PEDS 2007       Adaptation of Motor Parameters in Sensorless PMSM Drives                                    Antti Piippo, ...
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TABLE I                 IV. PARAMETER ADAPTATION                                                              MOTOR DATA  ...
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0.6                                                                                ACKNOWLEDGEMENT     I           0.5   -...
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Adaption of motor paramenters in sensorless pmsm driver

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Adaption of motor paramenters in sensorless pmsm driver

  1. 1. PEDS 2007 Adaptation of Motor Parameters in Sensorless PMSM Drives Antti Piippo, Marko Hinkkanen, and Jorma Luomi Power Electronics Laboratory Helsinki University of Technology P.O. Box 3000, FI-02015 TKK, Finland Abstract-The paper proposes an on-line method for the error. On the other hand, the back-emf is small at low speeds,estimation of the stator resistance and the permanent magnet and the stator resistance estimate plays an important role influx in sensorless permanent magnet synchronous motor drives. the estimation.An adaptive observer augmented with a high-frequency signalinjection technique is used for sensorless control. The observer Several methods have been proposed to improve the per-contains excess information that is not used for the speed and formance of a PMSM drive by estimating the electricalposition estimation. This information is used for the adaptationparameters. In [7], an MRAS scheme is used for the on-of the motor parameters. At low speeds, the stator resistance isline estimation of the stator resistance and the PM flux withestimated, whereas at medium and high speeds, the permanent position measurement. Reactive power feedback is used formagnet flux is estimated. Steady-state analysis and small-signal estimating the PM flux in [9]. The stator current estimationanalysis are carried out to investigate the parameter estimation,and adaptation mechanisms are defined for the parameters. The error and a neural network can be used for estimating both theconvergence of the parameter estimates is shown by simulations PM flux and the stator resistance [10]. The stator inductancesand laboratory experiments. The stator resistance adaptation and the PM flux are estimated using the steady-state voltageworks down to zero speed in sensorless control. equations and the flux harmonics, respectively in [11]. A DC- current signal is injected to detect the resistive voltage drop I. INTRODUCTION for the resistance estimation in [12], and the PM flux linkage Permanent magnet synchronous machines (PMSMs) are is estimated by taking it as an additional state of an extendedused in many high-performance applications. For vector con- Kalman filter in [13].trol of PMSMs, information on the rotor position is required. Some parameter estimation schemes have also been devel-In sensorless control, the methods for estimating the rotor oped for sensorless control methods. In [7], an MRAS schemespeed and position can be classified into two categories: is applied for the stator resistance estimation. A parameterfundamental-excitation methods [1], [2] and signal injection estimator is added to two position estimation methods formethods [3], [4]. The methods can also be combined by estimating the stator resistance and the PM flux in [14]. Inchanging the estimation method as the rotor speed varies [5], [15], these parameters are estimated using both the steady-[6]. state motor equations and the response to an alternating The fundamental-excitation methods used for sensorless current signal. In [14], [15], the convergence of the estimatedcontrol are based on models of the PMSM. Hence, the parameters to their actual values is not shown. [16] proposes aelectrical parameters are needed for the speed and position method where the resistance and the inductances of a salientestimation [7]. The errors in the stator resistance estimate PMSM are extracted from an extended EMF model. Threeresult in an