Active-Flux-Based, V/f-with-Stabilizing-Loops Versus Sensorless Vector Control of IPMSM Drives

Ana Moldovan*, Frede Blaabjerg**, Fellow, IEEE, Ion Boldea*, Fellow, IEEE

*Dept. of Electrical Engineering, University Politehnica of Timisoara, 2 Vasile Parvan Blvd., 300223 Timisoara, Romania ** Institute of Energy Technology, Aalborg University, 101 Pontoppidanstraede, 9220 Aalborg East, Denmark

E-mail: anamoldovan2003@yahoo.com, fbl@et.aau.dk, boldea@lselinux.upt.ro

Abstract–This paper proposes two control methods for Interior Permanent Magnet Synchronous Motor (IPMSM) Drives. The first one is a V/f control with two stabilizing loops: one loop based on active flux balance for voltage magnitude correction and a second, based on speed error, with voltage phase correction. By this control strategy, a fast dynamic speed response, without steady state error and without speed or current regulators, for all AC machines is obtained. The second control method is a sensorless vector control strategy which also has been implemented and tested, just for comparison.

Comprehensive simulations of both proposed V/f and sensorless vector control have been implemented by using a Matlab/Simulink package and a dSpace based platform has been built.

Rather promising fast dynamic performance is obtained, both in simulations and in laboratory experiments for the proposed IPMSM Drive.

Index terms–fast dynamics, stabilizing loop, IPMSM, active flux, sensorless control.

I. INTRODUCTION

nterior Permanent Magnet Synchronous Motors (IPMSMs) are known to have several advantages, like

increased efficiency (the copper loss associated with field windings does not exist), rugged construction (the lack of brushes and the use of PMs to generate the field allow to design these machines with less weight and compact size), high torque density (as the d, q-inductances are not equal, the reluctance torque contribution has also to be considered). Moreover, the capability of operating above base speed (in case of high saliency, the speed domain at constant power goes above 3/1), easy maintenance, high power factor, lower PM cost of IPMSMs have lead to their increased use during the last two decades in industrial applications, as high performance variable speed motors.

The use of a PMSM for electric drive applications requires the initial rotor position information [1-3], provided in general by an encoder or a resolver. Position sensors have their disadvantages like higher cost of the drive, the machine size is increased (in case of small power drives), while the system reliability may also be decreased. Therefore, many papers have as their main focus to eliminate position sensors; consequently, motion-sensorless field oriented control (FOC) and direct torque and flux control (DTFC) drives are used more and more [4-9].

Most flux, position, speed estimators for motion sensorless drives are based on fundamental model methods [4-6] and thus, they are limited to 3-5 rpm minimum speed safe operation (with some torque perturbation rejection) though,

occasionally, down to zero speed operation is demonstrated in peculiar conditions [10]. For nonhesitant starting under load, and prolonged 1-5 rpm operation, frequency injection (or special PWM voltage) state estimators are used [11-12].

Stability improvement as well as fast speed and torque dynamic response are two main goals in what concerns the proposed V/f controlled IPMSM. Recent V/f control method uses two correction loops [13-16]. One for the voltage amplitude, the second for the voltage phase, to improve the stability of the V/f – controlled Surface Permanent Magnet Synchronous Motor (SPMSM). Undesirable sustained oscillations in Standard V/f-controlled SPMSM drive systems can often be noticed in the steady state with or without load.

FOC [17] or DTFC [15-17] for general sensorless AC drives, even for the speed control range in the 20/1-100/1 range is common when fast dynamic torque response is required, at the price of rather sophisticated software and hardware for the control. Regarding this, a question to be answered is: is it possible to obtain high dynamics response control in general AC drives with less on-line computation effort and less costly digital control hardware by quickly stabilizing the V/f control system?

A comparison between the proposed V/f control method and FOC for IPMSM (Appendix) will also be discussed.

The estimation of the initial rotor position is also essential for sensorless control of synchronous machines; a few solutions are presented in [18].

The same active flux observer, used in V/f-control for voltage amplitude correction, is used in sensorless FOC for speed and angle estimation. The active flux concept has been introduced [19] and it represents the base for the two novel stabilizing loops proposed in this paper.

The use of the proposed control strategy avoids the usual switching from signal injection-based [20] to model-based position estimation in FOC and DTFC during start-up.

