Speed Sensorless Asynchronous Motor Drive with Inverter Output LC Filter1

1 This work was supported in part by the Science Fund for the years 2008–2010 for the first author. Additionally, this publication was made possible by an NPRP grant (No. 08-369-2-140) from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Jaroslaw Guzinski(*), Haitham Abu-Rub(**)

(*) Gdansk University of Technology, Gdansk, Poland, e-mail: jarguz@pg.gda.pl (**) Texas A&M University at Qatar, Doha, Qatar, e-mail: haitham.abu-rub@qatar.tamu.edu

Abstract—In this paper a speed sensorless ac drive with inverter and output LC filter is proposed. A nonlinear, decoupled field oriented control algorithm with a flux and speed close-loop observer is used. In spite of using LC filter on the inverter output, the sensorless system works precisely. That result are obtained as a result of the appropriate estimation and control system use. The theory, simulation, and experimental results are presented.

Keywords—AC motor drives, inverters, low-pass filters, observers.

I. INTRODUCTION In adjustable speed drives (ASD) voltage inverters are

commonly used. In ASD the motor supply voltage contains a high frequency rectangular shape. This generates some problems in the motor e.g. motor bearings and stator windings insulation degradation with motor efficiency decreasing etc. [1]-[3]. The use of long cable connection between inverter and motor increases these problems. To avoid these problems differential and common mode passive filters are used [4]-[9].

Three kinds of the inverter output filters are used: dU/dt, common mode and differential. Only the differential filter has significant influence on the drive control [7], [10]- [14]. A typical structure of the LC differential filter is presented in Fig. 1. An example of the waveforms of the voltages and currents in the drive with LC filter are presented in Fig. 2.

When the filters are installed, a drop of the motor supply voltage and phase shifts between filter input and output voltages and currents appear. Such deviations can influence the drive proper function and can cause an abnormal operations of some electric drives with filters – particularly in the case of speed sensorless drives [10]-[14]. It is because induction motor control algorithms operate with the assumption that inverter output voltages and currents are equal to the motor input voltages and currents. Unfortunately in the drive with the differential LC filter it is not correct.

Some papers are dedicated to solving such control problems by adding additional sensors for motor voltages and current measurement [9], [10], [15], [16]. However

this solution is practically not acceptable because it requires changing in the inverter structure – the LC filter is an external element of the inverter, which imposes that external sensors and additional wiring system is needed. Such an approach complicates the hardware system and is an uneconomical solution. More practically, an accepted solution is to leave the inverter hardware without any changes and only to provide certain improvements to the control algorithms [10]-[14].

Fig. 1. Adjustable ac speed drive with inverter output LC filter.

Fig. 1. Waveforms in ASD with LC filter for 50% of motor nominal

speed and 100% of motor nominal load (in gray are filter input voltage and current, in black are filer output voltage and current)

14th International Power Electronics and Motion Control Conference, EPE-PEMC 2010

978-1-4244-7855-2/10/$26.00 ©2010 IEEE T5-1

Unfortunately the existing solutions for the speed-sensorless ASD require complex control and observer structure. This make it difficult to tune the control system because of using controller and observer systems with numerous parameters presence. E.g. in [9]-[13] the multi-loop feedback controllers were used so the controllers numbers has bee doubled versus the same drive without LC filter. In [11]-[13], the observer structure was also nearly twice enlarged with additional differential and algebraic equations. Previously proposed modifications of the drives with LC filter force the use of more powerful and expensive control system. Also the system complexity decreases the system robustness as the result of the numerous motor parameters presence in the structure.

This paper presents a simple solution for speed sensorless induction motor drive with inverter output LC filter and without additional measurements on the filter output. The goal is obtained by choosing proper control and estimation structure which provide high robustness of the over-all system. In contrary to other solutions only small modifications for control and estimation process are done. The simplified multi-loop structure was used and instead of complicated adaptive or disturbance observer use the simple flux and speed estimator was used. The properties of the proposed simple speed-sensorless ASD are practically the same as for ASD without LC filter.

