Rasmussen, Henrik

Methods for estimation of the parameters in the inverter and the PM motor, based on special designed experiments, are given. Input to the system is the reference values for the stator voltages given as duty cycles for the Pulse With Modulated power device. The system output is the measured stator currents. Inverter parameters, stator resistance and inductance are measured at stand-still before the initial start-up of the drive. The strength of the permanent magnet is measured during a initial manual start-up of the drive. The measured parameters are used in a field oriented control system and the performance is experimentally verified

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    Aalborg UniversitetSelf-Commissioning for sensorless Field Oriented Control of PM motorsRasmussen, HenrikPublished in:Proceedings of the 11th International Power Electronics and Motion Control ConferencePublication date:2004Document VersionPublisher's PDF, also known as Version of recordLink to publication from Aalborg UniversityCitation for published version (APA):Rasmussen, H. (2004). Self-Commissioning for sensorless Field Oriented Control of PM motors. In Proceedingsof the 11th International Power Electronics and Motion Control ConferenceGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            ? Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            ? You may not further distribute the material or use it for any profit-making activity or commercial gain            ? You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us at vbn@aub.aau.dk providing details, and we will remove access tothe work immediately and investigate your claim.Downloaded from vbn.aau.dk on: April 25, 2017Self-commissioning for sensorless field oriented control of PM motorsH. RasmussenAalborg University, Fredrik Bajers Vej 7DK-9220 Aalborg, Denmarkemail: hr@control.auc.dkAbstract— Methods for estimation of the parameters in the in-verter and the PM motor, based on special designed experiments,are given. Input to the system is the reference values for the sta-tor voltages given as duty cycles for the Pulse With Modulatedpower device. The system output is the measured stator currents.Inverter parameters, stator resistance and inductance are mea-sured at stand-still before the initial start-up of the drive. Thestrength of the permanent magnet is measured during a initialmanual start-up of the drive. The measured parameters are usedin a field oriented control system and the performance is experi-mentally verified.NOMENCLATUREa complex spatial operator ej2pi/3isA,B ,C stator phase currents A,B and CusA,B ,C stator phase voltages A,B and Cis stator current complex space vectorus stator voltages complex space vectorψs stator fluxψr rotor fluxRs stator resistancesLs stator inductanceω synchronous angular frequencyωmech rotor speedp time derivative operatord/dtZp number of pole pairθ rotor positionθf filtered rotor positionI. INTRODUCTIONBecause standard inverters must be able to operate on differ-ent PM motors, the parameters of the PM motor have to beknown before starting the drive. Even if the operator werefamiliar with system identification, it would be too expen-sive to let him carry out a system identification procedureevery time installing a PM motor drive. This calls for an au-tomated process, where the required electrical parameters(inverter parameters for dead time compensation and sta-tor resistance, inductance and the strength of the permanentmagnet for field angle estimation) are obtained from on-linemeasurements. For Induction motors two main groups deal-ing with this are separated. One is identification during thefirst power-up, based on special designed test cycles on themotor ( Schierling [11], Summer and Asher [12], Vas [13],Rasmussen et. all [7] and [8]), and the other group is on-lineidentification of parameters in normal operation of the drive( Garces [1], Nilsen and Kazmierkowski [5], Marino et.all[4], Ortega and Espinosa [6], Hurst et. all [2] and Leonhard[3]).The first group, usually called self-commissioning, is thescope of this paper for field oriented control of PM motorsThe steps taken in this paper is shortly described by the fol-lowing.1. For standard power converters using IGBT’s, the turnon and turn off time of the device change significantlywith current level, resulting in a