In the paper by Vaclavek et al. (IEEE Trans. Ind. Electron., vol. 60, no. 8,
pp. 3047-3059, Aug. 2013), the local observability of both induction machine
and permanent-magnet synchronous machine (PMSM) under motion-sensorless
operation is studied. In this letter, the "slowly varying" speed assumption is
discussed, and the PMSM observability condition at standstill is revisited

Duc, Gilles

Koteich, Mohamad

Maloum, Abdelmalek

Sandou, Guillaume

IEEE Transactions on Industrial Electronics

English

arXiv

International audienceIn the paper by Vaclavek et al. (IEEE Trans. Ind. Electron., vol. 60, no. 8, pp. 3047-3059, Aug. 2013), the local observability of both induction machine and permanent magnet synchronous machine under motion sensorless operation is studied. In this letter, the " slowly varying " speed assumption is discussed, and the permanent magnet synchronous machine observability condition at standstill is revisited

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Mohamad Koteich

Abdelmalek Maloum

Gilles Duc

Guillaume Sandou

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Discussion on “AC Drive Observability Analysis”

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Discussion on ” AC Drive Observability Analysis ”Mohamad Koteich, Abdelmalek Maloum, Gilles Duc, Guillaume SandouTo cite this version:Mohamad Koteich, Abdelmalek Maloum, Gilles Duc, Guillaume Sandou. Discussion on ”AC Drive Observability Analysis ”. IEEE Transactions on Industrial Electronics, Institute ofElectrical and Electronics Engineers, 2015, IEEE Transactions on Industrial Electronics, pp.2.<http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7115092&searchWithinHAL Id: hal-01163016https://hal-centralesupelec.archives-ouvertes.fr/hal-01163016Submitted on 11 Jun 2015HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 1Discussion on “AC Drive Observability Analysis”Mohamad Koteich, Student Member, IEEE, Abdelmalek Maloum, Gilles Duc and Guillaume SandouAbstract—In the paper by Vaclavek et al. (IEEE Trans.Ind. Electron., vol. 60, no. 8, pp. 3047-3059, Aug. 2013), thelocal observability of both induction machine and permanentmagnet synchronous machine under motion sensorless operationis studied. In this letter, the “slowly varying” speed assumptionis discussed, and the permanent magnet synchronous machineobservability condition at standstill is revisited.Index Terms—Observability analysis, AC drives, inductionmachine, synchronous machine, sensorless control.I. INTRODUCTIONIN the above paper [1] the local observability of the induc-tion machine (IM) and the permanent magnet synchronousmachine (PMSM) is studied. Obviously, it is a very goodpaper as it has been referred to by many others since it waspublished [2] [3] [4]. To the best of our knowledge, it is thefirst paper that presents the PMSM observability conditionsin the rotating reference frame, which provides useful explicitconditions.The observability analysis in [1] is restricted to the “slowlyvarying” speeds. This means that the obtained observabilityconditions for both machines are valid only under constant(or nearly constant) speed operating conditions. One can arguethat this is not the case for a wide range of electrical driveapplications.II. FURTHER REMARKS ON THE IM OBSERVABILITYIt is worth mentioning that the IM observability study madeby de Wit et al. [5] covers both cases: 1) constant speed,which leads to the 5−dimensional machine model adoptedby [1], and 2) varying speed under slowly varying load torqueassumption, which leads to a 6−dimensional model by addingthe load torque to the state vector [6]. The only additionalparameter needed in the second case is the rotor and loadinertia, which can be fairly accurately known in numerous ap-plications. The observability condition of the 6−dimensionalmodel can be expressed, using the same notations as [1], as:ξ2ω2e + ξ22dωedtΨ∗r .