This paper successively presents: • the equations of the model of the induction motor in

per unit system, • basic structure of the field oriented control (FOC)

principle including nonlinear decupling, • inverter output LC filter model, • modification of the motor control system taking into

account filter dependencies, • state observer for the flux, mechanical speed, and

other state variables calculation taking into account the filter model as well,

• and simulation and experimental results for a 1.5kW induction motor ASD.

II. INDUCTION MOTOR MODEL The most used mathematical model of the induction

motor is the model described in the rectangular coordinates noted as xy. State variables could be choose as: stator current and rotor flux components and motor mechanical speed noted as isx, isy, ψrx, ψry and ωr respectively. In this paper the per unit system, presented in Tab. I is used [7], [13], [14], [17], [18].

Equations of induction motor in rectangular frame of references xy rotating with arbitrary angular speed ωa have the form [17], [18]:

sx4ryr3syarx2sx1sx uaaiaiaddi +ψω+ω+ψ+=τ , (1) sy4rxr3sxary2sy1sy uaaiaiaddi +ψω−ω−ψ+=τ , (2)

( ) sx6ryrarx5rx iaadd +ψω−ω+ψ=τψ , (3) ( ) sy6rxrary5ry iaadd +ψω−ω−ψ=τψ , (4)

( )( ) JtLLiidd Lrmsxrysyrxr −ψ−ψ=τω , (5) where: Rr, Rs, Lr, Ls, Lm – motor equivalent circuit parameters, tL – motor load torque, J – motor inertia, a1..a6 are combination of the motor parameters:

σ

+−=wL

LRLRar

2mr

2rs

1 , σ

=wLLRa

r

mr2 ,

σ=

wLa m

3 , σ

=wLa r

4 ,

r

r5 L

Ra −= , r

mr6 L

LRa = , sr LLw σ=σ and

( )rs2m LLL1−=σ

The motor model (1)-(5) is given to clarify further transformations. In our analysis the rotating dq coordinates is adopted, where d axis is assigned to motor rotor flux vector 0jrdr +ψ=ψ position, which makes the system rotor flux oriented vector control.

TABLE I. DEFINITION OF PER UNIT VALUES

Definition Description

nb U3U = base voltage

nb I3I = base current

bbb IUZ = base impedance

( ) 0bbb pIUT Ω= base torque

0bb U Ω=Ψ base flux

p0b Ω=Ω base mechanical speed

bbb IL Ψ= base inductance

( )0bbb TJ ΩΩ= base inertia

t0Ω=τ relative time

III. DECOUPLED FIELD ORIENTED CONTROL The most popular industrial induction motor (IM)

control is rotor field oriented control (RFOC) [5]. In classical RFOC the coupling between flux and torque exists. Therefore, to improve the RFOC properties a decoupling control is usually used. The most popular decoupling system relies on adding electromotive rotation compensation components appearing in (1) and (2):

ryr3a ψω , rxr3a ψω− to the motor commanded voltages comsxu , com

syu . Other solutions for decoupling of the motor also exist. One of such methods was proposed in [17] in order to control a motor electromagnetic torque te instead of the q current component (in [17] the controlled te variable was noted as x):

rdsqe it ψ= , (6) The motor torque te is accepted as additional state

variable. With such an assumption the motor model equations (1)-(5) could be rewritten using the rotating dq coordinates as follows:

sd4rdrerd2sd1sd uataiaddi +ψω+ψ+=τ ψ , (7) ( )

( ) sqrd4rd3sdrdr

rdsde6ers5euaai

itatwLRaddtψ+ψ+ψω−

−ψ+−=τ

ψ

σ, (8)

sd6rd5rd iaadd +ψ=τψ , (9) ( ) JtLLtdd Lrmer −=τω , (10)

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where: rrdsq6r ia ω+ψ=ωψ , (11)

and isd, isq, usd, usq, ψrd are motor stator current, voltages and rotor flux in dq coordinates.

Equations (7)-(10) describe the model of the induction motor in dq coordinates which is a nonlinear and coupled system. If the following control variables v1 and v2 are used:

( ) sqrd4rd3sdrdrrdsde61 uaaiitav ψ+ψ+ψω−ψ= ψ , (12) sd4rd2rder2 uaatv +ψ+ψω= ψ , (13)

the motor model dq (7)-(10) is converted into two linear decoupled subsystems:

2sd1sd viaddi +=τ , (14) sd6rd5rd iaadd +ψ=τψ , (15)

( ) 1e4s5e vtaRaddt +−=τ , (16) ( ) JtLLtdd Lrmer −=τω , (17)

Base structure of the nonlinear filed oriented control method is presented in Fig. 3.