incorrect back-emf estimate and, consequently, electrical parameters are estimated simultaneously, but theimpaired position estimation accuracy. The operation can also behavior of the stator resistance estimate is not convincing.become unstable at low speeds in a loaded condition. The This paper proposes a method for the online estimation ofdetuned estimate of the permanent magnet (PM) flux results the stator resistance and the PM flux in sensorless control.in incorrectly estimated electromagnetic torque [8], and also The method is based on a speed-adaptive observer that isimpairs the position estimation accuracy. Errors in the d- augmented with a high-frequency (HF) signal injection tech-and q-axis inductances of a salient PMSM also affect the nique at low speeds [17]. The excess information availableestimation and the torque production, and can degrade the in the observer is used for the adaptation of the parameters.current control performance. At medium and high speeds, the PM flux is estimated from The stator resistance and the PM flux depend on the motor the d-axis current estimation error. At low speeds, the statortemperature, and thus change rather slowly. On the other hand, resistance is estimated from a speed correction term producedmagnetic saturation decreases the inductances, which thus by the signal injection method. The sensitivity of the d-axisdepend on the load condition. The inductances can be modeled current estimation error and the speed correction term to theas functions of the stator flux or the stator current, but an parameter errors are investigated by means of steady-state andestimation scheme is required for the stator resistance and the small-signal analyses, and adaptation laws are designed for thePM flux. The rotor back-emf is proportional to the PM flux and estimation of the parameters. The stability and the convergencethe resistive voltage drop to the stator resistance. At medium of the parameter estimators are investigated by means of sim-and high speeds, the effect of the PM flux estimation error is ulations and laboratory experiments. The resistance adaptationmore significant than that of the stator resistance estimation is shown to work down to zero speed in sensorless control. 1-4244-0645-5/07/$20.00©2007 IEEE 175
  2. 2. i/ F£ where estimated quantities are marked by ^ and Us,ref is the stator voltage reference. The estimate of the stator current and Us,ref Ad- + / m the estimation error of the stator current are ==>justable L-(,Os -,pm) --A1t model js is = (5) AL is~ ~ 1 is = il *1 - is (6) respectively, where iV is the measured stator current expressed Fig. 1. Block diagram of the adaptive observer. in the estimated rotor reference frame. The feedback gain matrix A is proportional to the rotor speed up to the nominal speed [17]. II. PMSM MODEL The speed adaptation is based on an error term The PMSM is modeled in the d-q reference frame fixed tothe rotor. The d axis is oriented along the PM flux, whose Fe = Clis (7)angle in the stator reference frame is 0m in electrical radians.The stator voltage equation is where Ci = [O Lq], i.e., the current error in the estimated q direction is used for adaptation. The estimate of the electrical Us Rsis + s WmJ+5 + (1) angular speed of the rotor is obtained using a PI speedwhere us [ud Uq ]T is the stator voltage, is [id iq ]T the adaptation mechanismstator current, sb= [bd /q ]T the stator flux, Rs the statorresistance, Wm =m the electrical angular speed of the rotor, Wm =-kpF -kiJ Fedt (8)andThe stator flux is J K0 -1 I where kp and ki are nonnegative gains. The gain selection is described in [17]. The estimate Om for the rotor position is evaluated by integrating Win sb= Lis+ bpm (2) B. High-Frequency Signal Injectionwhere 14pm = [/pm O]T is the PM flux and The adaptive observer described above is augmented with a HF signal injection method to stabilize the speed and position L L Lq Ld fq] estimation at low speeds [17]. By using the HF signal injection method with an alternating voltage u, as a carrier excitationis the inductance matrix, Ld and Lq being the direct- and signal [18], an error signal E 2K Om