A Class of Fast Dynamics V/f Sensorless AC General Drives with PM-RSM as a Case Study

Ion Boldea*, Fellow, IEEE, Ana Moldovan*, Vasile Coroban Schramel*, Member, IEEE, Gheorghe Daniel Andreescu**,

Senior Member, IEEE, Lucian Tutelea*, Member IEEE *Dept. of Electrical Engineering, **Dept. of Automation and Applied Informatics,

University Politehnica of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania E-mail: boldea@lselinux.utt.ro, anamoldovan2003@yahoo.com, Vasile.Coroban.Schramel@continental-corporation.com,

daniel.andreescu@aut.upt.ro, luci@lselinux.utt.ro,

Abstract–Field oriented (FOC) and direct torque and flux (DTFC) control of AC drives are credited with fast torque response, but, in general purpose sensorless AC drives, the on-line software and hardware control effort and their reliability may seem prohibitive for general applications or, at least for synchronous motors, a starting strategy is necessary. The present paper presents a novel class of V/f sensorless AC general drives with two stabilizing loops–one based on active flux balance and one based on speed error–that provide fast speed dynamics response without steady state error, without speed or current regulators; flux weakening conditions are built in.

The exposition of principles is followed by exemplification for IMs, SPMSM, IPMSM, and DC excited SMs and by digital simulations on a PM-RSM (with weak PMs and reasonably high magnetic saliency Ld/Lq>3). Rather promising fast dynamics performance is obtained, in digital simulations for a PM-RSM case study, but more theoretical and then experimental work (which is under way) are needed to fully establish the proposed solutions as practical.

Index terms–fast dynamics, stabilizing loop, PM-RSM, active flux, sensorless control.

I. INTRODUCTION

lternating current (AC) motor drives are today a mature technology for torque levels from about 0.02 Nm to a

few MNm and from high speeds (500 krpm at 100W) to low speeds (16 rpm, 3 MW PM synchronous wind generator). The absence of mechanical brushes, the implicit four quadrant operation and motion-sensorless digital control via reasonable cost PWM converters have all contributed to this situation.

The speed control range and torque response quickness discriminates between general drives and so called servodrives. A 5(10)/1 speed range with full torque change in stable conditions within hundreds of milliseconds indicates a general AC drive, while a more than 1000/1 speed range with full torque response within milliseconds (1-2ms) refers to high quality servo-drives.

The Field Oriented Control (FOC) [1] and the direct torque and flux control (DTFC) [2-4] have spread to practically all servodrives. In between servodrives and general drives (speed control range between 10/1 and 1000/1, but with fast full torque response (2-4 milliseconds), motion-sensorless FOC and DTFC drives have spread in a spectacular way [5-16]. Most flux, position, speed estimators for motion sensorless drives are based on fundamental model methods [5-8] and thus are limited to 3-5 rpm minimum speed safe operation (with some torque perturbation rejection), though,

ocasionally, down to zero speed operation is shown in peculiar conditions [9]. For nonhesitant starting under load, and prolonged 1-5 rpm operation, frequency injection (or special PWM voltage) state estimators are used [10-14].

We have to take into consideration that using FOC or DTFC control method, some problems usually arise at startup because of the unknown initial rotor position.

And then the question arises: is it possible to obtain high dynamics response control in general AC drives (speed control range 10/1-30/1) with implicit self-starting capability by adequately and quickly stabilizing V/f control systems.

But before answering this question, let us see where we stand with V/f (I-f) control [17-27]. Assessing carefully the progress so far, we notice that, with two exceptions [22], [27], all stabilizing loops are slow in action.

They provide: slip frequency compensation in IMs for stability and small steady state error without speed close loop [17]; voltage on stator leakage reactance boost and slip frequency compensation in IMs [18], dynamic damping [19], better low speed (1.2) Hz by stator resistance voltage vector drop compensation and a novel nonlinear torque-speed estimation based slip frequency compensation for IMs [17] and frequency dynamic correction based on the DC-link power pulsations with stability analysis [20] for speeds up to 2500 rpm for PMSMs.