noticeable change inoutput mean-voltage. Particularly at low voltages, thisinverter nonlinearity has to be considered when usingvoltage references instead of measured voltages. Thisexperiment also gives the stator resistance.2. The current control system is adjusted in advance by anauto-tuning method for PI controllers for the d-axis andq-axis currents [14].3. The stator inductance is calculated from the relay ex-periment data or by measuring the open loop current re-sponse for a step in the stator voltage.4. The strength of the permanent magnet is measured in aclosed loop current system. Variation of the stator cur-rent vector leads to a variation of the angle of the perma-nent magnet and the strength is computed based on thevoltage in the stator.In the first tree experiments the motor is given a single phaseexcitation, i.e., two of the phases are impressed the samevoltage. No net torque is acting on the rotor and the motoris at stand-still. The stand-still experiments are performedbefore the initial start-up of the motor. The last item is per-formed as the first part of the command for running the mo-tor in the direction specified.II. PM MOTOR MODEL AND ROTOR FLUXOBSERVERFigure 1 shows the rotor field oriented control system de-scribed in details in [10] and [9]. The observer for the angleof the permanent magnet is shown in fig. 2. It is based oncomplex space phasors for voltage and currentsis = 23 (isA + aisB + a2isC)us = 23 (usA + ausB + a2usC)(1)The dynamics for the motor is then given by the followingstator voltage equation and flux linkage equationsdψsdt = us −Rsisψs = Lsis + ψrψr = ψMejθ(2)Fig. 1. Rotor Field Oriented ControlFig. 2. Signal flow graph of the rotor angle observerwhere θ is the rotor angle. The electrical rotor speed is ex-pressed from the mechanical rotor speed asdθdt= ω = Zpωmech (3)The estimation of ψr given in (2) requires an open integra-tion of the voltage equation. The unavoidable offsets con-tained in the inputs make the output drift. If the offsets aremodelled as uˆoff the estimator for the rotor flux ψˆr isdψˆsdt = = us −Rsis + uˆoffψˆr = ψˆM ejθˆ(4)where uˆoff has to be designed in a way leading to a fluxestimate with constant amplitude |ψˆr|.Figure 2 shows how this is obtained by a feedback of theestimated error ψM,ref − ψˆM . For known magnitude of thepermanent magnet ψM,ref = ψM is used and the observermay then be seen as a rotor field angle estimator.At zero and very low speed BEMF gives no information ofthe field angle. A new principle is introduced in this situa-tion by impressing a current in the direction of the default es-timated angle. This current then forces the permanent mag-net to align to this angle and in this way the estimated anglebecomes the correct one only with the error caused by fric-tion and load.Figure 3 shows the signal flow graph for the rotor speed es-timator. The arg(eje) block solves the modulus problem.Fig. 3. Speed estimator−0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5−505101520253035Inverter Nonlinearityisd [A]modelled and measured u sd [U]Fig. 4. Inverter nonlinearity giving Rs = 4.5, Uth = 11 andIth = 0.07The algorithm for the estimator then becomesdψˆsdt = us −Rsis + c1(ψM,ref − ψˆM )ejθˆψˆr = ψˆs − Lsisθˆ = arg(ψˆr)ωˆ = Kp(1− 1Tip ) arg ej(θˆ−θf )dθˆfdt = ωˆ(5)III. STATOR RESISTANCE AND INVERTERPARAMETERSFigure 4 shows the modelled and measured stator referencevoltage us,ref as a function of a slow sweep in the statorcurrent is. The stator resistance and the parameters in theinverter model are based on a static measurement of the ref-erence stator voltage us,ref as a function of the stator currentis.The correction of phase voltages are given byusA,ref = usA + Uinv(isA)usB,ref = usB + Uinv(isB)usC,ref = usC + Uinv(isC)withUinv(i) ={+Uth(1− e−i/Ith) for i > 0−Uth(1− e+i/Ith) elseIn the experiment we have isB = isB = 0.5isA givingfinv(isd) = real{23(Uinv(isd)+aUinv(−isd2)+a2Uinv(−isd2)}Inv.+Motor-Fig. 5. Setup for relay experimentA least square fit of Rsisd+ finv(isd) to the measured valuefor usd gives as shown in fig. 4 the parameters Rs, Uth andIth.IV. TUNING OF CURRENT CONTROLLERSFig. 