Control Of The Permanent Magnet Synchronous Motor Using Model . - WSEAS
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang XiaomingControl of the Permanent Magnet Synchronous Motor Using ModelReference Dynamic InversionZHANG YAOU, ZHAO WANSHENG, KANG XIAOMINGSchool of Mechanical EngineeringShanghai Jiaotong University, Shanghai,PEOPLE’S REPUBLIC OF CHINAYaou zhang@sjtu.edu.cn, zws@sjtu.edu.cn, xmkang2002@gmail.comAbstract: Worldwide energy-saving emission has stimulated extensive application of permanent magnet synchronousmotor in industry. This work is a contribution to velocity control of the permanent magnet synchronous motor. Themodel of the permanent magnet synchronous motor has multi-variable, highly nonlinear, strong coupling characterwith external load; in order to control this complicated nonlinear model, the hierarchy model reference dynamicinversion control method has been developed. Based on the band of the different variables of the system, the controlsystem can be divided into long period control loop and short period control loop. The model reference dynamicinversion method is proposed as the kernel controller in different loops. Based on the desired closed loop referencemodel, the open loop controller can be designed for the long period loop and short period loop respectively, and thisopen loop controller can make the response of the system the same as that of the reference model. Comparing with thetraditional control method, this model reference dynamic inversion control method combine the virtues of the modelreference controller with that of the dynamic inversion controller, and this method is a fully nonlinear control methodin essence, which can avoid linearization error when using the approximate linearization controller and the problem ofthe parameter tuning when utilizing the traditional PI hierarchy controller. Finally, the simulation experiments havebeen set up and the simulation results have illustrated that this control method can control the permanent magnetsynchronous motor stably and successfully.Key words: Permanent Magnet Synchronous Motor (PMSM), Dynamic Inversion (DI), Velocity Tracking Control,model reference, hierarchy controllerThe typical construction of a PMSM consists of athree phase stator winding and a solid iron rotor withmagnets attached to its surface or inserted into the rotorbody. Permanent magnet synchronous motor controlsystem mainly consists of two parts, the main drivecircuit and the control circuit. The main drive circuittopology remains basically unchanged, while the studyof the control system focuses on the control circuit andcontrol strategies. The construction of the PMSM resultsin a magnetic field fixed to the rotor position. Since suchmachines are not capable of directly starting from themains, excitation by voltage source inverters (VSI)controlled by field orientation is required. Control1. IntroductionPermanent magnet synchronous motors (PMSMs) are ofgreat interest, particularly for industrial applications inthe low-medium power range, since it has superiorfeatures such as compact size, high torque/weight ratio,and high torque/inertia ratio [1]. Moreover, comparedwith induction motors, PM synchronous motors have theadvantages of higher efficiency [2]; due to the absenceof rotor losses and lower no-load current below the ratedspeed, its decoupling control performance is much lesssensitive to the parameter variations of the motor[3,4].ISSN: 1991-8763301Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang Xiaomingopen loop controller, which making the real reactiontracing that of the desired reference model. In order touse not only the virtue of the directly nonlinear controlbut also that of the model reference control, the modelreference dynamic inversion control method is utilizedto control the PMSM.This paper is arranged as follows: In section 2 themodel of the PM synchronous servo motor is introduced;In section 3, the kernel of the system controller, modelreference dynamic inversion, is described in detail; thePMSM controller based on the hierarchy modelreference dynamic inversion control method is designedin section 4; In section 5, the control effects andperformance of the hierarchy model reference dynamicinversion controller on PMSM are evaluated underdifferent loads with simulink in Matlab; Finally,conclusions are summarized in section 6.techniques