Again, none of the above V/f (I/f) control schemes with stabilizing loop is characterized by quick response in torque (full torque change in even tens of milliseconds) or speed.

In contrast, in [27], for a surface permanent magnet synchronous motor (SPMSM), a V/f control strategy with two stabilizing loops: ΔV for reference voltage amplitude and Δγ for voltage reference angle are applied: the first one slow, the second one faster, but both, based on zeroing the interior steady state reactive power Qi (implicitely id=0 control):

Qi≈ Qinput-3⋅|ω|⋅Ls⋅|is|2=0 (1)

Qinput is the input reactive power Starting from this situation, we introduce here a more

general, fast dynamics, V/f control with two stabilizing loops for all AC drives, again one for voltage amplitude (ΔV) and one for voltage angle (Δγ). But this time, ΔV loop is based on active flux balance for maximum torque/current, while Δγ loop is based on speed error.

A

453978-1-4244-7020-4/10/$26.00 '2010 IEEE

2010, 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2010

The active flux concept is introduced in reference [24] and the present paper uses it to develop the two novel stabilizing loops for V/f control.

The use of the proposed control strategy avoids the usual switching from signal injection based to model-based position estimation in FOC and DTFC during starting.

All on-line calculations are based on the active flux concept [24] in order to simplify mathematical expressions with securing both flux weakening and (or) close to maximum efficiency operation in the process.

The paper is organized as follows: Section II The proposed active flux balance for voltage

amplitude stabilizing loop; Section III The proposed voltage angle stabilizing loop; Section IV The proposed control system; Section V Case study for high saliency PM-RSM drive and Section VI Conclusions.

II. THE PROPOSED ACTIVE FLUX ERROR-BASED VOLTAGE STABILIZING LOOP

The core of the proposal consists in driving to zero, through a closed loop, the active flux error between its reference a*

dΨ and estimated value adΨ . The active flux a

dΨ [24] of any AC machine is defined as:

a

d S SqL iΨ =Ψ − ⋅ (2)

Where SΨ is the stator flux vector, Si the stator current vector and Lq is q axis machine inductance.

As by this concept all ac machine models “loose” their magnetic saliency [24], (Fig.1):

* *( )Ψ = − ⋅ad s sc dL L i -for induction motor (IM) in rotor flux

coordinates (3) * *( )

ad PM d q dL L iΨ =Ψ + − ⋅ -for interior PMSM (IPMSM) and

permanent magnet reluctance synchronous motor (PM-RSM) in rotor coordinates (4)

* *( )ad dm f d q dL i L L iΨ = ⋅ + − ⋅ -for dc excited synchronous motor

(SM) (5) Ls, Lsc -are no-load and short-circuit IM inductances; Ld, Lq - d, q synchronous inductances; Ldm-d axis magnetisation inductance; ΨPM - PM flux linkage; If -field current; For active flux estimation (2), stator flux estimation is

crucial. A combined voltage/current model observer is used here for the scope based on [24].

To avoid rotor position estimation we need to “fix” the desired longitudinal current id

* versus stator current is such that to consider both maximum torque/current below base speed for up to full torque and at low torque during flux weakening.

Maximum torque per flux for limited voltage (during full available torque requirement with flux weakening) at high speeds is obtained by adding a correction -Δid

* to id* when

reference voltage Vs*> Vsmax (Vsmax - maximum PWM inverter

voltage vector). For the IM and RSM this operation is synthesized in (6), (7):

jq

qjisisV

s sR i

ω ψr sj

di

ψs

q sL i

( )ψ =ψ + −a

PM d q dd L L id

Fig. 1. Vector diagrams with active flux a

dΨ , for PM-RSM

id*=idi

*, *

2= s

dii

i if ΔV=Vs*-Vsmax<0 (6)

id*=idi

*-Δid* for ΔV>0; Δid

*=kp⋅(1+1/Ti⋅s)⋅ΔV; (7) kp, Ti – PI regulator parameters

For the SPMSM, maximum torque/current corresponds to: idi

*= 0; id*= 0, if ΔV<0 (8)

id*= -Δidi

*; Δidi*=kp⋅(1+1/Ti⋅s)⋅ΔV, if ΔV>0 (9)