proportional to thequadrature-axis inductances, respectively. The electromagnetic position estimation error 0m = m 0-m is obtained, KStorque is given by being the signal injection gain. The error signal is used for correcting the estimated position by influencing the direction Te = 3p2TJTis (3) of the stator flux estimate of the adjustable model. For the combined observer, the adjustable model (4) is modified towhere p is the number of pole pairs. III. SPEED AND POSITION ESTIMATION Qs = Us,ref -Rss- (m - )JQs + Als (9)A. Adaptive Observer where An adaptive observer [17] is used for the estimation of thestator current, rotor speed, and rotor position. The speed and SE: = apE + -aj + dt (10)position estimation is based on the estimation error between is the speed correction term, -yp and tYj being the gains of thetwo different models; the actual motor can be considered as a PI mechanism driving the error signal E to zero. In accordancereference model and the observer including the rotor speed with [6], these gains are selected asestimate Wm as an adjustable model. The error term usedin a speed adaptation mechanism is based on the estimation 2Ki 2 (1 1)error of the stator current. The estimated rotor speed, obtained /yP 2K 6KEusing the adaptation mechanism, is fed back to the adjustablemodel. where ai is the approximate bandwidth of the PI mechanism. The adaptive observer is formulated in the estimated rotor At low speeds, the combined observer relies both on thereference frame. The block diagram of the adaptive observer signal injection method and on the adaptive observer. Theis shown in Fig. 1. The adjustable model is based on (1) and influence of the HF signal injection is decreased linearly as the(2), and defined by speed increases by decreasing both the HF excitation voltage and the bandwidth ai. At speeds higher than a threshold speed ,bs = Us,ref -Rsis- mJQs + Ais (4) WoA, the estimation is based only on the adaptive observer. 176
  3. 3. TABLE I IV. PARAMETER ADAPTATION MOTOR DATA The current estimation error is of the adaptive observer Nominal voltage UN 370 Vcontains information that can be used for the parameter Nominal current IN 4.3 Aadaptation. In [7], [10], the components of is are used for Nominal frequency fN 75 Hz Nominal torque TN 14.0 Nmthe adaptation of two parameters in a PMSM drive equipped Stator resistance RS 3.59 Qwith a motion sensor. Solving the parameters from the steady- Direct-axis inductance Ld 36.0 mHstate voltage equations as in [11] would require filtering to Quadrature-axis inductance Lq 51.0 mH PM flux <bpm 0.545 Vsprevent incorrect operation in transients. It is to be noted that Total moment of inertia 0.015 kgm2the PMSM dynamics offer only two degrees of freedom. Sincethe component iq is used for the speed estimation in this paper,one parameter can thus be adjusted using id because it is controlled to a considerably smaller value than In low-speed operation, the HF signal injection method the q component. In the component form, the result isprovides additional information through the speed correction Rterm w . Instead of solving the parameters directly from the Rs -Lqiq10I 0° L gmELd opm j ej L- q - Om opmresponse to the injected signal [12], wo is used here for the (16)parameter adaptation. Hence, if wo differs from zero in steady For investigating the sensitivity of id and wo to the pa-state or if the current estimation error id is nonzero, the motor rameter errors, the variables id and wo are solved from (16).parameter estimates are inaccurate and the variables wo and d Assuming Rs<pm »> WmoLdLqiq the result iscan be driven to zero by adjusting the parameter estimates. R,Wmiq L 2L q [.td Rl k ;qqiq Rs M l (17)A. Steady-State Analysis Stator Resistance Adaptation L ej fpm L Som - L opm At low speeds, the stator resistance estimate plays an im- It can be seen that both variables on the left-hand side dependportant role in the speed and position estimation, particularly both on Rs and <pm. The correction term w, is selected forin loaded conditions. To extract the sensitivity of the d-axis parameter adaptation because iq has more effect on id than