such as vector control [5] or direct torquecontrol (DTC) [6] are standard for this type of drives.Based on the characteristics of the model ofpermanent magnet synchronous motor, many moderncontrol methods and intelligent control methods havebeen applied to the permanent magnet synchronousmotor, such as nonlinear control [7,8] and sliding modecontrol[9] have been developed to address the speed andposition control of PMSMs. The state feedbacklinearization of nonlinear systems control theory hasbeen introduced into the motor control in [10]. Theadaptive control strategy has been used in the control ofpermanent magnet synchronous motor in [11]. Besidesthese nonlinear control methods mentioned above, theintelligent control methods, such as the artificialintelligence expert system [12], fuzzy control [13], andneural networks [14, 15] have also been utilized in themotor drive system, and the great progress has beenachieved. Brock [16] used fuzzy logic controllers toadjust the gain of a controller in a sliding mode controllerfor speed and position control of PMSM. The controlstrategies in which recurrent fuzzy neural networks(FNN) were used to adjust the gain of the SMC forposition control of a PMSM was used by Wai [17].The purpose of this paper is to address theapplication of a relatively new control system designapproach known as model reference dynamic inversionto design the speed servo controller for highperformance PMSMs. Dynamic inversion is thenonlinear control method in essence and has beensuccessfully applied to large flexible complicatedsystem in documents. There has been a considerableamount of work in the application of dynamic inversionto control helicopters [18] and other aircraft [19].Dynamic inversion method has proven to be a veryeffective technique for the control of the nonlinearsystem. The model reference adaptive control has alsobeen successfully used in many systems [20, 21]; withthis control method, the response of the reference modelto the input signal is the same as the reaction of thecontrolled system with the controller acted upon; Inorder to fulfill this function, the minus of the output ofthe response of desired model reference and the outputof the reaction of the real system is utilized to adjust theISSN: 1991-87632. Mathematical model of PMSMA PMSM is composed of three phase’s stator windingsand permanent magnets mounted on the rotor surface(surface mounted PMSM) or buried inside the rotor(interior PMSM). The electrical equations of the PMsynchronous motor can be described in the rotor rotatingreference frame, written in the (dq) rotor flux referenceframe [22].The mathematic model of PMSM is based on thefollowing assumptions:(1) Neglecting the saturation of armature;(2) Neglecting the wastages of eddy and magnetichysterics;(3) There is no rotor damp resistance.The relations of voltage, torque and flux of PMSMare described as follows: L iɺq R ɺ id ω r 1 ωr iq L L id 0 R 01L 0 uq u d ω r φ L (1)where id and iq are the d and q axis stator currents,R and L are the stator phase resistance and inductance302Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLrespectively; ωr istherotorelectricalZhang Yaou, Zhao Wansheng, Kang Xiaomingof these two kinds of motor is similar, for simple, thesurface mounted PMSM is chosen as the control objectin this paper.speed;ud and uq are the stator voltages expressed in the dqreference frame and φ is the flux established by rotor3. Control Schemepermanent magnets; P is the number of pole pairs.Equation (1) describes electrical dynamics and isnonlinear since they involve products of state variables.ωs PωrDynamic inversion has been shown to provide asystematic approach for development of feedbackcontrol algorithms for nonlinear continuous timesystems. If given a nonlinear dynamic system describedas(2)ωs is inverter frequency [23].xɺ f ( x) g ( x)u (t )The electromagnetic torque is given byTe 3P φ iq ( Ld Lq )id iq (3)In equation (6),(6)f ( x) and g ( x) are nonlinearIf id 0 , the electromagnetic torque Te is proportionalfunctions of the system state vector x .If g ( x ) isto iq .This description is similar to the torque generatedinvertible for all values of x , then the dynamic inversioncontrol law can be designed byin a DC motor with independent field excitation. Thisfeature can simplify the controller design of the PMSM,which is used in the controller simulation