Table 1 and Figure 3 it can be seen that theCLPSO-OBL shows the best performances in terms of meanstandard deviations and t-values compared to the existingpeer hybrid PSOs (ie HPSOWM CLPSO A-CLPSO andAPSO) Furthermore the convergence speed of CLPSO-OBLis faster than other hybrid PSOs as shown in Figure 4

It is evident that the optimality convergence and algo-rithmic efficiency of CLPSO is improved thanks to theOBL operator which enhanced the global convergence ofCLPSO and pushed it out from the local point As canbe seen from Table 1 the estimated winding resistance(0334Ω) by the CLPSO-OBL is quite coincident with itsnominal value (033Ω) under normal temperature conditionAlso the estimated flux linkage 120595 (7916mWb) by CLPSO-OBL is quite close to its nominal value (776mWb) Theslight difference between the estimated and nominal valuesof machine parameters may be caused by nonlinearity ofmachine operation condition

The parameters of PMSM are easily changed by theenvironment temperature In order to check the performanceof the proposedmethod andwhether it can track the variationof parameters with the changing temperature condition aheater is used to heat the prototype PMSM for 20minutes andthen to measure the data for experiment test The identifiedresults of temperature variation operation condition are listedin Table 2 and the comparison with different PSOs is as



Resis

tanc

e (Ω

)

03

031

032

033

034

035

036

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

(a) The estimated stator resistance

0 50 100 150 200 250 30000785

0079

00795

008

Iteration number

Flux

link

age (

wb)

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

(b) The estimated rotor PM flux linkage

Figure 5 The curve of estimated parameters with normal temperature

Table 2 Results of PMSM parameter identification with tempera-ture variation

119879 = 300 HPSOWM CLPSO A-CLPSO APSO CLPSO-OBLParameters Results119877 (Ω) 0455 0463 0455 0475 0454120595 (mWb) 00769 7669 7692 764 769Fit

Mean 906 4892 1709 26539 847Std dev 232 2972 945 12678 052119905-value 172 962 643 1433 0

Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101

Figure 6 The convergence curve of several PSOs on PMSMparameter estimation under temperature variation (with heating for20min)

shown in Figures 6 and 7 respectively FromTable 2 it is clearthat CLPSO-OBL outperforms other peer PSOs in terms ofmean standard deviation and 119905-test values From Figure 5it can be noticed that CLPSO-OBL has a faster convergencespeed than other hybrid PSOs

The analysis results show that the estimated windingresistance 119877 and rotor flux linkage 120595 vary with the changingtemperature condition For example the estimated windingresistance value increases from 0334 (Ω) to 0454 (Ω) withheating for 20 minutes under high temperature This phe-nomenon indicates that the metal resistance value increaseswith increasing temperature due to metal thermal efficiencyThe estimated rotor flux linkage decreases from 7916 (mWb)to 769 (mWb) the abrupt drop in the estimated rotor fluxlinkage after 20-minute heating This phenomenon indicatesthat magnetic field density decreases with the increasingtemperatureThese results show that the proposed parameterestimator can simultaneously track the stator resistance androtor PM flux linkage of PMSM

5 Conclusion

Stator resistance and rotor PM flux linkage are importantfor controller design and conditionmonitoring of permanentmagnet synchronous machine (PMSM) system In this studyan improved CLPSO with OBL strategy is proposed forestimating stator resistance and rotor PM flux in surface-mounted PMSM In the presented algorithm frameworkan OBL strategy is used for Pbest particles reinforcementlearning to improve the dynamic performance and globaloptimization ability of the CLPSOThe proposedmethod notonly retains the advantages of diversity in the CLPSO butalso has inherited global exploration capability of the OBLFinally the proposed method has been successfully appliedinto the estimation of the stator resistance and rotor PM fluxlinkage of SPMSM The experimental results show that theCLPSO-OBL has better performance inestimating windingresistance and rotor PMflux linkage compared to the existinghybrid PSOs Furthermore the proposed method can trackthe variation of machine parameters effectively with thechanging work conditionMoreover the proposed parameterestimation model is simple and with fast convergence andeasy digital implementation Thus the proposed method



Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL


0 50 100 150 200 250 300Iteration number

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)


Figure 7 Identified parameters under temperature variation (with heating for 20min)

can be used for the condition monitoring of the statorwinding and rotor PM flux linkage of PMSM With theincreasing of industrial real-time demand we will carry it outon Field-Programmable Gate Array (FPGA) and real-timeperformance control of PMSM will be greatly improved infuture

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China under Grants 61503134 and61573299 the China Postdoctoral Science Foundation fundedproject under Grants 2013M540628 and 2014T70767 and theHunan Provincial Education Department outstanding youthproject under Grant 15B087 The first author (Jian He isan Undergraduate Student) acknowledges the guidance ofteacher Xiao-Hua Li who is with the School of Informationand Electrical Engineering Hunan University of Science andTechnology