All on-line calculations are based on the active flux concept, thus providing simplicity for the mathematical expressions and securing both flux weakening and (or) close to maximum efficiency operation in the process. Using the active flux observer to estimate the speed, the position and the flux, the proposed V/f-control gives up the usual current and speed controllers. We intend here to prove the reliability and performance of this control method as an alternative to sensorless vector control. For this reason, experiments at low (5 rpm) and higher speed (1400 rpm) have been conducted and results are compared for both control methods.

I

978-1-4244-9312-8/11/$26.00 ©2011 IEEE 514

The paper is organized as follows. Firstly, the proposed V/f control with the stabilizing loops is described in SectionII. Next, the active flux based sensorless vector control of IPMSM is presented during SectionIII. Simulation results for both control methods are shown during SectionIV. Finally, experimental results to validate both the sensorless vector control and the V/f with stabilizing loops control methods follow in SectionV. In SectionVI, the conclusion is presented.

II. THE PROPOSED V/F CONTROL WITH THE STABILIZING LOOPS

The main purpose of the proposed V/f control is to achieve fast dynamics speed and torque response, without using current or speed regulators and without coordinate transformations. Instead, it uses two corrections; the first one is the “active flux” error, between its reference *a

dΨ and estimated value a

dΨ , to correct the voltage vector amplitude, and then the speed error is used to correct the phase of the applied voltage vector. “Active flux or torque-producing flux” [19] is also known to be the flux which multiplies the iq current in the dq-model torque expression. This concept turns all salient-pole rotor AC machines into nonsalient-pole ones, so the rotor position and speed estimation become simpler (see Fig.1).

* *( )

ad PM d q d= L L iΨ Ψ + − ⋅ -for IPMSM (1)

*a

d s q s= L iΨ Ψ − ⋅ (2)

Ld, Lq - d, q synchronous inductances; ΨPM - PM flux linkage; For the active flux estimation (2), the stator flux estimation

is crucial; thus a combined voltage/current model observer is used as shown in Fig. 2.

To calculate the reference active flux, we have to “fix” the desired longitudinal current *

di versus stator current si by making use of the 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 speed is obtained by adding a correction *

di−Δ to *di when the

reference voltage Vs*> Vsmax, where Vsmax is the maximum

PWM inverter voltage vector.

a)

\ b) Fig. 1. Vector diagrams for IPMSM, Ld<Lq: a) IPMSM structure;

b) IPMSM vector diagram highlighting the active flux adΨ

*2 * 22 ( ) /( )d d PM d q si i L L = i⋅ + ⋅ −λ ; (3)

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

2s

di

i > − , for ΔVs=Vs*-Vsmax<0 (4)

For IPMSM, the maximum torque/current conditions are reflected by (5) using (3) and (4):

2

* 21 1 1 24 2 4

PM PMd s

d unsat q unsat d unsat q unsat

i IL L L L

⎛ ⎞= − ⋅ − ⋅ ⋅ + ⋅⎜ ⎟⎜ ⎟− −⎝ ⎠

λ λ ; (5)

where Ld unsat, Lq unsat – are the unsaturated values for Ld,Lq; λPM, Isn, Ld, Lq - in p.u. values, for ΔVs<0;

*di = *

di - *diΔ ; * 11d p s

i

i k VT s

⎛ ⎞Δ = ⋅ + ⋅Δ⎜ ⎟⋅⎝ ⎠

for ΔVs>0, * PMd

d

iL

Ψ≤− (6)

With *di given in *a

dΨ , formula (5), the corresponding *qi

current is straightforward * 2 2q s di = i i− , with si as the

measured stator phase current amplitude. Thus the active flux error is:

* * *a a ad d d=ΔΨ Ψ − Ψ (7)

Equation (8) reflects the PI closed loop that will correct the voltage amplitude *VΔ of the V/f–system:

* 1ap idV = k k

s⎛ ⎞Δ −ΔΨ ⋅ + ⋅⎜ ⎟⎝ ⎠

(8)

The second correction is for the voltage phase angle, Δγ and it is based on the speed error, rΔω , between its reference *

rω and the estimated one, rω , which is the speed of the active

flux: ( ) [ ] [ ] [ ] [ ]

[ ]

1 12

a a a ad k d k d k d ka

r da

s d kT

− −Ψ ⋅ Ψ − Ψ ⋅Ψ= Ψ =

⋅ Ψ

α β β αω ω (9)

where Ts is the sampling time and the index [k-1] denotes variables delayed with one sampling period.

The main drawback of this solution is that the estimated speed accuracy is strictly dependent on the active flux component estimation accuracy. To reduce the influence of the noise from the estimated speed a low-pass filter (LPF) is used: HLPF=kpF/(TiF*s+1).