5 shows the relay experiment setup for tuning of thecurrent controllers. The tuning of the PI-controller is basedon Ziegler-Nichols ultimate period method. An automaticand robust method giving this performance is developed byA˚stro¨m and Ha¨gglund [14] based on a relay experiment withthe controller replaced by a relay. When steady state isachieved, the ultimate period Tu is approximated by the pe-riod of the limit cycle.With the notation ∆u and ∆i for thechange of us and is, the relay experiment gives, as shownby A˚stro¨m [14], an approximation of the ultimate gain Ku :Ku ≈ 4∆upi∆iWith Ku and Tu determined from the relay experiment infig. 6, the parameters for a PI-controller may be computedas K = 0.45Ku and Ti = Tu/1.2 if Ziegler-Nichols rulesare used. In this paper the tuning parameters are chosen asK = 0.3Ku and Ti = Tu. The step response for a currentcontroller tuned with these parameters is shown in fig. 7With all the motor parameters estimated, a controller, givinga faster response, may be designed and used in the field ori-ented control system. Lots of laboratory tests have shownthat not much is gained in the total performance by doingthis.V. STATOR INDUCTANCEThe stator inductance Ls may be calculated from an experi-ment where us,ref is switched between u0s,ref and u0s,ref+das shown in fig. 8. u0s,ref is the steady state value foris,ref = is,0 From the initial slope of the curve α0 the statorinductance is calculated asLs =∆udα0(6)It is also possible to obtain Ls from the relay experimentusing the steepest slope as α0 in (6). For the motor used thedifference between the two methods was less than 10%. Thestep response method is considered as the most reliable andis used in the following.0 0.2 0.4 0.6 0.8 1 1.2 1.4−60−40−200204060Relay Experimenttime [msec]usd [U] and 100*i sd [A]Fig. 6. Relay experiment giving Ku = 169 and Tu = 0.000125−2 −1 0 1 2 3 400.511.522.5step response for current controllertime [msec]i sd   and   isd,ref   [A]Fig. 7. Step response for current controllerVI. THE PERMANENT MAGNETThe strength of the permanent magnet is measured in aclosed loop current system. The stator current vector is ro-tated with a constant velocity ω0 giving the relationψM =1ω0(usq −Rsisq)− LsisdAveraging over a cycle gives the strength of the permanentmagnet. Fig. 9 shows that it is possible to obtain a betterapproximation by looking at the angle dependency.VII. MEASURED MACHINE PARAMETERSFor comparison the following table shows values for the mo-tor in the test setup and factory measured values at 20◦CRs Ls ψM Zp NmechFact. meass 4.0 0.013 0.30 3 1500Self comm. 4.5 0.016 0.32(7)−5 0 5 10 15 20 250.811.21.41.61.822.2open loop step responsetime [msec]i sd  [A]Fig. 8. open loop step response giving Ls = 0.016−200 −150 −100 −50 0 50 100 150 20000.050.10.150.20.250.30.350.4ψM estimatedrotor angle [deg][Vs]Fig. 9. ψM estimated with forced speed during one cycle. Aver-aging gives ψM = 0.318Comments on the result:• Rs: Because reference voltages to the inverter are used inthe estimate of the stator resistance internal output resis-tance of the inverter is included in the result. This fact aswell as the temperature variation may explain the differ-ence between the estimated and the factory measured re-sistance, and correction would be possible, but becausereference voltages are used later in the controller, themeasured resistance is more appropriate.• Ls: The difference between the factory measured and theestimated value may be explained by saturation effects.What value is most correct is difficult to say, and for theoverall control performance it is not important at all.• ψM : The difference between the factory measured andthe estimated values may be explained by the angle de-pendency, which is not considered in the factory mea-sured data. The peaks on fig. 9 is due to uncompensatedFig. 10. Laboratory setupinverter nonlinearities.VIII. EXPERIMENTSFig. 1 shows the rotor field oriented control system. Havingthe parameters for dead time compensation, the motor pa-rameters for flux and speed estimation and the current con-trollers only parameters for the speed controller have to bedetermined. A relay method as used for the current con-trollers may be used for on line tuning of PI or PID controllerfor the speed. At zero and low speed the reference value forisd is given a value different from zero. If the rotor angle isestimated correctly a value for isd 6= 0 gives no torque. Ifthe rotor angle is estimated with an error the rotor is forcedin the direction of θˆ used in the controller. This new prin-ciple means that no manual mode at zero and low speed isnecessary, closed loop control is obtained for all values ofthe speed reference. The function for isd,ref isisd,ref = iref0e−|ωˆr|/ω0 (8)The laboratory setup shown in Fig. 10 is based on Real TimeWorkshop, Simulink from MathWorks and a DSP basedcontrol board from dSPACE. The drive system is via a signalconditioner connected to a DSP board in the computer. Thecontrol software is Simulink blocks written in C. Figure 11shows a step response for the speed and fig. 12 shows theresponse of the isd,ref -function. A high speed step responseis shown in fig. 13 and low speed step response is shown infig. 