References

[1] Z Chen J M Guerrero and F Blaabjerg ldquoA review of thestate of the art of power electronics for wind turbinesrdquo IEEETransactions on Power Electronics vol 24 no 8 pp 1859ndash18752009

[2] Z-H Liu J Zhang S-W Zhou X-H Li and K Liu ldquoCoevo-lutionary particle swarm optimization using AIS and its appli-cation in multiparameter estimation of PMSMrdquo IEEE Transac-tions on Cybernetics vol 43 no 6 pp 1921ndash1935 2013

[3] F F M El-Sousy ldquoIntelligent optimal recurrent wavelet elmanneural network control system for permanent-magnet syn-chronous motor servo driverdquo IEEE Transactions on IndustrialInformatics vol 9 no 4 pp 1986ndash2003 2013

[4] S Kwak U-C Moon and J-C Park ldquoPredictive-control-baseddirect power control with an adaptive parameter identificationtechnique for improved AFE performancerdquo IEEE Transactionson Power Electronics vol 29 no 11 pp 6178ndash6187 2014

[5] Z H Liu X H Li H Q Zhang L H Wu and K Liu ldquoAnenhanced approach for parameter estimation using immunedynamic learning PSO based on multi-core architecturerdquo IEEESystemsMan and CyberneticsMagazine vol 2 no 1 pp 26ndash332016

[6] Y C Shi K Sun L P Huang and Y Li ldquoOnline identificationof permanent magnet flux based on extended Kalman filter forIPMSM drive with position sensorless controlrdquo IEEE Transac-tions on Industrial Electronics vol 59 no 11 pp 4169ndash4178 2012

[7] E Monmasson L Idkhajine M N Cirstea I Bahri A Tisanand M W Naouar ldquoFPGAs in industrial control applicationsrdquoIEEE Transactions on Industrial Informatics vol 7 no 2 pp224ndash243 2011

[8] M Rashed P F A MacConnell A F Stronach and P AcarnleyldquoSensorless indirect-rotor-field-orientation speed control of apermanent-magnet synchronous motor with stator-resistanceestimationrdquo IEEE Transactions on Industrial Electronics vol 54no 3 pp 1664ndash1675 2007

[9] S Moreau R Kahoul and J-P Louis ldquoParameters estimationof permanent magnet synchronous machine without addingextra-signal as input excitationrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 1 pp371ndash376 Ajaccio France May 2004

[10] R Ramakrishnan R Islam M Islam and T Sebastian ldquoRealtime estimation of parameters for controlling and monitoringpermanent magnet synchronous motorsrdquo in Proceedings of theIEEE International Electric Machines and Drives Conference(IEMDC rsquo09) pp 1194ndash1199 Miami Fla USA May 2009

[11] S J Underwood and I Husain ldquoOnline parameter estima-tion and adaptive control of permanent-magnet synchronousmachinesrdquo IEEE Transactions on Industrial Electronics vol 57no 7 pp 2435ndash2443 2010

[12] F F M El-Sousy ldquoRobust wavelet-neural-network sliding-mode control system for permanent magnet synchronousmotor driverdquo IET Electric Power Applications vol 5 no 1 pp113ndash132 2011


[13] L Liu W X Liu and D A Cartes ldquoPermanent magnet syn-chronous motor parameter identification using particle swarmoptimizationrdquo International Journal of Computational Intelligence Research vol 4 no 2 pp 211ndash218 2008

[14] Z-H Liu S-W Zhou K Liu and J Zhang ldquoPermanentmagnet synchronous motor multiple parameter identificationand temperature monitoring based on binary-modal adaptivewavelet particle swarm optimizationrdquo Acta Automatica Sinicavol 39 no 12 pp 2121ndash2130 2013

[15] Z-H Liu X-H Li L-H Wu S-W Zhou and K Liu ldquoGPU-accelerated parallel coevolutionary algorithm for parametersidentification and temperature monitoring in permanent mag-net synchronous machinesrdquo IEEE Transactions on IndustrialInformatics vol 11 no 5 pp 1220ndash1230 2015

[16] J J Liang A K Qin P N Suganthan and S BaskarldquoComprehensive learning particle swarm optimizer for globaloptimization of multimodal functionsrdquo IEEE Transactions onEvolutionary Computation vol 10 no 3 pp 281ndash295 2006

[17] R S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolutionrdquo IEEETransactions onEvolutionary Computation vol 12 no 1 pp 64ndash79 2008

[18] Z-H Liu J Zhang X-H Li and Y-J Zhang ldquoImmune co-evolution particle swarm optimization for permanent magnetsynchronous motor parameter identificationrdquo Acta AutomaticaSinica vol 38 no 10 pp 1698ndash1708 2012