The stator flux components Ψα and Ψβ have to be estimated, thus the voltage model is used as shown in Fig.2 and calculated:

( )*

1 comp sT V V R isT

Ψ = ⋅ + − ⋅+α α α ; ( )*

1 comp sT V V R isT

Ψ = ⋅ + − ⋅+β β β ;

ad qL iΨ = Ψ − ⋅α α α ; a

d qL iΨ = Ψ − ⋅β β β ; (10)

The active flux adΨ observer is based on the voltage model

of stator flux sΨ as shown in Fig. 2 after substracting q sL i⋅ , where is is measured.

The compensation voltage is also taken into account and it is based on the error between the voltage model and current model for active flux calculation through a PI regulator. The compensation voltage takes care of the inverter nonlinearities [22], like deadtime, integrator offset, stator resistance variation. The compensation voltage shows a notable influence at low speed.

515

adΨ

adΨ

adαΨ

adβΨ

rω

asαΨ

asβΨ

a a 2 a 2d d d( ) ( )α βΨ = Ψ + Ψ

ad

ωΨ

*s compV i R Vβ β− ⋅ +

*s compV i R Vα α− ⋅ + T

1 sT+

T1 sT+

*Vα

iα

iβ*Vβ

iα

iβ

Fig. 2. Active flux amplitude and its speed (rotor speed) observer.

Fig. 3. Standard V/f scheme

During experiments, the magnetic saturation was considered constant, as the IPMSM under investigation has the data given in Appendix A, that show a low rated saliency Lq/Ld = 1.1.

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

* 1r p ik k

s⎛ ⎞Δ = −Δ ⋅ + ⋅⎜ ⎟⎝ ⎠

γ ω (11)

The reference speed, angle and voltage (See Fig. 3) are calculated with the reference frequency ramp, where

*2 f dt= ⋅ ∫θ π and * *0V f k V= ⋅ + , with V0≈RS*IN; k=const.

The proposed V/f with the stabilizing loops control scheme is illustrated in Fig. 4 and it is characterized by a V*/f*-control to provide self-starting and satisfactory no load operation at all speeds of interest and by two stabilizing loops to correct the voltage vector amplitude by ΔV* and phase by Δγ*. The two stabilizing loops (See Fig. 5) embody PI regulators on the active flux amplitude error *a a a

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

ad

r ΨΔ = −ω ω ω to produce

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

dΨ

ωθ

eT

* * *sV V Vα β= +

a*d Eq.(1)Ψ =

Fig. 4. V/f control with two active flux stabilizing loops: ΔV* and Δγ*.

*dV*V

V*Ψad

*Ψad

1⋅−

sK Tz

(a) *dγ

*θ θ*ω

ω1

⋅−

sK Tz

(b) Fig. 5. Correction loops for stabilizing a) Voltage amplitude, ΔV*; b) Voltage

phase, Δγ*.

III. ACTIVE FLUX BASED SENSORLESS VECTOR CONTROL OF IPMSM

For fair comparisons, a sensorless vector control of the IPMSM used as case study was implemented and the block diagram is shown in Fig. 6. Experiments have been conducted both at no load and at load, for a speed range between 0.3 –100 % of nominal speed. This control method uses the same active flux state observer, for speed and position calculation as in the proposed controllers.

* * *sV V Vα β= +

a*d Eq.(1)Ψ =

Fig. 6. Sensorless vector control used for bench-marking study.

The reference speed is calculated from the frequency ramp, and the speed and current regulators are used for the voltage calculation, which is then used in the space vector modulation block (SVM) to create the modulation method signals for the inverter. The active flux observer has the same structure as the one presented in §II.

IV. SIMULATION RESULTS

For sensorless vector control, simulations have been done and the controller parameters obtained are:

TABLE I PARAMETERS OF THE CONTROLLERS USED IN SENSORLESS VECTOR CONTROL

SIMULATIONS PI speed controller Kp=0.4 Ki=2.5 PI id controller Kp=30 Ki=2000 PI iq controller Kp=30 Ki=3000

We have to mention that during both digital simulations and experiments, the MTPA conditions have been used (eq. 5).

Comprehensive simulations have been performed for both the proposed V/f control and the sensorless vector control. For theoretical validation of the performance and response accuracy of the active flux observer, a sensorless vector control scheme for IPMSM has been implemented in the Matlab/Simulink package.