Ψr −dΨrdt×Ψr 6= 0 (1)Manuscript received February 18, 2015; revised April 3, 2015; acceptedMay 2, 2015.Copyright c© 2015 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.Mohamad Koteich is with Renault S.A.S. Technocentre, 78288 Guyancourt,France, and also with L2S - CentraleSupe´lec - CNRS - Paris-Sud University,91192 Gif-sur-Yvette, France (e-mail: mohamad.koteich@renault.com).Abdelmalek Maloum is with Renault S.A.S. Technocentre, 78288 Guyan-court, France (e-mail: abdelmalek.maloum@renault.com).Gilles Duc and Guillaume Sandou are with L2S - CentraleSupe´lec- CNRS - Paris-Sud University, 91192 Gif-sur-Yvette, France (e-mail:gilles.duc@centralesupelec.fr; guillaume.sandou@centralesupelec.fr).One can design an observer for the IM under slowly varyingspeed operating conditions. In this case, the observabilitycondition (1) becomes equivalent to the condition calculatedfor the 5−dimensional model (as discussed in [5]). Thisprovides a more general IM local observability analysis.III. COMMENTS ON THE PMSM OBSERVABILITYThe slowly varying speed assumption is not required inthe PMSM observability analysis, where only the first orderderivatives of the stator currents are evaluated. Thus, thePMSM observability conditions presented in [1] are valid forany rotor acceleration.The determinant of the observability matrix numbered (97)in the paper under discussion can be written as1:D =1LdLq[(∆Lid +Ke)2+ ∆L2i2q]ωe+∆LLdLq[∆Ldiddtiq − (∆Lid +Ke) diqdt](2)In their analysis of the above equation, the authors in [1]formulate the following observability condition at standstill:∣∣∣∣id + Ke∆L∣∣∣∣ |C| 6= |iq| (3)They claim that it is not necessary to determine the value ofthe constant C, and that in the zero or low-speed region “therotor position will be observable if stator current componentsin rotating reference frame id, iq are changing and not keptto be linearly dependent. Stator current space vector shouldchange not only its magnitude but also direction in the rotatingreference frame”.The above conclusion is unclear and yet inaccurate. Firstof all, the conclusion should not only concern the rotorposition, the rotor angular speed observability should alsobe concerned. Even though it seems to be intuitive that theloss of observability concerns rather the position, this cannotbe proved unless a detailed study of the indistinguishabledynamics is done, similarly to the study done in [7] forinduction machines. In addition, the stator current space vectorcan change both its magnitude and direction without ensuringthe motor observability at standstill, as shown in the sequel.The observability condition D 6= 0 can be written as:ωe 6=(∆Lid +Ke) ∆Ldiqdt −∆Ldiddt ∆Liq(∆Lid +Ke)2+ ∆L2i2q(4)which gives:ωe 6= ddtarctan(∆Liq∆Lid +Ke)(5)1Symbolic math software is used to reproduce the determinant expression.IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2αβΨOθOdqKe∆Lid∆LiqθeFig. 1. Vector diagram of the fictitious observability vector (dashed).Let’s define a fictitious observability vector ΨO = ΨOd +jΨOq which has the following components in the rotating (dq)reference frame:ΨOd = ∆Lid +Ke (6)ΨOq = ∆Liq (7)Then, the condition (5) can be formulated as:ωe 6= ddtθO (8)where θO is the phase of the vector ΨO in the rotatingreference frame (Figure 1). The following sufficient conditionfor the PMSM local observability can be stated:Proposition 1: The PMSM is locally observable if the an-gular speed of the fictitious vector ΨO in the dq referenceframe is different from the rotor electrical angular speed inthe stator reference frame.At standstill, the above condition becomes: the vector ΨOshould change its orientation in order to ensure the localobservability. This provides a better formulation of the PMSMobservability conditions.It turns out that the d−axis component of the vector ΨO isnothing but the so-called “active flux” introduced by Boldeaet al. in [8] (also called “fictitious flux” by Koonlaboon et al.