Fig. 3. Base control system for decoupled rotor field oriented method

In Fig. 3 the angle ρψr represents the position of the rotor flux vector and ud is the voltage in the inverter dc link. A block marked as dq/αβ represents the Park transformation from rotating dq into stationary αβ frame of references. The αβ coordinates are natural for PWM

space vector algorithm.

IV. INVERTER OUTPUT LC FILTER MODEL To analyze the system with the LC filter it is

convenient to accept the two-phase dq rotating coordinates as the case of motor model. An equivalent circuit for the LC filter for the two-phase components is presented in Fig. 4 [7].

Fig. 4. Equivalent filter circuits for LC filter two phase components.

For the LC filter the inverter input currents i1d, i1q and output voltages usd, usq are state variables. The model of the LC filer could be described in dq coordinates as follows [7], [13], [14]:

1cdsd Ciddu =τ , (18) ( ) 1sd1d1d Luuddi −=τ , (19)

1cqsq Ciddu =τ , (20) ( ) 1cq1q1q Luuddi −=τ , (21)

sd1dcd iii −= , (22) sq1qcq iii −= , (23)

where: L1, C1 are filter parameters and iCd, iCq are capacitor C1 currents.

In the presented system the LC filter L1=11.2mH and C1=10μF motor was used. The nominal voltage drop for the filter is 4% of the motor rated voltage. In the filter, the small damping resistors R1=1.1Ω were connected in series with capacitors for preventing the problems with resonance. The resistance was omitted in filter model and in control.

V. EXTENDED CONTROL SYSTEM In order to assure controllability of the system with LC

filter, the motor control structure presented in section III should be extended using additional controllers.

The cascaded multi-loop PI controllers are used to control the motor supply voltages usd, usq and inverter output currents i1d, i1q [9], [15], [16]. In the filter control subsystem the disturbances compensation on the stator voltage controllers were used [13].

In order to eliminate a phase shift in the PI units the control of the filter state variables is done in the synchronous dq coordinates synchronized with the rotor flux vector - the same coordinates as used in the basic RFOC control system.

The disadvantage of multi-loop solutions is a necessity of the motor voltage and current knowledge. Unfortunately the real sensors are not practically in this solutions as noted in the introduction. The variables are calculated on-line in the complex observer structure.

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In this paper, instead of the full multi-loop structure, only the PI controllers for direct inverter output voltage was implemented. The whole structure of the extended control system of the drive with induction motor, inverter and LC filter is presented in Fig. 5.

Fig. 5. Induction motor and LC filter nonlinear field oriented control system structure

In the proposed extended control system presented in

Fig. 5, two additional PI controllers appear. The controllers directly control the inverter output voltage. The inverter output voltage current is not controlled explicitly. This happens because the capacitor current is small in contrary to motor current. The motor current controllers are present in FOC structure so that the inverter output current is controlled indirectly.

The commanded inverter voltage components u1dcom

and u1qcom are transformed to stationary αβ coordinates

u1αcom and u1β

com and are treated as the inputs of the PWM module.

VI. CLOSE-LOOP OBSERVER For the speed sensorless ac drives, many estimation

method exist [19]-[21]. Some of them are based on the

motor stator circuit model. These methods are rather simple in implementation but have inseparable problem e.g. with voltage drift [19], [20]. In literature some suggestions for motor stator based estimation improvements are proposed [21]-[23]. E.g. in [23] the observer is based on the voltage model of the induction motor with combination of rotor and stator fluxes and stator current relationships [24]:

s'srrss

's kdd uψψψ τ+=+τ⋅τ , (24)

where [ ]Tsss ˆ,ˆˆ βα ψψ=ψ is stator flux vector , [ ]Trrr ˆ,ˆˆ βα ψψ=ψ , [ ]Tsss u,u βα=u , ss

's RLσ=τ is tme

constant and rmr LLk = is rotor coupling factor. To prevent the problems of the voltage drift and offset

errors, instead of pure integrators, low pass filters were used. The limitation of the estimated stator flux was tuned to the stator flux nominal value. Additionally the extra compensation part was added as presented in [23].