[19] S H Ling H H C Iu K Y Chan H K Lam B C W Yeungand F H Leung ldquoHybrid particle swarm optimization withwavelet mutation and its industrial applicationsrdquo IEEE Trans-actions on Systems Man and Cybernetics Part B Cyberneticsvol 38 no 3 pp 743ndash763 2008

[20] H Wu J Geng R Jin et al ldquoAn improved comprehensivelearning particle swarm optimization and its application tothe semiautomatic design of antennasrdquo IEEE Transactions onAntennas and Propagation vol 57 no 10 pp 3018ndash3028 2009

[21] Z-H Zhan J Zhang Y Li and H S-H Chung ldquoAdaptiveparticle swarm optimizationrdquo IEEE Transactions on SystemsMan and Cybernetics Part B Cybernetics vol 39 no 6 pp1362ndash1381 2009

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identification some enhanced operators are introduced intothe PSO and produced new hybrid PSO to design theparameters estimator of PMSM For example a coevolutionbased parameter estimator by combining multiple popu-lation PSO and artificial immune algorithm was investi-gated to improve multiparameter estimation performance ofPMSM [2] In order to improve the efficiency of parameteridentification a parallel implementation using an immune-cooperative dynamic learning particle swarm optimization(PSO) algorithm with multicore computation architecturesis presented for PMSM parameter estimations [5] anothermethod of graphic processing unit (GPU) accelerated parallelcoevolutionary immune PSO was designed for parameterestimation and temperature monitoring of a PMSM [15]for which the performance of the parameter estimation wassignificantly improved by those new PSO methods

In this paper in order to estimate the stator resistanceand rotor flux linkage of surface-mounted PMSM effectivelythe parameter estimation of PMSM is converted to anoptimization problem and then a novel comprehensive learn-ing particle swarm optimization (CLPSO) with opposition-learning strategy is proposed to explore optimal parameterthe proposed parameter optimizationmethod called CLPSO-OBL The CLPSO was firstly proposed by Liang et al [16]where all the flying directions of individuals are updated byrandomly selected particle of the whole population duringthe iteration process and it is superior in diversity keptfor solving multimodal optimization problem In order toimprove the global convergence of theCLPSO an opposition-based-learning (OBL) strategy is used for Pbest particleslearning and helps it jump out of local optima OBL is a rein-forcement learning strategy using computing and countercomputing simultaneously which can be used to acceleratethe convergence performance of other evolutionary algo-rithms [17] Finally the proposed CLPSO-OBL is applied toestimate the stator resistance and rotor flux linkage of surface-mounted PMSM The tests show that the proposed methodcan simultaneously accurately estimate stator resistance androtor flux linkage performance much better than the existingimproved hybrid PSOs

The structure of this paper is as follows An estimatormodel for the identification of stator resistance and rotor fluxlinkage of a PMSM is described in Section 2 A CLPSO-OBLalgorithm is proposed in Section 3 where the optimizationprocedure and steps are described Experimental results andthe analysis are given in Section 4 Finally some conclusionsand future work are presented in Section 5

2 PMSM Model and Design of ParameterEstimation Model

21 PMSM Model In order to estimate the parameters ofa PMSM the 119889119902-axis voltage equations of the machine areused

119906119889 = 119877119894119889 + 119871119889

119889119894119889

119889119905minus 119871119902120596119894119902

119906119902 = 119877119894119902 + 119871119902

119889119894119902

119889119905+ 119871119889120596119894119889 + 120595120596

(1)

PMSM

CLPSO-OBL

Ud

Uq

y

y

minus

+

f(p)

Ld = Lq and is fixed to p

ud(k) = Rid(k) minus Lq120596(k)iq(k)

uq(k) = Riq(k) + Ld120596(k)id(k) + 120595120596(k)

the measured value

Figure 1 PMSM parameter estimation model

where 120596 119906119889 119906119902 119894119889 and 119894119902 are electrical angular velocity119889119902-axis stator voltage and current and the parameter set119877 119871119889 119871119902 120595 is winding resistance 119889119902-axis inductances androtor PM flux linkage respectively where 119871119889 = 119871119902 = 119871 forSPMSM Equation (1) can be discretized as follows when themachine is on steady state

119906119889 (119896) = 119877119894119889 (119896) minus 119871119902120596 (119896) 119894119902 (119896)

119906119902 (119896) = 119877119894119902 (119896) + 119871119889120596 (119896) 119894119889 (119896) + 120595120596 (119896)

(2)