During the simulations some approximations have been made: - the inverter was considered as ideal;

- for stator flux calculation, a pure integrator was used; The simulation results are shown in Fig. 7, where fast speed

response (100ms) and rather fast speed recovery (120ms) after load step of 50% rated torque has been applied and the results can be seen for the sensorless vector control. Fig. 8 shows the proposed V/f control corresponding to the simulation results. Table II specifies the data used. The machine starts under the load of 50 % rated torque at target speed (load torque is proportional to speed), which explains the 50 ms delay during start-up. The 50 ms delay during the torque response can also be noticed. As the simulation results show, the machine has almost the same behavior during the two control methods.

516

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-400

-200

0

200

400

time[s]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

500

1000

1500

reference speed

estimated speed

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10

0

10

20

30

estimated Te

reference Te

Fig.7. Simulated IPMSM start-up response and sudden 50% rated torque for

sensorless vector control at 0.5s.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-20

-10

0

10

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-400

-200

0

200

4000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-20

-10

0

10

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500

0

500

1000

1500

reference speed

estimated speed

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

10

20

30

40

estimated torque

reference torque

Fig. 8. Simulation of IPMSM start-up under 50% rated torque for V/f with

stabilizing loops control. TABLE II

PARAMETERS OF THE STABILIZATION LOOPS CONTROLLERS IN SIMULATION Active flux basedPI controller Kp=150 Ki=10 Speed error PI controller Kp=0.0068 Ki=0.1

They have been obtained by trial and error. To filter the estimated speed, a low pass filter with kpF=1

and TiF=0.0033s, has been implemented. The simulation constraints were investigated by the

presented laboratory experiments.

V. EXPERIMENTAL RESULTS

Using the active flux observer in Fig. 2 and the V/f with voltage magnitude and phase correction, the control scheme (Fig. 4) presented in §III, the experimental tests have been conducted.

The experimental platform contains of a 2.2 kW IPMSM as the main component, a three-phase Danfoss Inverter-FC302 type, dSpace 1103 system and a 2.2 kW IPMSM , as load.

The experimental results for the proposed V/f with correction loops control, where the parameters are specified in Table III, with self-starting from zero position angle and a PM generator using a resistive load (6 Nm at 1400 rpm) up to 1400 rpm are shown in Fig. 9. An acceptable 10 % speed overshoot can be observed in Fig. 9b, followed by the position representation in Fig. 9c, where a slight difference of less than 0.005 rad between the reference, estimated and the encoder values can be seen in the zoomed region. A 6 Nm load is also visible in Fig. 9d.

Fig. 10 shows the experimental steady-state results at 5 rpm (after self-acceleration (not shown) by V/f control with stabilizing loops) at no load. Small oscillations of 3 rpm can be distinguished in Fig. 10b. A less than 2 electrical degrees difference between the estimated and the encoder position can also be seen in Fig. 10c. The last two graphs, Fig. 10e and Fig. 10f show the outputs of the two correction loops.

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-20

-10

0

10

20

-6

6

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0

500

1000

1500

1390

1400

1405w encoder w reference

w estimated

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-3.14

0

3.14

4.5 4.57

th encoder th reference

th estimated

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-30

-20

-10-60

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-10

0

10

20

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-300

-200

-100

0

100

200

300

-270

270

Fig. 9. V/f control with stabilizing loops–experimental results for 1400 rpm

at 50 % of rated torque. TABLE III

PARAMETERS OF THE STABILIZATION LOOPS CONTROLLERS Active flux based PI controller Kp=3 Ki=700 Speed error PI controller Kp=0.001 Ki=0.15 Voltage compensation Kp=15 Ki=15

517

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.4

-0.2

0

0.2

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

5

10

w encoder w estimated w reference

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

0

5

th encoder th estimated th reference

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-5

0

5

1.w enc-w est 2.w ref-w enc21

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.025

-0.02

-0.015

-0.01

-0.005

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 515.6

15.7

15.8

Fig. 10. V/f control with stabilizing loops – experimental results for 5 rpm at

no load, during steady state.

A faster stabilization for angle correction loop can be noticed, in comparison with the voltage loop. The controllers parameters were determined by trial and error.

Experimental results for sensorless vector control are further presented in Fig. 11 and in Fig. 12. As it can be noticed, some additional ripple is present in the vector control at high speed. The acceleration time of 150 ms, from zero to 1400 rpm (See Fig.11), is equal with the one for V/f control with stabilizing loops. This is believed to be a confirmation of the main goal: fast torque (speed) response for a wide speed range. Vector control with encoder feedback was used first for motor start-up, then, switched to sensorless control at 1.7 s and 50 % of rated torque is applied afterwards, at 3.6 s.