For PM-RSM and IPMSM, the maximum torque/current conditions are reflected by equation (10)[23]: 2⋅idi

*2+ idi*⋅λPM/(Ld-Lq)=is

2; (10)

As Ld-Lq<0 and id*<0, *

2> − S

dii

i , for ΔV<0 (11)

A close approximation of the maximum torque/current formula may also be considered:

* * / 2 12 ( )

PMd di S

d unsat q unsat sni i i

l l Iλ= ≈− ⋅ +

⋅ − ⋅; (12)

λPM, Isn, Ld, Lq - in p.u. values, for ΔV<0

id*=id

*-Δid*; *

1(1 )d pi

i k VT s

Δ = ⋅ + ⋅Δ⋅

for ΔV>0, *Ψ≤− PM

did

iL

(13)

With *di given in a*

dΨ formulae (2-5), the corresponding *qi

current is straightforward * 2 *2= −q S di i i , with Si (stator phase current amplitude), as measured.

The active flux, adΨ , has to be estimated (2) - see the next

paragraph - and thus the active flux error is: *ΔΨ =Ψ −Ψa a a

d d d (14)

* ( ) ( )1

pva ad SMR d

iv

kV k sign

T sΔ =−ΔΨ ⋅ − ⋅ ΔΨ

+ ⋅ (15)

Equation (15) reflects a hybrid PI and simplified sliding mode (SM) close loop that will correct the voltage amplitude of the V/f system.

454

III. THE PROPOSED VOLTAGE ANGLE STABILIZING LOOP

A novel stabilizing loop for voltage phase angle correction Δγ in the V/f control is proposed here. It is based on the speed error Δωr

*; rω is the estimated speed which happens to be the speed of the active flux:

[ 1] [ ] [ 1] [ ]2

[ ]

( )(

a a a aa d k d k d k d k

r d as d kT

α β β αω ω ψ − −Ψ ⋅Ψ −Ψ ⋅Ψ= =⋅ Ψ

(16)

Ts is the sampling time; some filtering is required. Alternatively, a PLL observer based on (2), may be used.

The stator flux components Ψα and Ψβ have to be estimated and, at least above 2-3 Hz, only the voltage model may be used:

*( )1 S

T V R isTαα α αΨ = ⋅ − ⋅

+; *( )

1 ST V R isTβ β βΨ = ⋅ − ⋅

+;

ad qL iα α αΨ =Ψ − ⋅ ; a

d qL iβ β βΨ =Ψ − ⋅ (17) T is in the order of one second. Correction for dc offset of the integral, of inverter

nonlinearities and of stator resistance for low speed estimation of Ψα, Ψβ are feasible but they complicate the drive which is considered general (it operates above 2 Hz).

The angle stabilizing loop, based on * *Δ = −r r rω ω ω is:

* ( ) ( )1

pir SMi r

ii

kk sign

T sγ ω ωΔ =−Δ ⋅ − ⋅ Δ

+ ⋅ (18)

IV. THE PROPOSED CONTROL SYSTEM

The generic control system with the two stabilizing loops may be illustrated as in figures 2 and 3 for all ac drives.

Summarizing on the stabilizing loops we may infer that they may be equivalent to two model reference adaptive systems. The proposed control (Figs.2,3) characterization follows:

∗ It contains a V*/f* control to provide self-starting and satisfactory no load operation at all speeds of interest;

∗ It adds to it two stabilizing loops to correct voltage vector amplitude by ΔV* and phase by Δγ*, via two regulators;

∗ It provides default approximate maximum torque/ current operation until the reference voltage Vsc

* goes over maximum inverter voltage Vmax; in this latter case, the ΔV=Vs

*-Vmax>0 triggers, by a PI controller, a correction in the reference id

*current by (-Δid*) until the machine operates

at Vmax, towards maximum torque/flux mode; full flux weakening is thus implicit.

