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1 Powere by TCPDF ( This is an electronic reprint of the original article. This reprint may iffer from the original in pagination an typographic etail. Piippo, Antti; Hinkkanen, Marko; Luomi, Jorma Combination of voltage moel an high-freuency signal injection for sensorless permanent magnet synchronous motor rives Publishe in: International Conference on Electrical Machines (ICEM'4) Publishe: 5/9/4 Document Version Peer reviewe version Please cite the original version: Piippo, A., Hinkkanen, M., & Luomi, J. (4). Combination of voltage moel an high-freuency signal injection for sensorless permanent magnet synchronous motor rives. In International Conference on Electrical Machines (ICEM'4) Cracow, Polan. This material is protecte by copyright an other intellectual property rights, an uplication or sale of all or part of any of the repository collections is not permitte, except that material may be uplicate by you for your research use or eucational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offere, whether for sale or otherwise to anyone who is not an authorise user.

2 Combination of Voltage Moel an High-Freuency Signal Injection for Sensorless Permanent Magnet Synchronous Motor Drives A. Piippo, M. Hinkkanen, J. Luomi Power Electronics Laboratory, Helsinki University of Technology, Finlan P.O. Box 3, FIN-15 HUT, Finlan, phone: antti.piippo@hut.fi Abstract The paper proposes a metho for the rotor spee an position estimation of permanent magnet synchronous motors, applicable in a wie spee range incluing stanstill. A moifie voltage moel is use at high spees, an it is combine with a high-freuency signal injection techniue at low spees. The fast ynamic response of the voltage moel is thus augmente with the steay-state accuracy of the highfreuency signal injection techniue. The stability an robustness of the combine observer are emonstrate by simulations an experiments. I. INTRODUCTION Knowlege of the rotor position is neee for the vector control of a permanent magnet synchronous motor (PMSM). In sensorless control, an estimation algorithm is use instea of a mechanical position sensor, resulting in reuce costs an increase reliability. The methos use for the estimation of the rotor spee an position can be classifie into funamental-excitation methos an signal injection methos. Funamental-excitation methos rely on a ynamic moel of the motor. The rotor spee an position can be estimate by a voltage moel [1] or a more complicate observer [] [4]. These methos have goo ynamic properties but are not suitable for low-spee operation. In signal injection methos, a high freuency (HF) voltage signal is superimpose on the stator voltage, an the resulting current response is use for etecting the anisotropy cause by rotor saliency or magnetic saturation [5] [7]. If persistent HF excitation is applie, the signal is either a revolving voltage vector [6], [7] or a voltage alternating in the estimate rotor reference frame [8] [1]. The position estimation can be base on a tracking scheme [6], [8] [1] or on irect evaluation of the rotor position [7], [11], [1]. Signal injection methos work at low spees an stanstill but ten to have restricte ynamic properties. The methos aresse above have ifferent avantages an isavantages. Therefore, it woul be natural to combine a funamental-excitation metho with a HF signal injection metho [13]. Such a combine metho has been implemente in sensorless control of inuction motors [14]. For PMSMs, a funamental-excitation metho is use at higher spees an a signal injection metho or a combine metho at low spees in [15], [11], [1]. This paper proposes a combine metho, in which a moifie voltage moel is use throughout the whole spee range, an the estimation is augmente with HF signal injection at low spees. The simple combine metho results in goo steay-state an ynamic properties over a wie spee range. II. PMSM MODEL The PMSM moel is presente in the - reference frame fixe to the rotor. The axis is oriente along the permanent magnet flux, whose angle in the stator reference frame is in electrical raians. The stator voltage components are u ψ = + (1a) t Rsi ωmψ ψ u = Rsi + + ωmψ (1b) t where i an i are the stator current components, R