In real application the 119889119902-axis inductance belongs to theslowly varying parameters within a certain range comparedto the stator resistance and the rotor PM flux linkage soit can be considered constant and fixed to measured valuesduring parameter estimation process The parameters vector119877 120595 is unknown and needs to be identified in this studyThe estimation of the parameters is formulated as a systemoptimization problem by optimizing the designed objectivefunction in this study The fitness function is defined as adiscrepancy between the model output and the measuredactual system output The estimation of the parameters canbe addressed as an optimization problem via optimizingobjective function The PMSM parameter estimation modelis as shown in Figure 1 From Figure 1 by comparing modeloutput and actual output the objective function (3) forestimating the winding resistance and rotor flux linkage isdesigned as follows

119891 () = 119865 (119877 120595)

=1

119899

119899

sum

119896=1

(1003816100381610038161003816119906119889 (119896) minus 119889 (119896)

1003816100381610038161003816 +10038161003816100381610038161003816119906119902 (119896) minus 119902 (119896)

10038161003816100381610038161003816)

(3)

where the symbol ldquordquo means that they are computed voltagesby the estimated parameters and measured value The actualmachine parameter values can be obtained if the designedobjective function is minimized by the proposed CLPSO-OBL Actually the objective function (3) is a nonlinearmultidimensional function optimization problem and hasmany local points as it relates to the actual motor systemwhose system variables are easy to change

3 The Proposed Improved CLPSO Using OBL

31 Principle of Basic PSO Algorithm Inspired by the intel-ligent behavior of birds a swarm of particles are to find



119881119894119889 (119905 + 1) = 120601119881119894119889 + 1205821


+ 1205822


119883119894119889 (119905 + 1) = 119883119894119889 (119905) + 119881119894119889 (119905 + 1)

(4)



V119896+1119894119889


119896

119894119889)


119896

119894119889))

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(5)



Measurementdata

M M

SPMSMDC motor

(load)

DSP drive


Current signals

DC voltage


minus +



= 119886 + 119887 minus 119909 (6)


119894 = 119886119894 + 119887119894 minus 119909119894 (7)


119900119875119887119890119904119905119894119889(119895) = 119874119886119889 (119905) + 119874119887119889 (119905) minus 119875119887119890119904119905119894119889(119895)

119874119886119889 (119905) = min (119875119887119890119904119905119894119889(119895))

119874119887119889 (119905) = max (119875119887119890119904119905119894119889(119895))

(8)





Begin

End




Fitnesscalculation


Optimal results


Yes

No

Datameasurement


Objectivefunction







Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101

100









Resis

tanc

e (Ω

)

03

031

032

033

034

035

036

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL


0 50 100 150 200 250 30000785

0079

00795

008

Iteration number

Flux

link

age (

wb)

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL






Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101




5 Conclusion




Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL



HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119881119894119889 (119905 + 1) = 120601119881119894119889 + 1205821


+ 1205822


119883119894119889 (119905 + 1) = 119883119894119889 (119905) + 119881119894119889 (119905 + 1)

(4)



V119896+1119894119889


119896

119894119889)


119896

119894119889))

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(5)



Measurementdata

M M

SPMSMDC motor

(load)

DSP drive


Current signals

DC voltage


minus +



= 119886 + 119887 minus 119909 (6)


119894 = 119886119894 + 119887119894 minus 119909119894 (7)


119900119875119887119890119904119905119894119889(119895) = 119874119886119889 (119905) + 119874119887119889 (119905) minus 119875119887119890119904119905119894119889(119895)

119874119886119889 (119905) = min (119875119887119890119904119905119894119889(119895))

119874119887119889 (119905) = max (119875119887119890119904119905119894119889(119895))

(8)





Begin

End




Fitnesscalculation


Optimal results


Yes

No

Datameasurement


Objectivefunction







Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101

100









Resis

tanc

e (Ω

)

03

031

032

033

034

035

036

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL


0 50 100 150 200 250 30000785

0079

00795

008

Iteration number

Flux

link

age (

wb)

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL






Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101




5 Conclusion




Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL



HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Begin

End




Fitnesscalculation


Optimal results


Yes

No

Datameasurement


Objectivefunction







Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101

100









Resis

tanc

e (Ω

)

03

031

032

033

034

035

036

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL


0 50 100 150 200 250 30000785

0079

00795

008

Iteration number

Flux

link

age (

wb)

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL






Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101




5 Conclusion




Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL



HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Resis

tanc

e (Ω

)

03

031

032

033

034

035

036

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL


0 50 100 150 200 250 30000785

0079

00795

008

Iteration number

Flux

link

age (

wb)

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL






Mea

n fit

ness


HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

102

101




5 Conclusion




Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL



HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Resis

tanc

e (Ω

)

042

043

044

045

046

047

048

HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL



HPSOWMCLPSOA-CLPSO

APSOCLPSO-OBL

00765

0077

00775

0078

Flux

link

age (

wb)




Competing Interests


Acknowledgments


References

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article estimation of stator resistance and...

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