The two stabilizing loops embody PI plus SM regulators on the active flux amplitude error a a* a

d d dΔΨ =Ψ −Ψ and, respectively, on the speed error a

d

*r ΨΔω =ω −ω to produce

ΔV*(amplitude) and Δγ*(angle) corrections to the V/f standard control tailored after no load.

The active flux adΨ observer is based here on the voltage

model of stator flux sΨ (Fig.3) after substracting q sL * i , with is measured; such an observer is to be used above a certain minimum frequency fmin (reference speed) of a few Hz. Pure V/f control is used for f*<fmin.

Fig. 3. Active flux amplitude and its speed (rotor speed) estimators

The reference rather than measured voltages Vα*, Vβ

* are used, with adequate corrections for inverter nonlinearities. Inverter maximum voltage vector Vmax is estimated by measuring only the dc voltage.

The reference active flux amplitude a*d s(i )Ψ is not constant,

but dependent on the measured is, such that to provide maximum torque/current conditions by using equations (7)-(14) to settle *

d si (i ) and then a*d s(i )Ψ . For various ac machines

the a*d s(i )Ψ function looks like in equations (2)-(5). Magnetic

cross-coupling saturation is known to produce errors in stator flux or rotor position estimation [16]; in our case (Fig. 2), the active flux observer is ”touched” by cross-coupling saturation only by its influence on Lq. According to the unique d and q magnetic curves model for cross-coupling saturation, Lq is approximately a sole function of is, which is measured.

With the exception of PM-RSM, Lq is only slightly dependent on magnetic saturation because in IMs Lq=Lsc, in RSMs Lq<<Ld and in d.c. excited SM Lq<Ld; in PM-RSM by further simplification *

q qL ( i ) may be used with * 2 *2q s di i i= − .

The complete Lq (id*,iq

*) function may be found, from a pure V/f commissioning sequence, based also on the active flux but is not detailed here for lack of space.

To a first approximation: * *

q q q0 sat qL (i ) L k i= − ⋅ (19) For the induction machine the slip frequency compensation

(sω1)*(Fig.2) is produced as:

2 *2s d*

1 *d r

i iS

i T−

ω ≈ ; rr

r

LTR

= (20)

For maximum torque/current (sω)*=1/Tr, (id*=iq

*). To avoid accounting for saturation or temperature influence on Tr (20), its average value may be considered.

Note: The proposed control system avoids the speed and current regulators (and the coordinate transformations), but still uses two stabilizing loops (for voltage amplitude and angle) and a correction loop for id

* reference current (by -Δid*) when the

reference voltage surpasses the maximum inverter voltage. However, it provides selfstarting and wide speed control with implicit maximum torque/current operation and up to maximum torque/flux operation, covering the maximum available load torque/speed curve (that is full flux weakening is also implicit).

455

Fig. 2. V/f control with two active flux stabilizing loops: ΔV* and Δγ*(for ΔV<0, max torque/current operation); for ΔV>0, towards max torque/flux operation

is provided for max torque /speed envelope (flux weakening)

The above attributes and the fact that the proposed control covers basically all ac motor drives with small particularization changes for various ac motor types, should suggest its full potential. A case study for PM-RSM follows.

V. CASE STUDY FOR HIGH SALIENCY PM-RSM DRIVE

The PM-RSM under investigation has the data given in the Appendix: it shows a rated saliency Lq/Ld = 4/1 so most torque is reluctance torque while the PM flux is rather small: wide torque-speed range is thus secured with reasonable max-speed emf (<150%).

The MATLAB implementation of the two correction loops in Fig.3 is shown in Fig.4.