s is the stator resistance, an ωm = θm / t is the electrical angular spee of the rotor. The stator flux components are ψ = Li + ψ (a) ψ = (b) Li where L an L are the - an -axis inuctances, respectively, an ψ is the permanent magnet flux. The electromagnetic torue is given by 3 Te = p ψ i + ( L L) ii (3) where p is the number of pole pairs. III. OBSERVER STRUCTURE A. Moifie Voltage Moel The pure voltage moel suffers from rift problems ue to the open-loop integration. The integration can be replace by low-pass filtering an error compensation [16], [17]. The moifie voltage moel in the estimate rotor reference frame is forme from (1) an () as ψˆ = eˆ + αv ( ψ ψˆ ) (4a) t eˆ ˆ ωm = (4b) ψˆ where the estimates of the back-emf components are ˆ ˆ i ˆ e ˆ ˆ = u Rsi L + ωmli (5a) t

3 i ˆ ˆ eˆ ˆ ˆ = u Rsi L ωmli (5b) t Estimates are marke by the symbol ˆ, ψ is the presume value of the permanent magnet flux, an α v is a nonnegative gain. Furthermore, the estimate of the rotor position is obtaine by integrating ˆm ω. The pure voltage moel is obtaine by choosing α v =. For α v >, the open-loop integrator is replace with a low-pass filter having the banwith of α v, an the error so introuce is compensate using ψ. B. High-Freuency Signal Injection An alternating voltage is use for HF signal injection [8] [1]. A carrier excitation signal fluctuating at angular freuency ω c an having amplitue u ˆc, i.e., uc = uˆ ccos( ωct) (6) is superimpose on the component of the stator voltage in the estimate rotor reference frame. An HF current response is etecte in the irection of the estimate rotor reference frame, amplitue moulate by the rotor position estimation error. The principle of the emoulation scheme is shown in Fig. 1. The component of the measure current is ban-pass filtere (BPF), giving the current signal i c varying at the signal injection freuency. The current signal is then emoulate an low-pass filtere (LPF) to extract an error signal { ic ωct } = LPF sin( ) (7) Ieally, this error signal is [8] uˆ L L c = sin( θm ) ωc 4LL K where K is the signal injection gain an θ ˆ m = θm θm is the estimation error of the rotor position. The emoulation scheme is implemente as follows. Instea of using a ban-pass filter, the filtering of i is achieve by t (8) 1 ic = i it T (9) c t T c where Tc = π / ωc, i.e. by zero averaging over one perio of the injection signal. The algorithm (9) can be interprete as a high-pass filter, an its computational cost is lower than that of relevant ban-pass filters. The low-pass filtering of the signal ic sin( ω ct) is implemente using two filters: a moving-average filter an a first-orer low-pass filter. The moving-average filter removes the angular freuency ω c an its multiples effectively an causes only a short time elay, while the first-orer low-pass filter reuces stochastic noise more effectively than the movingaverage filter. Due to the short elay of the movingaverage filter, only the ynamics of the first-orer low-pass filter are consiere in the following. After filtering, the amplitue of is limite to avoi errors uring transients. i BPF sin( ω c t ) i c LPF Figure 1. Principle of error signal emoulation. u, u i, i Moifie voltage moel γ i γ p + + eˆ / ψˆ ˆm ω + + θˆm Figure. Block iagram of the combine observer. C. Combine Observer The combination of the moifie voltage moel an the HF signal injection metho is illustrate in Fig.. The rotor spee an position estimates are obtaine by eˆ ˆ ωm = + γ i t ψˆ (1a) ˆ θm = ( ˆ ωm + γ p) t (1b) where γ p an γ i are positive gains, ψ ˆ is estimate using (4a), an e ˆ an e ˆ (5) are evaluate using ˆm ω from (1a). The HF signal injection an a phase-locke loop (PLL) [13], [9] are use to augment the spee estimate obtaine by the moifie voltage moel. The PI mechanism in (1) rives the error signal to zero in steay state. At low spees, the combine observer relies both on the signal injection metho an the voltage moel: the signal injection metho ominates in steay state whereas the voltage moel commans at transients. The PI mechanism use in a PLL can be tune analytically [9]. The transfer function ˆ θm()/ s () s, corresponing to the linearize close-loop system shown in Fig. 3, can be use for etermining the gains γ p an γ i. From (8), a linear approximation K θm (11) is use when etermining the close-loop transfer function. The influence of the voltage moel is omitte, but the lowpass filter use in (7) is taken into account. The transfer function of the first-orer low-pass filter having the banwith α lp is αlp Fs () = (1) s + αlp an the transfer function of the PI mechanism is