oncurrent estimation error id and the speed correction term w, w . When using relative parameter errors, the speed correctionto the parameter errors, the combined observer is investigated term isin steady state. The position estimation error is assumed zero 1 ( Rs + 4bpmbecause the HF signal injection method is in use. W = Ypm Rsi jR mpm s opmbm (18) In steady state, the equations of the PMSM and the adaptiveobserver can be written as The dependence between the stator resistance error and wo is proportional to the resistive voltage drop, whereas the Us = Rsis + WmJ(Lis + /pm) (12) dependence between the PM flux error and wo is proportional to the back-emf. Us = Rsis + (Win - o)J(Lis + pm)- Ais (13) The effect of the parameter errors on w, was calculatedrespectively. The estimated quantities are expressed in terms numerically, using the parameters given in Table I. The effectof their actual values and estimation errors, i.e. x = x. of the stator resistance error Rs /R, =-0.1 is illustrated inThe stator voltage is eliminated by combining (12) and (13), Fig. 2(a), and the effect of the PM flux error <pm/<)pm -0.1yielding in Fig. 2(b). The results obtained from the approximate equa- tion (18) are shown. In addition, the figures show the results Rsis + WmJ(Lis + ,pm) (14) obtained using (15) and the results of steady-state simulations. = (Rs - Rs) (is--Is) The speed values used for the calculation and simulation in Fig. 2(a) are -0.067 p.u., 0 p.u., and 0.067 p.u, and the torque + (Wmi-n )J[L(is-i-) +(spm 14pm)] -Ais values used in Fig. 2(b) are -TN, 0, and TN. According toWhen it is assumed that the estimation errors and the speed Fig. 2, the assumptions used in (18) result in only a small error.correction term wo are small, their products can be omitted At low speeds and large values of load torque, the resistiveand the equation reduces to voltage drop dominates, and the stator resistance is thus a reasonable selection for the adaptation. (RsI + WmJL + A)is (15) For the stator resistance adaptation, the closed-oop system shown in Fig. 3 is investigated. The gain -Ris- WmJ/npm - J(Lis + v/pm) FR -tq/pm= (19) The q component of the current estimation error is zeroin steady state because it is driven to zero by the adaptation corresponds to (17) with bpm 0= . The stator resistance ismechanism (8). The observer gain A is proportional to the rotor estimated by integration from w , the transfer function of thespeed and is also omitted since low speeds are investigated. adaptation mechanism thus beingIn addition, the d component of the stator current is ignored GR(S) -kR/S (20) 177
  4. 4. 50 tpm~~~~~~~~<p qJpm+~ F, (s) 0 -G Vpm s - 0 2-50 Fig. 4. Closed-oop system of the PM flux adaptation. -1 0 1 Te /TN (a) The estimates are replaced with the actual quantities and their 50 errors, i.e. x = x, and the estimation errors are assumed TC small so that their products can be omitted. In addition, (23b) is substituted for the current error in (23a), the result being - 0 Q = (-RsL- -WmJ- AL-1) s 72 -50 A -0.05 0 0.05 Wm (p.u.) + (R5L- + AL-1) /pm Rsis (24a) (b) BFig. 2. Effects of parameter estimation errors on speed correction term wE: (a) i, = LC 0s L1 14pm D (24b)effect of resistance error R/R =R - 0.1 as a function of torque for various C Drotor speed values and (b) effect of PM flux error <-pm/<-pm =-0.1 as afunction of rotor speed for various electromagnetic torque values. Solid lines The stator resistance error can be detected from is onlyshow the calculated values from (15) without additional assumptions, dashed when the motor is loaded, and when the stator current is varies,line shows calculated values from (18), and the circles are simulated values. the gain from Rs to is changes. Because the stator resistance is estimated at low speeds using the HF signal injection, only Rs the PM flux is selected for the adaptation at medium and RS+ _ R, FR GR(S) high speeds. It is also to be noted that only two quantities, the current error components d and tq, can be used for the adaptation and only two quantities can thus be estimated. Since Fig. 3. Closed-oop system of the stator resistance