The control system parameters in Fig.4 with PI plus sliding mode (SM) controller type, refer to the active flux error controller: kp_dΨ=51, ki_dΨ=13.6, ksm_dΨ=0.1, while for the speed error controller, kp_dω=0.0007, ki_dω=1.01, ksm_dω=0.0001. All these parameters have been introduced by the trial and error method. The V/f parameter, k, which represents the proportionality between the voltage and the frequency is k=0.105, while the initial (boost) voltage of about 0.1V, characterize the standard V/f scheme (Fig.5).

First, a d-q current vector control system was programmed and run in Matlab to check the performance of the speed estimator (active flux speed rω ) and the active flux estimator ( a

dΨ ).

a) Voltage amplitude correction loop

b). Voltage phase correction loop.

Fig. 4. Voltage amplitude(a) and phase(b) correction stabilizing loops.

Fig. 5. Standard V/f scheme.

Figure six shows the results during rather fast speed transients. Quick acceleration by vector control to 1500rpm at no load, is shown in Fig.6a.

The persistent oscillations in the speed rω and active flux a

dΨ estimators, mainly due to a compromise between response quickness and stability during fast speed and torque perturbations, need further treatment, but for the time being, they are considered acceptable to prove the concept.

Then, a step speed reduction from 1500rpm to 1400rpm at 0.2s, followed by a step speed recovery back to 1500rpm at 0.3s and then a step 5Nm torque at 0.4s perturbation is presented in Fig.6b. Next, the same speed transient as in Fig.6 with vector control and encoder (acceleration under no load from zero to 1500 rpm, within about 100ms) has been simulated and the results are shown in Fig.7a for the proposed V/f with two stabilizing loops system (Fig.2).

456

Fig. 6. Vector control: a) Estimated speed, torque response and both stator flux and active flux variation during acceleration at no load; b) Estimated

speed, torque response and both stator flux and active flux variation at 5Nm load, after a speed transient between 0,2 and 0,3 seconds

The speed response is fast but some small speed oscillations around the target persist. They are believed to be caused by the not so good quality of the rω and a

dΨ observers (Fig. 6). Some further work will be devoted to eliminate the oscillations of the estimated speed.

A comparison between the stator and active flux is also shown, both at load and at no load (Fig.6). We can observe that the active flux increases and then it decreases, when the machine accelerates and then increases slightly when the 5Nm load occurs.

Fig. 7. Speed and torque response and flux variation at no load (a) and at a ramp 5Nm load (b) when the proposed V/f control with two stabilizing loops

is considered

An 800 ms ramp 5Nm torque perturbation was applied at t=0.2s (Fig.7b). The machine response is still stable but some small speed oscillations still persist as under no load. A step 5Nm load, as in vector control (Fig.6b), was tried, but at this moment, the proposed drive did not survive this severe transient test, which warrants more work in this direction.

For comparisons, the same transients as in figures 6, 7 were tried with standard V/f with results as in Fig.8.

The standard V/f no-load acceleration time (Fig.8a) is about 500ms, much larger than for the proposed control system (100ms in Fig.7).

457

Fig. 8. No load acceleration attempt with standard V/f open loop control, a) free acceleration as in Fig.6,7; b) fastest frequency acceleration available and

800ms, 5Nm ramp at 0,5s response.

The collapse of the drive under 800ms ramp 5Nm torque perturbation is evident; this indicates the usefulness of the two proposed stabilizing loops.

VI. CONCLUSIONS

The paper proposes two stabilizing loops to the standard V/f control, based on active flux concept, introduced by some of the authors of this paper [24], which is amenable to all ac motor drives.

The two new stabilizing loops that „correct” the voltage vector amplitude ΔV* and angle Δγ* are based on active flux

adΔΨ and speed Δ rω errors.

The method also provides default max torque/ current operation unless the voltage ceiling of the PWM is surpassed, when the d axis reference current id

* is corrected toward max torque/flux conditions. Consequently, wide torque-speed operation is implicit, with close to optimum efficiency.

The speed and current control loops are eliminated while current sensors are not.

As the built-in V/f control provides for light load starting (typical to pumps, blowers, centrifugal air compressors), the proposed method avoids a dedicated starting strategy (for synchronous motors).