4 θm + θ m K F() s Gs () ˆm θ ref,, ref, Spee control i, i u ref c u, ref, u, + + Current control αβ ref Figure 3. Block iagram of the close-loop system. f ( ˆ ) 1 θˆm ˆm ω Combine observer Error signal i, i αβ PMSM ω ˆm ω Figure 5. Block iagram of the control system. Figure 4. Depenence of signal injection amplitue an PLL banwith on rotor spee. Freuency converter PMSM Servo Freuency converter γ i Gs () = γ p + (13) s For the close-loop system in Fig. 3, the transfer function is ˆ θ m () s Kαlpγ ps+ Kαlpγi = (14) θ () 3 m s s + αlps + Kαlpγ ps+ Kαlpγ i To ensure stability an to avoi oscillations, all three poles of (14) are place to the point α on the real axis yieling the selection rule αlp = 3α (15) for the low-pass filter banwith an the selection rules α α γ p =, γi = (16) K 6K for the gains of the PI mechanism. The propose esign metho allows gain selection using only one esign parameter α corresponing to the approximate banwith of the close-loop system (14). In orer to obtain a smooth transition between the lowspee an high-spee regions, the injection voltage amplitue u ˆc an the banwith α are ecrease linearly with increasing spee, an the signal injection is isable above transition spee ω, i.e., uˆc = f( ˆ ωm) uˆc, α = f( ˆ ωm) α (17) where u ˆc an α are the values corresponing to zerospee operation an function f ( ˆ ) is shown graphically in Fig. 4. The parameters α lp an γ i are varie accoring to (15), (16), an (8). The parameter γ p remains constant accoring to (16) an (8). IV. CONTROL SYSTEM The block iagram of the control system comprising cascae spee an current control loops is shown in Fig. 5. The current control is implemente as PI-type control in Spee for monitoring Computer with DS113 Figure 6. Experimental setup. Mechanical loa is provie by the servo rive. the estimate rotor reference frame, where the cross-coupling terms an the back-emf are ecouple [18]. PI-type spee control with active amping is use. The current references i ref, an i ref, are calculate accoring to maximum torue per current control [19]. The clink voltage of the converter is measure, an simple current feeforwar ea-time compensation is applie []. V. RESULTS The propose observer was investigate by means of simulations an laboratory experiments. The experimental setup is illustrate in Fig. 6. A.-kW internal-magnet PMSM is fe by a freuency converter controlle by a SPACE DS113 PPC/DSP boar. The base values an the motor parameters are given in Table I an the parameters of the control system in Table II. The sampling is synchronize to the moulation, an both the switching freuency an the sampling freuency are 5 khz. The c-link voltage is 54 V. The signal injection freuency is 5 Hz, an the transition spee ω =.13 p.u. At zero spee, the amplitue of the HF voltage signal is u ˆc = V, an the measure rms value of the HF current is 19 ma, i.e..4 p.u. The electromagnetic torue is limite to Nm, i.e. Tmax / T N = An incremental encoer is use to monitor the actual rotor spee an position, which is further use to calculate the rotor position estimation error. The MATLAB/Simulink environment was use for the simulations. The parameters of the motor moel use in the simulations correspon to the parameters of the motor

5 TABLE I. MOTOR DATA Nominal power. kw Nominal/base voltage 37 V Nominal/base current 4.3 A Nominal/base freuency 75 Hz Nominal spee 15 r/min Nominal torue T N 14. Nm Number of pole pairs p 3 Stator resistance R s 4.1 Ω Direct axis inuctance L.36 H Quarature axis inuctance L.51 H Permanent magnet flux ψ.545 Vs Total moment of inertia.15 kgm TABLE II. CONTROL SYSTEM PARAMETERS Signal injection amplitue u ˆc V Signal injection angular freuency ω c π5 ra/s Banwith α π1 ra/s Voltage moel gain α v π15 ra/s Current controller banwith π ra/s Spee controller banwith π.5 ra/s use in the experiments. In the simulations, white noise having an rms value of 1 ma was ae to the measure phase currents of the