adaptation. the rotor speed is estimated using the q component of the current estimation error, the d component is selected for the PM flux adaptation.where kR is the stator resistance adaptation gain. The closed- For investigating the behavior of the PM flux adaptation, theloop system has a bandwidth closed-oop system of Fig. 4 is studied. The transfer function aR = iqkR/4pm from the scalar-valued flux error pnpm to the current error id (21) is obtained fromwhich can be affected by properly selecting the gain kR. F. (s)= [1 0]{C(sI-A) 1B+D}[1 O]T (25)B. Small-Signal Analysis PM Flux Adaptation Integration is used for the adaptation of <pm, and the transfer At medium and high speeds, the speed correction term w, function corresponding to the adaptation isis not available since the HF signal injection is not used. Theparameter adaptation can be based on d, which is obtained G1,p(s) =-kp-Ld/S (26)from the adaptive observer. Small-signal analysis is used for whereobtaining the sensitivity of td to the parameter errors. kp is the adaptation gain. The closed-oop transfer function , , For the analysis, the rotor speed is assumed constant, and theobserver is written assuming zero orientation error, yielding Ff G(s) G, IX- + (s) (s) (s) 1 + (s)G (27) Fp, Gp ,bs = u5 Rsis-WmJQs + Ais (22a) from Opm to <pm can be evaluated in any operating point. is = L l (,Os- Opm) (22b) The closed-oop transfer function (27) was analyzed nu- merically in different operating points. The parameter valueswhere only the stator resistance and the PM flux errors are given in Table I were used for the calculations. Fig. 5 showstaken into account. The stator flux error Qs and the stator poles and Fig. 6 unit step responses obtained with a constantcurrent error is are solved by subtracting the estimates in (22) adaptation gain k= O.2WB, where WB is the base angularfrom the actual variables solved from (1) and (2). The result speed. The speed varies from 0 to 1 p.u. in Fig. 5. Theis stator current and the rotational direction have no effect on the results. Due to symmetry, only the upper half-plane is shown I ,Os =Rsis + Rsis-S,J+bs Ais I - (23a) in the pole plot. The step responses in Fig. 6 were obtained is = L- (,Os -,pm) (23b) at speeds Wm = 0.25 p.u., 0.5 p.u., 0.75 p.u., and 1.0 p.u. 178
  5. 5. 1.5 1I 1 --: I - Wm (p.U.) 0.2 0.5 -1 H1. -v) WA 0 Wm L WOm 0. 5- Fig. 7. Functions f (wm,) (solid) and g(wm ) (dashed) as functions of 0 10.5 0 estimated rotor speed. -8.2 0 0 . -1 -0.5 0 Re{s} (p.u.)Fig. 5. Pole plot of the closed-oop system of PM flux adaptation. Thevicinity of the origin is also shown as a magnification. 0 /0 0 0.025 0.05 0.075 0.1 t (s)Fig. 6. Step response of the closed-oop system of PM flux adaptation forvarious rotor speeds. Fig. 8. Block diagram of the control system. According to the results, the small constant gain gives arelatively slow response. However, the actual PM flux changes load, IB is the base value of the current, and f(Jm) is aslowly since it depends on the temperature. Although there speed-dependent function shown in Fig. 7.are complex poles, the dominant pole is real-valued and it is The gain kp, for the PM flux adaptation is varied accordingalmost constant as the speed increases above 0.5 p.u. Hence, tothe response time to a changing PM flux does not vary kV, = ko g9(Wm) (30)significantly at higher speeds, which can also be seen from where kpo is a positive constant and g(Wm ) is a speed-the step responses in Fig. 6. dependent function shown in Fig. 7. At speeds higher thanC. Gain Scheduling w1,p, the gain kp is thus kept constant. The adaptation of the stator resistance is in use only at low V. SIMULATION RESULTSspeeds in which the HF signal injection method is used. The The proposed method was investigated by means of simu-PM flux adaptation is not used simultaneously with the statorlations and laboratory experiments. Fig. 8 shows the blockresistance adaptation, and is enabled when the rotor speed isdiagram of the control system comprising cascaded speedhigher than WA. The adaptation gains kR and kp are changed and current control loops. P14ype speed control with activewith the