About ten times higher values for the currents can be seen at load, compared to no-load operation, shown in Fig. 11a. When the load is applied, the speed decreases with about 50 rpm and in 35 ms it reaches the target again, see Fig. 11b. The estimated position follows rather closely the encoder for the entire working period. The measured mechanical position has also been represented in Fig.11c. The value for the applied load can be seen in Fig. 11d, while Idq currents are shown in Fig. 11e and Fig. 11f shows the error between the estimated and real speed.

Fig. 12 shows the results for sensorless vector control at 5 rpm in steady-state at no load, where the parameters used are given in Table IV. The motor start-up has been done using encoder feedback, then, during steady state, the switching to sensorless operation has been applied. It can be noticed that the speed oscillates around the reference with about 5 rpm, though a few spikes around 8 rpm are also present. This makes the sensorless speed response for low speed values apparently worse than for the proposed V/f control.

-10

-5

0

5

10

15

20

-5

0

5

10

0

500

1000

1500

-200

-100

0

100

200

-4-3.14

-2

0

23.14

4

-10

-5

0

5

10

1350

1400

1430

estimated speed

encoder speed referencespeed

th encoder

th mechanical

th estimated

Fig.11. Vector control no-load starting to 1400 rpm with position feedback,

with switching on sensorless operation at 1.7 s and sudden 6 Nm load at 3.6 s

0 1 2 3 4 5 6 7 8 9 100

0.5

1

time [s]

0 1 2 3 4 5 6 7 8 9 10-0.2

0

0.2

0.4

0.6

0 1 2 3 4 5 6 7 8 9 10-4

-2

0

2

4

th reference th estimated th mechanical

0 1 2 3 4 5 6 7 8 9 100

5

10

15

w encoder w estimated w reference

0 1 2 3 4 5 6 7 8 9 10-0.4

-0.2

0

0.2

0.4

0 1 2 3 4 5 6 7 8 9 10-10

-5

0

5

10

1enc-est 2 ref-enc2

1

Fig.12. Sensorless vector control at 5 rpm during steady-state.

TABLE IV PARAMETERS VALUES FOR THE SENSORLESS VECTOR CONTROL

CONTROLLERS PI speed controller Kp=0.1 Ki=0.2 PI id controller Kp=50 Ki=5000 PI iq controller Kp=30 Ki=3000

518

Voltage compensation Kp=1 Ki=1 The controllers parameters were determined by trial and error.

VI. CONCLUSION

The paper presents a novel V/f control method with two stabilizing loops - one based on active flux balance for the voltage amplitude correction, the other one based on the speed error for the voltage phase correction. Both simulation and experimental results are shown during the same working conditions. Results show that the machine starting response time to 1400 rpm (150 ms) is the same in both simulation and experiments.

To prove the main claim of the novel control – fast speed (torque) dynamic response – sensorless vector control was also implemented and tested, again during both simulation and experiments. The experimental results show that in vector control, the acceleration time from zero to 1400 rpm is around 150 ms, as for the V/f control with stabilizing loops.

Even more, V/f control, with correction loops, for low speed (5 rpm) - steady state operation, seems to follow the target better than sensorless vector control, as indicated by the V/f control, where the speed oscillations are less than for sensorless vector control.

Improvements are still needed for V/f with stabilizing loops control, e.g. full load step, has yet to be tested .

APPENDIX A PARAMETERS OF THE IPMSM

Number of pole pairs (p) 3 Rated power(PN) 2.2 kW Rated speed(nN) 1750 rpm Rated torque 12 Nm Rated frequency 87.5 Hz Rated phase to phase voltage (Vs) 380 V(rms) Rated phase current (Is) 4.1 A(rms) Stator resistance per phase (Rs) 3.3 Ω d-axis inductance (Ld) 41.6 mH q-axis inductance (Lq) 57.1 mH Rotor permanent – magnet (λPM) 0.483 Vs/rad Inertia of the rotating system (J) 10.1e-3 kg*m2 Viscous friction coefficient (Bm) 20e-4 Nms/rad Windings connection Star connection

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 Aalborg University, Denmark. Thanks are due to Prof. Ewen.Ritchie of University of Aalborg, Denmark; Dr. Sorin Agarlita and Dr. Razvan Ancuti of University Politehnica Timisoara, Romania for fruit-full discussions.

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