motor, an the current signals were uantize in steps of 1 ma. Figs. 7 9 show simulation results uring a slow spee reversal at nominal loa torue. The spee reference was change linearly from. p.u. to. p.u. between t = s an t = 8 s. The stator resistance estimate R ˆs is accurate in Fig. 7, whereas the stator resistance is 1 % unerestimate in Fig. 8 an 1 % overestimate in Fig. 9. The results show that a parameter error causes an orientation error, but at low spees, the signal injection techniue nearly removes the estimation error of the rotor position. The transition between the voltage moel an the combine observer is smooth, an the spee estimate follows the actual spee with a goo accuracy although a parameter error is present. Fig. 1 shows experimental results uring the slow spee reversal at nominal loa torue. The results show stable operation both in the motoring an regenerating moes. Furthermore, it can be seen that the experimental results correspon well to the simulation results. At low spees, however, the rotor position estimation error varies more in the experimental results than in the simulation results. This ripple consists mostly of a sixth harmonic component. Therefore, proper compensation of inverter nonlinearities is a suitable topic of future research. Fig. 11 shows experimental results at no loa when the spee reference was change stepwise from zero to. p.u. at t = 1 s, then reverse to. p.u. at t = s, an finally set to zero at t = 3 s. The estimate rotor spee follows the actual spee smoothly an the rotor position estimation error stays in reasonable small values. Fig. 1 epicts experimental results when the spee reference was set to zero. The loa torue was first change stepwise from zero to the nominal value at t = 1 s, then reverse at t = s, an remove at t = 3 s. The error Figure 7. Simulation results showing slow spee reversal at nominal loa torue, R ˆs = Rs. First subplot shows electrical angular spee (soli), its estimate (ashe), an its reference (otte). Secon subplot shows estimate electromagnetic torue (soli) an loa torue reference (otte). Last subplot shows estimation error of rotor position in electrical egrees Figure 8. Simulation results showing slow spee reversal at nominal loa torue, R ˆ s =.9Rs. Explanations of the curves are as in Fig. 7. of the rotor position estimate is small even uring transients, inicating goo ynamic performance. Experimental results at the nominal loa torue are shown in Fig. 13. The spee reference was first change stepwise from zero to.66 p.u. at t = 1 s, then reverse to.66 p.u. at t = s, an finally set to zero at t = 3 s. The estimate rotor spee follows the actual spee smoothly even uring the transitions between the voltage moel an the combination of the voltage moel an HF signal injection.

6 θ m Figure 9. Simulation results showing slow spee reversal at nominal loa torue, R ˆ s = 1.1Rs. Explanations of the curves are as in Fig Figure 11. Experimental results showing spee reference steps at zero loa torue. Explanations of the curves are as in Fig θ m θ m Figure 1. Experimental results showing slow spee reversal at nominal loa. Explanations of the curves are as in Fig Figure 1. Experimental results showing loa torue steps at zero spee reference. Explanations of the curves are as in Fig. 7. VI. CONCLUSIONS A moifie voltage moel that is augmente with a high-freuency signal injection techniue at low spees is suitable for the estimation of the rotor spee an position of a permanent magnet synchronous motor in a wie spee range, incluing zero spee. The fast ynamic response of the voltage moel is combine with the steay-state accuracy of the high-freuency signal-injection metho. The signal injection scheme is base on a voltage carrier signal alternating in the estimate rotor reference frame an simple emoulation of the current response. Guie- lines for the gain selection of the tracking observer are obtaine analytically. Accoring to the simulations an experiments presente in the paper, the system base on the combine observer is stable an robust, an can cope with stepwise changes in the spee reference an with nominal loa torue steps. ACKNOWLEDGEMENT The authors gratefully acknowlege the financial support given by ABB Oy an the Finnish Cultural Founation.