experiment inthis paper.The equation of the motor dynamics isTe TL Bωr J ωɺ ru (t ) g 1 ( x)[[ xɺ ]des f ( x)]Where [ xɺ ]des is the time derivative of the desiredsystem state vector. Since the functions f and g are(4)smooth, this control law will change the original system(6) into a controllable linear first order uncoupleddifferential equations. It can be noticed that whensubstituting the equation (7) into the equation (6), theequation (8) can be achieved:TL stands for external load torque. B represents thedamping coefficient and J is the moment of inertia ofthe rotor.Thus, the mechanical dynamic of the PMSM can berewritten as3P φ iq ( Ld Lq )id iq TLBd ωr ω dtJ2JJxɺ [ xɺ ]des(8)This derivation is simple but very important for itformed the basis of the design of the model referencedynamic inversion controller of the PMSM.(5)The equation (5) shows that the electromagnetictorque is the product of state variables and it is nonlinear.The equations (1) and (5) constitute the whole controlmodel of the PMSM. The state-space model of theinterior PMSM is similar to the surface mounted PMSMonly that the model of the surface mounted PMSM doesnot have the product of the currents d-axis and q-axis inthe electromagnetic torque. However the control methodISSN: 1991-8763(7)The functions f and g , in general, depend on thenonlinear dynamic equation of the PMSM. It is easy tonotice that the basic concept behind dynamic inversionis to cancel out the nonlinear dynamics so it will followthe desired value.The dynamic inversion approach formulated abovecan be treated as two parts. The first part is equilibrium303Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang Xiaomingstate when xɺ 0 , the control input can be given asu 0 g 1 ( x ) f ( x )The preceding derivation suggests that any given systemwith appropriate properties can have the desireddynamic response. The application of dynamic inversioncontrol method requires that the control matrix g be(9)The second part is v , which can de designed asv(t ) g 1 ( x) [ xɺ ]desinvertible. The properties of the control law will dependon the properties of the control matrix. Obtaining aninvertible control matrix with suitable propertiesdepends on careful choices of the models to be used andthe states to be fed back.As for the high order system, such as the PMSM, thehierarchy control method, with model referencedynamic inversion as the kernel controller in each layer,can be utilized to fulfill such function. The approach isto apply dynamic inversion separately to the lowfrequency and high frequency dynamics of the system tobe controlled. The similar approach was demonstratedsuccessfully in the controller for the X-38[24].(10)Then, the whole control input is then taken as [19]u (t ) v(t ) u0 (t )(11)Letting[ xɺ ]des w(12)Combine with equation (8); using the Laplacetransform, the equation can be derived belowsX ( s ) W ( s )(13)If the W ( s ) is taken asW( s ) K ( s )[ X des ( s ) X ( s )]The proposed structure is shown in Fig. 1. ωd is the(14)desired velocity given by the engineer and the idcmd andThen combining with equation (10), the equation canbe givensX ( s ) K ( s )[ X des ( s ) X ( s )]the iqcmd are the desired currents of d-axis and q-axis(15)respectively. The structure is similar in form to that usedin classical control system design process, such as PIcontroller in the PMSM controller [25]. There is,however, a notable difference that the control laws indynamic inversion blocks are decidedly nonlinear.In both the cases of the long period and short perioddynamics, the dynamics to be inverted will depend onboth mechanical dynamics and electrical model of thePMSM.According to the equation (15), the transfer functionof the close loop isD( s ) X ( s)K ( s) X des ( s ) sI K ( s )(16)Then if the transfer function of the desired close loopreference dynamic model is chosen as D ( s ) , then theopen controller of the system could be selected as 1K ( s ) sD( s )[ I D ( s )]iqcmdωduq(17)ωrWhen designing the open loop controller, theproperties and dynamics of the resulting closed loopsystem can be selected according to the control requestgiven by the application engineer.idcmdiqudidFig. 