While fast speed response has been demonstrated through digital simulations, more theoretical and then experimental

work, (which is under way) is needed to fully prove the proposed method practicality.

APPENDIX

PARAMETERS OF THE IPMSM Number of pole pairs (p) 2

Rated power(PN) 2.35 kW Rated speed(nN) 1500 rpm

Rated torque 5Nm Rated battery voltage (Vbatt) 48V

Rated phase to phase voltage (Vs) 22 V(rms) Rated phase current (Is) 67 A(rms)

Stator resistance per phase (Rs) 0.05 Ω d-axis inductance (Ld) 0.45 mH q-axis inductance (Lq) 1.8 mH Rotor permanent - magnet (λPM) 0.0136 Wb Inertia of the rotating system (J) 1.6e-3 kg*m2 Viscous friction coefficient (Bm) 1e-4 Nms/rad

ACKNOWLEDGMENT

This work was partially supported by the strategic grant POSDRU 6/1.5/S/13, (2008) of the Ministry of Labour, Family and Social Protection, Romania, co-financed by the European Social Fund – Investing in People.

This work was also supported by EU-FP7 EE-VERT Project (Grant agreement no. SCP7-GA-2008-218598-EE-VERT).

REFERENCES [1] F. Blaschke, “The principle of field orientation as applied to the new

transvector closed loop control system in a PWM inverter induction motor drive”, Siemens Rev., vol. 39, no. 5, pp. 217–220, 1972;

[2] I. Takahashi and T. Noguchi, “A new quick-response and high-efficiency control strategy of an induction motor”, in Conf. Rec. IEEE IAS 1985 Annu. Meeting, pp. 496–502;

[3] M. Depenbrock, “Direct self-control (DSC) of inverter-fed induction machine”, IEEE Trans. Power Electron., vol.3, no.4, pp.420–429, 1988;

[4] I. Boldea and S. A. Nasar, “Torque vector control (TVC)—A class of fast and robust torque-speed and position digital controllers for electric drives”, Electric Mach. Power Syst., vol. 15, no. 3, pp. 135–148, 1988;

[5] C. Lascu, I. Boldea, and F. Blaabjerg, “Direct torque control of sensorless induction motor drives: A sliding-mode approach”, IEEE Trans.on Ind. Applicat., vol. 40, no. 2, pp. 582–590, Mar.–Apr. 2004;

[6] P. Guglielmi, M. Pastorelli, G. Pellegrino, and A. Vagati, “Position sensorless control of permanent-magnet-assisted synchronous reluctance motor”, IEEE Trans. on Ind. Applicat., vol. 40, no. 2, pp. 615–622, Mar.–Apr. 2004;

[7] Z. Chen, M. Tomita, S. Ichikawa, S. Doki, and S. Okuma, “Sensorless control of interior permanent magnet synchronous motor by estimation of an extended electromotive force”, in Conf. Rec. IEEE IAS 2000 Annual. Meeting, Rome, Italy, 2000, vol. 3, pp. 1814–1819;

[8] S. Morimoto, M. Sanada, and Y. Takeda, “Mechanical sensorless drives of IPMSM with online parameter identification”, IEEE Trans.on Ind. Applicat., vol. 42, no. 5, pp. 1241–1248, Sep./Oct. 2006;

[9] L. Harnefors, J. Luomi, M. Hinkkanen, „Reduced-Order Flux Observers with Stator-Resistance Adaptation for Speed-Sensorless Induction Motor Drives”, IEEE ECCE 2009;

[10] M. Linke, R. Kennel, and J. Holtz, “Sensorless speed and position control of synchronous machines using alternating carrier injection”, in Proc. IEEE Int. Electric Mach. Drives Conf. (IEMDC’03), Madison,WI, 2003, vol. 2, pp. 1211–1217;

[11] S. Shinnaka, “New “mirror-phase vector control” for sensorless drive of permanent-magnet synchronous motor with pole saliency”, IEEE Trans on. Ind. Applicat., vol. 40, no. 2, pp. 599–606, Mar.–Apr. 2004;