7 Figure 13. Experimental results showing spee reference steps at nominal loa. Explanations of the curves are as in Fig. 7. REFERENCES [1] R. Wu an G. R. Slemon, A permanent magnet motor rive without a shaft sensor, IEEE Trans. In. Applicat., vol. 7, no. 5, pp , Sept./Oct [] R. B. Sepe an J. H. Lang, Real-time observer-base (aaptive) control of a permanent-magnet synchronous motor without mechanical sensors, IEEE Trans. In. Applicat., vol. 8, no. 6, pp , Nov./Dec [3] J. Solsona, M. I. Valla, an C. Muravchik A nonlinear reuce orer observer for permanent magnet synchronous motors, IEEE Trans. In. Electron., vol. 43, no. 4, pp , Aug [4] S. Bolognani, R. Oboe, an M. Zigliotto, Sensorless fulligital PMSM rive with EKF estimation of spee an rotor position, IEEE Trans. In. Electron., vol. 46, no. 1, pp , Feb [5] M. Schroel, Sensorless control of AC machines at low spee an stanstill base on the INFORM metho, in Conf. Rec. IEEE-IAS Annu. Meeting, vol. 1, San Diego, CA, Oct. 1996, pp [6] P. L. Jansen an R. D. Lorenz, Transucerless position an velocity estimation in inuction an salient AC machines, IEEE Trans. In. Applicat., vol. 31, no., pp. 4 47, March/April [7] A. Consoli, G. Scarcella, an A. Testa, Inustry application of zero-spee sensorless control techniues for PM synchronous motors, IEEE Trans. In. Applicat., vol. 37, no., pp , March/April 1. [8] M. Corley an R. D. Lorenz, Rotor position an velocity estimation for a salient-pole permanent magnet synchronous machine at stanstill an high spees, IEEE Trans. In. Applicat., vol. 43, no. 4, pp , July/Aug [9] L. Harnefors an H.-P. Nee, A general algorithm for spee an position estimation of AC motors, IEEE Trans. In. Electron., vol. 47, no. 1, pp , Feb.. [1] M. Linke, R. Kennel, an J. Holtz, Sensorless position control of permanent magnet synchronous machines without limitation at zero spee, in Proc. IEEE IECON, vol. 1, Sevilla, Spain, Nov., pp [11] C. Silva, G. M. Asher, an M. Sumner, An hf signalinjection base observer for wie spee range sensorless PM motor rives incluing zero spee, in Proc. EPE 3, vol. 1, Toulouse, France, Sept. 3, pp [1] M. Tursini, R. Petrella, an F. Parasiliti, Sensorless control of an IPM synchronous motor for city-scooter applications, in Conf. Rec. IEEE IAS Annu. Meeting, vol. 3, Salt Lake City, UT, Oct. 3, pp [13] P. L. Jansen, M. J. Corley, an R. D. Lorenz, Flux, position, an velocity estimation in ac machines at zero an low spee via tracking of high freuency saliencies, in Proc. EPE 95, vol. 3, Sevilla, Spain, Sept. 1995, pp [14] K. Ie, J.-I. Ha, M. Sawamura, H. Iura, an Y. Yamamoto, A novel hybri spee estimator of flux observer for inuction motor rives, in Proc. IEEE ISIE, vol. 3, L Auila, Italy, July, pp [15] E. Robeischl, M. Schroel, an M. Krammer, Positionsensorless biaxial position control with inustrial PM motor rives base on INFORM- an back EMF moel, in Proc. IEEE IECON, vol. 1, Sevilla, Spain, Nov., pp [16] T. Ohtani, N. Takaa, an K. Tanaka, Vector control of inuction motor without shaft encoer, IEEE Trans. In. Applicat., vol. 8, no. 1, pp , Jan./Feb [17] H. Rasmussen, P. Vastrup, an H. Børsting, Sensorless fiel oriente control of a motor incluing zero spee, in Proc. IEEE IEMDC 3, vol., Maison, WI, June. 3, pp [18] F. Briz el Blanco, M. W. Degner, an R. D. Lorenz, Dynamic analysis of current regulators for AC motors using complex vectors, IEEE Trans. In. Applicat., vol. 35, no. 6, pp , Nov./Dec [19] T. Jahns, G. Kliman, an T. Neumann, Interior permanent-magnet synchronous motors for ajustable-spee rives, IEEE Trans. In. Applicat., vol., no. 4, pp , July/Aug [] J. K. Peersen, F. Blaabjerg, J. W. Jensen, an P. Thogersen, An ieal PWM-VSI inverter with feeforwar an feeback compensation, in Proc. EPE 93, vol. 5, Brighton, UK, Sept. 1993, pp