1 the structure of the controller of the PMSMThe difference equation of the d-axis stator currentmodel in equation (1) can be rewritten as4. Controller of the Permanent MagnetSynchronous MotorISSN: 1991-8763304Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLLdid Rid NdtZhang Yaou, Zhao Wansheng, Kang XiaomingThen the d-axis control voltage will be(18)ud ud 0 L [ω (icmd i )] RidThe control value of d-axis stator current model willhave the formN PLωr iq udAnother control voltage uq can be achieved by using the(19)hierarchy control method. The out loop has long periodwhile the inner loop has a short period. The out loop orlong period dynamic inversion section will controlvelocity of the PSMS, and the variable to be controlledThe d-axis stator current is equilibrium stateWhen iɺd 0 , this control input can be given as ud 0ud 0 PLωiqis ωr . As the features of the surface mounted PMSM,(20)the kinematics equation will beThe control voltage ud will be taken as the sum of the3Pφ iq TLBd ωr ωr dtJ2JJtrim value and control input as developed in thedynamic inversion formulation aboveud v ud 0The control value N can be defined asD( s) N v(22)The difference equation of the d-axis current modelwill beand ξ is the damping ratio of the desired second-ordersystem. The control value of the open transfer functionof the velocity controller will be(24)For the current loop can be treated as the short periodloop, the simplest of 1st order transfer function can beselected as desired reference dynamics model. Then thedesired loop transfer function can be taken as 1 ωn2K ( s) 21 2(31)2 2 s 2ξωn s ωn s 2ξωn s ωn sωn2Which reduces toωD( s) (25)s ωω is the coefficient of the desired close loop function.K ( s) Then, according to the derivation in section 3, thecontrol value of the open transfer function in d-axis willbeωn22ξωn s(32)The control law is given byωɺ r w(33)And then 1wɺ 2ξ wωn ωn2 [ωcmd ωr ](26)(34)The input to the long period controller shown above is thedesired speed. This command comes directly from thesystem which the PMSM is used in. The desired q-axiscurrent can be achieved with long period controller. TheThe desired current of id is given byISSN: 1991-8763(30)(23)v L iɺd des Rid iɺ des ω (icmd i )ωn2s 2 2ξωn s ωn2ωn is the natural frequency of the desired 2nd system,The control input v will be sω s K ( s) 1 s ω s ω ω(29)The desired response for the long period variables istaken as a classic 2nd order response(21)Liɺd Rid v(28)(27)305Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang Xiaomingmethod of design the short period controller of q-axiscontrol voltage is the same as that used in d-axis.Discussion: This controller is the combination of thehierarchy controller, the model reference controller andthe dynamic inversion controller; it is superior to thecommon used hierarchy PID controller in the PMSMcontrol in that this method is nonlinear controller, and thecontroller and the parameters are achieved directly fromthe desired reference model. If the desired referencemodel is given, then controller will be designedaccording to the reference model and the controller willmake the system trace desired trajectory the same as thereference model does.In the first simulation, the desired velocity is700rad/s, while desired current of the d-axis is 0A and theload is kept none all the time. Fig. 2 shows the velocitytracing process of the PMSM without load. The solid line(-) represents the desired velocity while the dot line (--) isthe real-time simulation velocity. With the controllerdesigned in last section, it can be seen that real-timevelocity arrived at the desired velocity very fast andremain the desired velocity in no-load situation withoutany vibration. Fig. 3 and fig. 4 show the control current ofthe q-axis and d-axis separately. The d-axis current staysat zero all the time, while the q-axis current increases atthe start process and keep static at almost 0.08A when thevelocity of the PMSM arrives at the desired velocity, thiscurrent is no zero due to the resistance of the stator. In theno-load simulation, the result proves the validity of thecontroller.5. Simulation Experiments1000DvRvIn this section, the proposed approach above has beencarried out in PMSM to verify the performance of themodel reference nonlinear dynamic inversion speedcontrol scheme, using MATLAB/Simulink. Theparameters of the PMSM are given in Tab. I. Thesimulation results are shown in Figs. 2-12.The dynamic performance of the control system isevaluated by three simulation experiments using the stepspeed of 700 rad/sec as desired input and three kinds ofdifferent