varying rotor speed and stator current. damping is used. The data of the six-pole interior-magnet In order to have a nonnegative bandwidth (21) for the stator PMSM (2.2 kW, 1500 rpm) are given in Table I. The baseresistance adaptation, the gain kR and the current iq must values for voltage, current, and angular speed are defined ashave the same sign. A constant bandwidth aR is infeasible, UB = 2/3UN, IB = W2N, and WB = 27fN, respectively.since iq = 0 would imply infinite adaptation gain. A signum The electromagnetic torque is limited to 22 Nm, which isfunction in the gain kR could cause chattering near zero tq. 1.57 times the nominal torque TN. The high-frequency carrierTherefore, the gain kR is changed proportionally to iq, i.e. excitation signal has a frequency of 833 Hz and an amplitude of 40 V. The threshold speeds WA = 0.13 p.u. and wX = 0.2 kR = OqROJTn)Pm I2 (28) p.u., the resistance adaptation bandwidth aRo = 0.01 p.U., B and the constant kpo = 0.2WB. The current and speed controlwhich results in the adaptation bandwidth bandwidths are 5.33 p.u. and 0.067 p.u., respectively, and the *2 bandwidth ai = 0.067 p.u. aR = aROf(Wrn)]y (29) The MATLAB/Simulink environment was used for the sim- B ulations. Fig. 9 shows results obtained at zero speed reference.The parameter aRO is a constant corresponding to the adap- Except the stator resistance, the parameter values used in thetation bandwidth at zero speed and at approximately nominal controller were equal to those of the motor model. In the 179
  6. 6. 0.1 0.6 7 -0.1 7 -0.2 1.5 2F 0 0O 0L -0.5 -0.5 0 20 0 20 2 -20 2 -20 0.1 1.2 0.05 = 0.6 C O vD~ 0 0 1 2 3 0 0.5 1 1.5 t (s) t (s)Fig. 9. Simulation results showing stator resistance adaptation. First subplot (a)shows electrical angular speed of the rotor (solid), its estimate (dashed), and its 0.6reference (dotted). Second subplot shows the load torque reference (dotted),the electromagnetic torque (solid), and its estimate (dashed). Third subplotshows the estimation error of the rotor position. Last sublot shows the stator S 0resistance (dashed) and its estimate (solid). 72 -0.2 2beginning of the simulation, the stator resistance estimate is 0O15 % smaller than the actual stator resistance. A nominal load -0.5torque step is applied at t = 1 s, and the stator resistance 20 0estimate starts converging to the actual resistance immediately.At t = 2 s, a 15 % step increase occurs in the stator resistance, t -20and its estimate again follows the actual stator resistance.The stator resistance estimate converges close to the actual 1.2resistance in less than 1 s. 0.6 Results showing the behavior of the estimated PM flux are 0depicted in Fig. 10. The estimated flux is 15 % bigger than 0 0.5 1 1.5its actual value in the beginning of the simulations, and other t (s)parameter estimates are equal to the actual values in the motor (b)model. The speed reference is changed from zero to 0.5 p.u. Fig. I 0. Simulation results showing PM flux adaptation: (a) withoutat t = 0.5 s, and a nominal load torque step is applied at parameter adaptation (b) with parameter adaptation. Explanations of the curvest = 1 s. In Fig. 10(a), the parameter adaptation is not in are as in Fig. 9 except that the last subplot shows the PM flux (dashed) and its estimate (solid).use, whereas in Fig. 10(b), the adaptation is used. Fig. 10(a)shows that the erroneous PM flux results in an error in therotor position estimate both at no load and when a load is compensation for dead times and power device voltage dropsapplied. In addition, the electromagnetic torque is smaller than is applied.the estimated torque. According to Fig. 10(b), the adaptation Results obtained in low-speed operation are depicted inpractically removes the PM flux error in less than 0.2 s after Figs. 12 and 13, showing the behavior of the stator resistancethe motor is started, and the errors in the rotor position and adaptation. Additional 1-Q resistors were added between thethe torque are avoided. frequency converter and the PMSM as shown in Fig. 11. The resistance was changed stepwise by opening or closing VI. EXPERIMENTAL RESULTS a manually-operated