[9]), which is, by definition, the torque producing flux alignedto the rotor d−axis. The q−axis component of the vector ΨOis related to the saliency (∆L) of the machine, and is alignedto the rotor q−axis.Figure 2 shows two observability vectors, ΨO1 (dotted) andΨO2 (dashed), that correspond to two different (in magnitudeand direction) current space vectors:i1 = id1 + jiq1 ; (id1 < 0 , iq1 > 0) (9)i2 = id2 + jiq2 ; (id2 > 0 , iq2 > 0) (10)It is obvious that, contrary to the conclusion drawn in [1] forthe IPMSM, at standstill (ωe = 0), the stator current spacevector can change both its magnitude and direction, followingthe constant-θO trajectory, without fulfilling the observabilitycondition (8). It should be noticed that this is related to theconstant C of the equation (3), which value is judged to beunnecessary in the paper under discussion.As for the surface-mounted (S) PMSM (∆L = 0) undersensorless operation, the fictitious observability vector is equaldqθOΨO2ΨO1Ke∆Li1∆Li2Fig. 2. Vector diagram illustrating two observability vectors that correspondto two stator current space vectors that differ in magnitude and direction.to the rotor permanent magnet flux vector, which is fixed in thedq reference frame. This means that the observability problemarises only at standstill, which is consistent with the conclusionon SPMSM observability in the discussed paper [1].ERRATUMIn the list of references of [1], the reference number 17 isnot correctly cited; the name of the first author is omitted. Thecorrect citation is [10].REFERENCES[1] P. Vaclavek, P. Blaha, and I. Herman, “Ac drive observability analysis,”IEEE Trans. Ind. Electron., vol. 60, pp. 3047–3059, Aug 2013.[2] G. Foo, X. Zhang, and D. Vilathgamuwa, “A sensor fault detection andisolation method in interior permanent-magnet synchronous motor drivesbased on an extended kalman filter,” IEEE Trans. Ind. Electron., vol. 60,pp. 3485–3495, Aug 2013.[3] P. Alkorta, O. Barambones, J. Cortajarena, and A. Zubizarrreta, “Effi-cient multivariable generalized predictive control for sensorless induc-tion motor drives,” IEEE Trans. Ind. Electron., vol. 61, pp. 5126–5134,Sept 2014.[4] L. Amezquita-Brooks, J. Liceaga-Castro, and E. Liceaga-Castro, “Speedand position controllers using indirect field-oriented control: A classicalcontrol approach,” IEEE Trans. Ind. Electron., vol. 61, pp. 1928–1943,April 2014.[5] C. de Wit, A. Youssef, J. P. Barbot, P. Martin, and F. Malrait, “Observ-ability conditions of induction motors at low frequencies,” in Proc. 39thIEEE Conf. Decis. Control, vol. 3, pp. 2044–2049, 2000.[6] M. Barut, S. Bogosyan, and M. Gokasan, “Speed-sensorless estimationfor induction motors using extended kalman filters,” IEEE Trans. Ind.Electron., vol. 54, pp. 272–280, Feb 2007.[7] S. Ibarra-Rojas, J. Moreno, and G. Espinosa-Pe´rez, “Global observabilityanalysis of sensorless induction motors,” Automatica, vol. 40, no. 6,pp. 1079 – 1085, 2004.[8] I. Boldea, M. Paicu, and G. Andreescu, “Active flux concept for motion-sensorless unified ac drives,” IEEE Trans. Power Electron., vol. 23,pp. 2612–2618, Sept 2008.[9] S. Koonlaboon and S. Sangwongwanich, “Sensorless control of interiorpermanent-magnet synchronous motors based on a fictitious permanent-magnet flux model,” in Conf. Rec. IEEE IAS 2005 Annu. Meeting,, vol. 1,pp. 311–318, Oct 2005.[10] M. Li, J. Chiasson, M. Bodson, and L. Tolbert, “Observability of speedin an induction motor from stator currents and voltages,” in Proc.44th IEEE Conf. Decis. Control, and European Control Conference,pp. 3438–3443, Dec 2005.

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