torques as load.V elocity (ra d/s)80060040020000Tab. 1 PMSM Parameters510152025time (s)3035404550Fig.2 the process of the velocity tracing of the PMSM withoutMachine parametersvalueResistance of the stator windings( Ω)2.875Number of pole pairs4Combined inertia of rotor and0.001load0.5q-ax is current (A )0.42load J (kg.m )Amplitude of the flux induced by the0.175permanent magnets of the rotor in the0.30.20.1stator phases φ (Wb)q and d axis inductances Lq Ld (H)0.0085Combined viscous friction of rotor and00010152025time (s)3035404550Fig. 3 the changing process of the current of the q-axis of thePMSM without loadload B(N.m.s/rad)ISSN: 1991-87635306Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROL5x 10Zhang Yaou, Zhao Wansheng, Kang Xiaoming-141000DvRvV e lo c ity (ra d /s )d-axis current (A)8000600400200-50510152025time (s)3035404550Fig. 4 the changing process of the current of the d-axis of the005101520PMSM without loadThe second simulation is to study and test the validityof the controller with abrupt plus step load. In the secondsimulation experiment, the desired velocity is 700rad/s,while desired current of the d-axis is 0A and a step load isacted upon the axis of the PMSM at one point after thePMSM has arrived at its desired velocity. Fig. 5 shows astep load with magnitude 0.2 N.m at 30s. This load issmall because the PMSM chosen in the simulation has avery small power. It is clear from the velocity tracingprocess in fig. 6 and the d-axis current changing processin fig.7 when the load is acted upon on the motor, thevelocity will decrease for a moment and will return to thedesired velocity at once; as the load increases, the currentof q-axis will increase too and will then return to theequivalent current in a few seconds; the current of d-axiswill remain zero all the time. This simulation experimenthave verified that this controller can control the PMSMwith abrupt plus load.25time (s)3035404550Fig.6 the process of the velocity tracing of the PMSM with aplus step load0.350.3q -a x is c u rre n t (A )0.250.20.150.10.0500510152025time (s)3035404550Fig.7 the changing process of the current of the q-axis of thePMSM with a plus step load8x 10-1460.34d-ax is c urre nt (A )T o rq u e (N .m )0.250.20.1520-2-40.1-60.05-800051015202530time (s)35404550510152025time (s)3035404550Fig. 8 the changing process of the current of the d-axis of theFig.5 the plus step load acted upon the PMSM in simulation 2PMSM with a plus step loadWhen the PMSM works in the real situation, it willISSN: 1991-8763307Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang Xiaomingmeet with the load which moves upward and downwardall the time. Thus, this simulation is carried out toguarantee the motor can keep the desired velocity withabrupt changing load. In the third simulation experiment,the desired velocity is 700rad/s, while desired current ofthe d-axis is 0A,the load will have some abrupt plus andminus steps. In the simulation process, the load actedupon the PMSM is in series which will increase from0N.m to 0.2N.m at 10s, and then remain static for 15sand then will increase to 0.3N.m and will remain at0.3N.m for another 15s, and then will decrease to0.2N.m and then remain 0.2N.m, which is shown in fig.9.It is can be noticed in fig.10 that the real-time velocitycan trace the desired velocity very well. The solid line (-)represents the desired velocity while the dot line (--) isthe real-time simulation velocity. In fig.10, when theload is increasing, the velocity will drop a little and willreturn soon, and when the load is decreasing, thevelocity will increase a little and will return soon. Thischanging situation coincides with the real controlprocess. Fig.11 shows that change of the current ofq-axis; it can be found that the current will goes to thestatic current soon and will keep at this value until thenew load acted upon; only the time when the load hasabrupt changes, the current will has some overshoots.These overshoots can be kept smaller by altering thecoefficients of the out-loop controller or by changing thedesired close loop reference model. Fig.12 shows thechange process of the current the d-axis. It can be seenthat the current of d-axis will keep zero all the time. Thethird simulation experiment shows that with the up-stepand down-step load, the controller can also make thePMSM work.Fig. 9 the load series acted upon the PMSM in