14.IX. CONCLUSIONSControllers for the d- and q-axis stator currents in a fieldoriented coordinate system is automatically tuned based onZiegler-Nichols ultimate gain method. By using a relay-feedback, approximate values for the ultimate gain and pe-riod are found and used for tuning the PI-controller. Byimpressing different functions for the current reference andmeasure values for (is, us,ref ), estimates of the inverter andmotor parameters are found. The basic idea of the methodsare the same as in the referenced self-commissioning liter-−1 −0.5 0 0.5 1 1.5 201002003004005006007008009001000Nmech[sec][rpm]Fig. 11. Normal Rotor speed step response 0− 1000rpm−1 −0.5 0 0.5 1 1.5 2−0.500.511.522.533.5isd[sec][A]Fig. 12. isd response for isd,ref function enabledature, but the implementation deviates in many ways fromthis literature, making it more feasible for a fully automatedprocess. Results for a 800W -motor are shown and com-pared to factory measurements. The auto-tuned field ori-ented control system is tested and the performance of thespeed sensor-less drive is excellent.REFERENCES[1] L.J.Garces. Parameter adaption for speed controlled static AC drivewith squirrel-cage induction motor. IEEE Trans. Ind. Appl., 1980, 16,pp.173-178.[2] Hurst K.D., T.G. Habetler, G. Griva, F. Profumo and P.L. Jansen(1995). A Self-tuning, Closed-loop Flux Observer for SensorlessTorque Control of Standard Induction Machines. PESC’95.[3] Leonhard W. Control of Electrical Drives. Springer Verlag Berlin(ISBN 3-540-13650-9), 1985.[4] Marino R., S. Peresada and P. Valigi (1993). Adaptive input-output lin-earizing control of induction motors. IEEE Tr. on Automatic Control,vol. 38, no. 2, pp.208-221.[5] R.Nielsen and M.P. Kazmierkowski. Reduced-order observer with pa-rameter adaption for fast rotor flux estimation in induction machines.IEE proc., Vol.136, No.1 pp35-43. January 1989.[6] Ortega R. and G. Espinosa (1993). Torque regulation of induction mo-tors. Automatica, vol. 29, no. 3, pp. 621-633.[7] H.Rasmussen, M.Tønnes and M.Knudsen (1995). Inverter and MotorModel Adaptation at standstill using reference voltages and measuredcurrents. EPE’95, Sevilla, Spain.[8] H. Rasmussen. Self-tuning torque control of induction motors for highperformance applications. PhD thesis, Department of Control Engi-neering, Aalborg University, Denmark, December 1995.−1 0 1 2 3 4 5−20002004006008001000120014001600High speed step responsetime [sec]Nmech [rpm]Fig. 13. High speed step response−1 0 1 2 3 4 5−20020406080100120Very low speed step responsetime [sec]Nmech [rpm]Fig. 14. Low speed step response[9] Rasmussen H., Vadstrup P. and Børsting H., ”Adaptive observer forspeed sensorless PM motor control”, IEEE IAS2003, Salt Lake City,Utah USA, Oct. 2003.[10] Rasmussen H., Vadstrup P. and Børsting H., ”Sensorless field orientedcontrol of a PM motor including zero speed”, IEMDC’03, Madison,Wisconsin, USA, June 2003.[11] Schierling H: Self-commissioning - a novel feature of moderninverter-fed induction motor drives. Third IEE Conference on PowerElectronics and Variable Speed Drives, 1988.[12] Sumner M. and G.M.Asher. Auto commissioning for voltage-referenced voltage-fed vector-controlled induction motor drives. IEEProc.-B, Vol.140, No.3, May 1993.[13] Vas Peter. Parameter Estimation, Condition Monitoring, and Diag-nosis of Electrical Machines. Clarendon Press - Oxford (ISBN 0-19-859375-9), 1993.[14] Aastro¨m K.J and T. Ha¨gglund. Automatic Tuning of PID Controllers.Instr. Society of America(ISBN 1-55617-081-5), 1988.

Self-Commissioning for sensorless Field Oriented Control of PM motors

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Self-Commissioning for sensorless Field Oriented Control of PM motors

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