1. PEDS 2007 Adaptation of Motor Parameters in Sensorless PMSM DrivesAntti Piippo, Marko Hinkkanen, and Jorma LuomiPower Electronics LaboratoryHelsinki University of Technology P.O. Box 3000, FI-02015 TKK, Finland Abstract-The paper proposes an on-line method for theerror. On the other hand, the back-emf is small at low speeds,estimation of the stator resistance and the permanent magnetand 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 andformance 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-signalestimating 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 simulationsPM flux and the stator resistance [10]. The stator inductancesand laboratory experiments. The stator resistance adaptationand 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 dropI. INTRODUCTIONfor 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/$20.002007 IEEE 175

2. i/Fwhere estimated quantities are marked by ^ and Us,ref is thestator voltage reference. The estimate of the stator current and Us,refAd- +/mthe estimation error of the stator current are ==>justableL-(,Os -,pm) --A1tmodel js is = (5) ALis~ ~ 1is = 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 gainmatrix A is proportional to the rotor speed up to the nominalspeed [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, whoseFe =Clis(7)angle in the stator reference frame is 0m in electrical radians.The stator voltage equation iswhere Ci = [O Lq], i.e., the current error in the estimated qdirection 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 theadaptation 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 JK0 -1I where kp and ki are nonnegative gains. The gain selection isdescribed in [17]. The estimate Om for the rotor position isevaluated by integrating Winsb= Lis+ bpm (2)B. High-Frequency Signal Injectionwhere 14pm= [/pm O]T is the PM flux andThe adaptive observer described above is augmented with aHF signal injection method to stabilize the speed and positionL L Lq Ld fq] estimation at low speeds [17]. By using the HF signal injectionmethod 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 electromagneticposition estimation error 0m = m 0-m is obtained, KStorque is given bybeing the signal injection gain. The error signal is used forcorrecting the estimated position by influencing the directionTe=3p2TJTis(3)of the stator flux estimate of the adjustable model. For thecombined 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 Observerwhere An adaptive observer [17] is used for the estimation of thestator current, rotor speed, and rotor position. The speed andSE: = apE + -aj+dt(10)position estimation is based on the estimation error betweenis the speed correction term, -yp and tYj being the gains of thetwo different models; the actual motor can be considered as aPI mechanism driving the error signal E to zero. In accordancereference model and the observer including the rotor speedwith [6], these gains are selected asestimate Wm as an adjustable model. The error term usedin a speed adaptation mechanism is based on the estimation2Ki 2 (1 1)error of the stator current. The estimated rotor speed, obtained/yP 2K6KEusing 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 rotorAt 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) andinfluence of the HF signal injection is decreased linearly as the(2), and defined by speed increases by decreasing both the HF excitation voltageand 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. TABLE I IV. PARAMETER ADAPTATIONMOTOR DATA The current estimation error is of the adaptive observer Nominal voltage UN370 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 fN75 HzNominal torque TN14.0 Nmthe adaptation of two parameters in a PMSM drive equipped Stator resistance RS3.59 Qwith a motion sensor. Solving the parameters from the steady- Direct-axis inductance Ld36.0 mHstate voltage equations as in [11] would require filtering to Quadrature-axis inductance Lq51.0 mHPM flux WmoLdLqiq the result iscan be driven to zero by adjusting the parameter estimates.R,WmiqL 2L q[.td Rlk ;qqiqRsMl(17)A. Steady-State Analysis Stator Resistance Adaptation L ejfpm 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, particularlyboth on Rs and