[12] M. W. Degner and R. D. Lorenz, “Using multiple saliencies for the estimation of flux, position, and velocity in AC machines”, IEEE Trans.on Ind. Applicat., vol. 34, no. 5, pp. 1097–1104, Sep./Oct. 1998;

458

[13] H. Kim, K. K. Huh, M. Harke, J. Wai, R. D. Lorenz, and T. A. Jahns, “Initial rotor position estimation for an integrated starter alternator IPM synchronous machine”, in Proc. 10th Eur. Conf. Power Electron. Applicat. (EPE-2003), Toulouse, France, 2003, pp. 1875–1881;

[14] S. Sul, Y. Yoon, S. Morimoto, K. Ide, „High Bandwidth Sensorless Algorithm for AC Machines Based on Square-wave Type Voltage Injection”, IEEE ECCE 2009;

[15] P.Guglielmi, M. Pastorelli, A.Vagati, ”Cross-Saturation Effects in IPM Motors and Related Impact on Sensorless Control”, Industry Applications, IEEE Transactions on, 2006, Vol. 42, Nr.6, pp: 1516-1522;

[16] N.Bianchi, S. Bolognani, “Sensorless-Oriented-Design of PM Motors”, Industry Applications Conference, 42nd IAS Annual Meeting. Conference Record of the 2007 IEEEPP., pp 668-675;

[17] K. Koga, R. Ueda, T. Sonada “Constitution of V/f control for reducing steady state error to zero in induction machine drive to zero in IM drive system”; IEEE Trans. on, vol. IA-28, no.2, 1992, pp.463-471;

[18] M. G. Alfredo, T.A.Lipo, D.A. Novotny “A new induction motor V/f control method capable of high performance regulation at low speeds”; Industry Applications IEEE Transactions on, Vol. 34, nov, 1998, pp. 813-821;

[19] M.Tsuji, S. Chen, S.I.Hamasachi, X.Zhao, Y. Yamada “ A novel V/f control of induction motors for wide and precise speed operation”. Record of IEEE-SPEEDAM, 2008, pp. 1130-1135;

[20] P.D.C.Perera, F. Blaajberg, J.K. Pedersen, P.T. Thogersen, “A sensorless stable V/f control method for PMSM drives”, Industry Application IEEE Trans. on Vol.39, no.3, 2003, pp.783-791;

[21] D. Montesinos, S. Galceran, A. Sudria, O.Gomis, F. Blaajberg, “Low cost sensorless control of MSMs an overview and evaluation”, record of IEEE-IEMDC, 2005, pp.1681-1688;

[22] R. Ancuti, I.Boldea, G.D. Andreescu, D. Iles, “Novel motion sensorless control of high-speed small-power surface mount PMSM drives with experiments”, Record of OPTIM -2008, vol.3, pp.11-18 (IEEExplore);

[23] I. Boldea “Reluctance Synchronous Machines and drives” book, chapter 7, OUP, Oxford, U.K., 1996;

[24] I.Boldea, M.C. Paicu, G.D. Andreescu, “Active flux concept for motion-sensorless unified ac. drives”, IEEE Transactions on Power Electronics, vol. 23, no.5, 2008;

[25] A.M. Kambadkone, I. Holtz “Vector controlled induction motor drive with a self-commissioning scheme”, IEEE Transactions on IE, vol.38, no.5, 1991, pp.322-327;

[26] M.Ruff, A.Bunte, M. Grotstollen, “A new selfcommissioning scheme for an asynchronous motor drive system”. Record of IEEE-IAS, 1994, Annual Meeting, part 1, pp.616-623;

[27] R.Ancuti, G.D. Andreescu and I.Boldea, “Four rotor position and speed simplified estimators for vector control of high-speed SPMSM with test comparisons”, Journal of electrical engineering, JEE, vol.7, no.4, Politehnica Publishing House, Timisoara, 2007.

459