simulation 31000DvRvv e lo c ity (ra d /s )80060040020000510152025time (s)3035404550Fig. 10 the process of the velocity tracing of the PMSM witha series of changing load0.40.35q -a x is c u rre n t(A )0.30.250.20.150.10.0500510152025time (s)3035404550Fig. 11 the changing process of the current of the q-axis of thePMSM with a series of changing load2x 10-131.5d -a x is c u rre n t (A )10.350.30.50-0.5Torque (N .m )0.25-10.2-1.50.15-200.10.0500510152025time (s)3035404550Fig. 12 the changing process of the current of the d-axis of the51015ISSN: 1991-87632025time (s)30354045PMSM with a series of changing load50308Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang XiaomingFrom the simulations above, it is noticeable that withthe controller designed in the last section, the PMSM cankeep desired velocity all the time, only when the load hasan abrupt change, the real-time velocity will have a littleovershoot and will return the desired velocity very soon.The control current of the q-axis will change along withthe load. The control current of the d-axis will accuratelyat the desired value zero. The simulations above haveguaranteed that the controller proposed above can controlthe PMSM and can be used quickly in the reality. Fordecoupling control performance of the PMSM is muchless sensitive to the parameter variations [3,4], when theaccurate parameters of the PMSM are given and thedesired close loop reference model which is decided bythe desired control performance is achieved, thecontroller designed above can be used in controlling thePMSM.short period or inner loop. The control performance ofthe hierarchy model reference dynamic inversioncontroller appeared to be superior in all respects to theclassical design for its high nonlinear character broughtby dynamic inversion controller and it has the virtues ofthe model reference controller. Three simulationexperiments have been done to test the controller withdifferent load. The results show that the controller cancontrol the velocity at desired value in differentoccasions. These simulation results guaranty the rightand validity of the controller designed. From thedescriptions above, it can be seen that hierarchy modelreference dynamic inversion can be a viable approach forthe control system design for PMSM.This compoundmethod can be a preferable control method for thecomplicated multi-input and multi-output (MIMO)system.Acknowledgements6. ConclusionsThe authors would like to thank The Ministry of Scienceand Technology of the People’s Republic of China forher financial support in project: 2007BAF19B04In order to meet with the worldwide demands forenergy-saving emission, in many areas, permanentmagnet synchronous motor is gradually replacing thetraditional three-phase asynchronous motor. This motoris a complex multi-variable, nonlinear, strong coupling ofthe multiple-input multiple-output system. It is difficultto design the controller. Therefore, the study of thecontrol strategy is currently a major problem in theindustry.According to the model of the PMSM, the hierarchymodel reference dynamic inversion speed controller forPMSM has been designed. Dynamic inversion is thenonlinear control method which is based directly on thenonlinear model, which can keep the high fidelitynonlinear information of the nonlinear dynamics andelectrical equation. The model reference method willmake the system have the desired response. Compared toclassical approaches, this compound method provided amuch more systematic approach for control law design.Based on the model of the PMSM, the two time scaleapproach was utilized in the control structure. Thevelocity was controlled in the long period or outer loopcontroller and the current controller was utilized in theISSN: 1991-8763References[1]. Slemon, G. R. Electrical machines forvariable-frequency drives. Proceeding of the IEEE [J],1994, 82(8):1123-1139.[2].Cetin E., Oguz U.A hybrid controller for the speedcontrol of a permanent magnet synchronous ):260-270[3]. Sen, P. C. Electric motor drives and control-past,present, and future[J], IEEE Transactions on IndustrialElectronics, 1990,37(1),562–575.[4]. Tzann-Shin Lee, Chih-Hong Lin, Faa-Jeng Lin. Anadaptive H controller design for permanent magnetsynchronous motor drives[J], Control EngineeringPractice,2005,13 (4): 425-439[5]. L. Tang, L. Zhong, M.F. Rahman, Y. Hu, A noveldirect torque control for interior permanent-magnetsynchronous machine drive with low ripple in torque309Issue 5, Volume 5, May 2010