three-phase switch connected in parallel The experimental setup is illustrated in Fig. 11. The PMSM with the resistors. The experiment in Fig. 12 corresponds tois fed by a frequency converter that is controlled by a dSPACE the simulation in Fig. 9. The error in the stator resistance isDS1 103 PPC/DSP board. Mechanical load is provided by decreased after the load torque step at t = 1 s. The estimateda PMSM servo drive. An incremental encoder is used for stator resistance follows well the actual resistance after themonitoring the actual rotor speed and position. The nominal stepwise increase at t = 2 s.DC4ink voltage is 540 V, and the switching frequency and In the experiment of Fig. 13, the drive was operating atthe sampling frequency are both 5 kHz. The dc-ink voltage very low speed (W -0.05 p.u.) in the regenerating mode.of the converter is measured, and a simple current feedforward The load torque was at the positive nominal value. The stator 180
  7. 7. 0.1 S 0 7 -0.1 1.5 E-- 0 -0.5 20 Computer with DS1103 0Fig. 11. Experimental setup. Mechanical load is provided by a servo drive. 2 -20 0.1 0.1 0 S 0.0 -0.5 1 1 2 3 4 l 5r F Ar t (s) Fig. 13. Experimental results showing stator resistance adaptation. Explana- 0- -0.5 °t tions of the curves are as in Fig. 12. 20 0.6 0 -20 a 0 t 7 -0.2 0.1 2F 0.05 = 0 0L &0, 1 t (s) 2 3 -0.5 0 20Fig. 12. Experimental results showing stator resistance adaptation. Firstsubplot shows the electrical angular speed of the rotor (solid), its estimate 2 -20(dashed), and its reference (dotted). Second subplot shows the load torquereference (dashed) and the electromagnetic torque estimate (solid). Third 1.2subplot shows the estimation error of the rotor position. Last sublot showsthe stator resistance (dashed) and its estimate (solid). 0.6 0 0 0.5 1 1.5 t (s)resistance estimate was forced to an incorrect value at t 0.6 Fig. 14. Experimental results showing PM flux adaptation. Explanations ofs. When the resistance adaptation is activated again at t 1 s, the curves are as in Fig. 12 except that the last subplot shows the PM fluxthe estimated resistance returns close to the actual resistance in (dashed) and its estimate (solid).about 1 second. After the stepwise decrease in the resistanceat t 2.5 s, the estimated resistance settles close to the new -value. It is to be noted that in the experiments in Figs. 12 15(b), respectively. The PM flux estimate was forced to anand 13, the inverter unidealities contribute to the resistance erroneous value at t 0.5 s, and the adaptation was enabled -seen by the controller. Therefore, the estimated resistance is again at t r-1 s. The erroneous PM flux estimate causes annot precisely the stator resistance shown in the figures. error in the electromagnetic torque estimate, and the position Figs. 14 and 15 show results in the medium-speed operation, estimation error also impairs the performance of the drive.where the PM flux adaptation is in use. The experiment in After t s, the estimated PM flux quickly converges close - 1Fig. 14 corresponds to the simulation in Fig. 10. The results to its actual value, leading to a reduced position estimationare comparable to that of the simulation, and the initial 15 error and improved torque estimation accuracy.% PM flux error is rapidly removed after the accelerationat t = 0.5 s. The PM flux estimate also stays close to VII. CONCLUSIONSthe actual flux when the load torque step is applied. Fig. This paper proposed a method for the estimation of the15 shows results in constant-speed operation, the rotor speed stator resistance and the PM flux in a sensorless PMSM drive.being 0.5 p.u. In Fig. 15(a), the load torque was at the positive The adaptive observer augmented with an HF signal injectionnominal value, while in Fig. 15(b) the load torque was at technique at low speeds was used for the adaptation of thethe negative nominal value. The drive operated thus in the parameters in addition to the speed and position estimation.motoring and in the regenerating modes in Figs. 15(a) and The system was investigated by means of steady-state and 181
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