WSEAS TRANSACTIONS on SYSTEMS and CONTROLZhang Yaou, Zhao Wansheng, Kang Xiaomingand flux a speed-sensorless approach[J], IEEETransaction Industry Application, 2003,(39):1748–1756.[6]. J. Rodrguez, J. Pontt, C. Silva, etc. PredictiveCurrent Control of a Voltage Source Inverter[J], IEEETransaction Industry Electronics,2007,54:495–503[7]. Baik, I. C., Kim, K. H. and Youn, M. J. Robustnonlinear speed control of PM synchronous motor usingboundary layer integral sliding mode control technique.IEEE Transactions on Control Systems Technology [J],2000, 8(1): 47-54.[8]. Solsona, J., Valla, M. I., Muravchik, C. Nonlinearcontrol of a permanent magnet synchronous motor withdisturbance torque estimation [J], IEEE Transactions onEnergy Conversion, 2000, 15(2):163-168.[9]. Paponpen, K., Konghirun, M., An improved slidingmode observer for speed sensorless vector control driveof PMSM[C].CES/IEEE 5th International PowerElectronics and Motion Control Conference, Shanghai,China,2007,2,972-976[10]. Hemici, B.; Nezli, L.; Tadjine, M.; Boucherit, M.S.Robust PID/backstepping control design for permanentmagnet synchronous motor drive[J].Control andIntelligent Systems,2006,34(3):194-204[11]. Lee Tzann-Shin, Lin Chih-Hong, Lin Faa-Jeng. AnNeural Network[C], IEEE International Symposium onIndustrial Electronics, 2007:30-35[16]. Brock S., Deskur, J. ,Zawirski, K. Robust speedand position control of PMSM[C]. In Proceedings of theIEEE International Symposium on Industrial Electronics.2003, 2: 667–672, Bled-Slovenija.[17]. Wai, R. J. Total sliding-mode controller for PMsynchronous servo motor drive using recurrent fuzzyneural network[J]. IEEE Transactions on IndustrialElectronics, 48(5), 926–944.[18].Du, J.F. Kondak, K. Zhang, Y.O.etc.Modelling andcontrol of a small-scale unmanned helicopter[J],Proceedings of the Institution of Mechanical Engineers,Part I: Journal of Systems and Control Engineering, 2008,222(6): 481-492[19]. Alfred C. Watts. Control of a High PerformanceManeuvering Reentry Vehicle Using DynamicInversion[C],AIAA Guidance, Navigation, and ControlConference and Exhibit, 2005, San Francisco,California,USA:1-16[20]. Uchiyama,N.,Mori, A. Model reference control forhuman-operated robots and application to a roboticmanipulator[J], Proceedings of the Institution ofMechanical Engineers, Part I: Journal of Systems andControl Engineering, 2009, 223(8):1163-1170[21]. Ohtake, H.,Tanaka, K., Wang, H. Fuzzymodel-based servo and model following control fornonlinear systems[J], IEEE Transactions on Systems,Man and Cybernetics, Part B: Cybernetics,2009,39(6):1634-1639[22]. Florent Morel, Xuefang Lin-Shi, Jean-Marie Retifetc.A predictive current control applied to a permanentmagnet synchronous machine, comparison with aclassical direct torque control [J],Electric Power SystemsResearch.2008, 78(8):1437-1447[23].Guchuan Zhu, Louis-A.Dessaint, t-Magnet Synchronous Motor wit
performance PMSMs. Dynamic inversion is the nonlinear control method in essence and has been successfully applied to large flexible complicated system in documents. There has been a considerable amount of work in the application of dynamic inversion to control helicopters [18] and other aircraft [19].
May 02, 2018 · D. Program Evaluation ͟The organization has provided a description of the framework for how each program will be evaluated. The framework should include all the elements below: ͟The evaluation methods are cost-effective for the organization ͟Quantitative and qualitative data is being collected (at Basics tier, data collection must have begun)
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Chính Văn.- Còn đức Thế tôn thì tuệ giác cực kỳ trong sạch 8: hiện hành bất nhị 9, đạt đến vô tướng 10, đứng vào chỗ đứng của các đức Thế tôn 11, thể hiện tính bình đẳng của các Ngài, đến chỗ không còn chướng ngại 12, giáo pháp không thể khuynh đảo, tâm thức không bị cản trở, cái được
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The permanent magnet linear synchronous motor usually can be divided into sine wave driving permanent magnet linear synchronous motor and the square-wave driving permanent magnet Brushless DC motor. In the paper, the two control strategies FOC and DTC were researched for PMLSM driven by three phase sine wave. II. THE MATHEMATICAL MODEL OF PMLSM