In this paper the observer system from [23] was changed adequately to fit the drive with LC filter requirements - the structure of [23] observer is extended, taking into account the model of the filter as proposed in [14]. For the drive with LC filter, the extra filter simulator relations were used. In the filter dynamics simulator bloc the estimated values of the motor current and voltage are calculated: si and su . These estimated variables are calculated on the base of the inverter commanded voltage u1

com and measured inverter output current i1. The simulator calculations are done in open loop according to (18)-(23) filter model:

( ) 1s1s Cˆdˆd iiu −=τ , (25) ( ) 1s11 Lˆdˆd uui −=τ , (26)

where: [ ]T111 i,i βα=i , [ ]T111 i,iˆ βα=i , [ ]Tsss i,iˆ βα=i ,

[ ]T111 u,u βα=u , [ ]Tsss u,uˆ βα=u .

The variable su is used in control process in Fig. 5. The other rotor flux and stator flux observer equations

are computed as follows: ( ) ( )11abs

'srrss ˆkˆˆkˆdˆd iiuψψψ −−+τ+−=τ , (27)

( ) rsssr kˆLˆˆ iψψ σ−= , (28)

where ⎥⎦

⎤⎢⎣

⎡ −=

AB

BAAB kk

kkk is observer gains matrix.

The rotor flux magnitude and angle position are: 2r

2rr ˆˆˆ βα ψ+ψ=ψ , (29)

( )ββψ ψψ=ρ rrr ˆˆtgarcˆ , (30) The estimated current si , appearing in (25), is:

( ) ( )srrss Lˆkˆˆ σ−= ψψi , (31) Rotor flux pulsation is the next:

τρ=ω ψψ dˆdˆ rr , (32) Rotor slip is obtained from the next expression:

( ) 2rsrsr2 ˆiˆiˆˆ ψαββα ψ−ψ=ω , (33)

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Rotor mechanical speed is the difference between the rotor flux pulsation and slip frequencies:

2ψrr ωωω −= , (34) The observer structure is presented in Fig. 6.

Fig. 6. Close-loop observer structure

The tests of the closed-loop flux observer have proved high robustness of the ASD with observer based on the stator model [25]. The observer is highly insensitive against stator resistance and other motor parameters mismatch. This significantly extends the stable operating region even without precise parameter tuning.

VII. RESULTS The proposed speed sensorless system was verified by

simulations and experiments. The data of 1.5 kW squirrel cage induction motor used in simulation and experimental tests are presented in Table II.

For simulation purposes, a dedicated program in C language was prepared. In the test bench a control system board with DSP processor and FPGA circuits were used. The electronic board was connected to the PC for communications and data acquisition purposes.

The action of the sensorless control system with LC filter is presented in Fig. 7.

TABLE II

INDUCTION MOTOR PARAMETERS Parameter Value Description

Pn 1.5 kW nominal power Un 400 V nominal phase to phase voltage In 3.5 A nominal current nn 1410 rpm nominal mechanical speed p 2 number of poles pairs fn 50 Hz nominal supply voltage frequency J 0.0028 kg·m2 inertia

Rs 4.75 Ω stator resistance Rr 4.76 Ω rotor resistance Ls 320.1 mH stator inductance (leakage + mutual) Lr 320.1 mH stator inductance (leakage + mutual) Lm 303.2 mH mutual inductance

In Fig. 8 and Fig. 9 experimental results for speed

sensorless control are presented. Fig. 8 shows results of the four commanded speed

changes. The measured speed is not used in the control process. The controllers’ gains were tuned for fast response. The small oscillations of the rotor flux are results of high dynamics of the system. In transients the controllers work in saturation region so the decoupling structure is disturbed.

Simultaneous changes of the motor speed and rotor flux are presented in Fig. 9. The flux changes have no influence on torque and speed control. The speed sensorless system works properly even in the low speed region.

More detailed waveforms for speed change are presented in Fig. 10. In Fig 10 the internal control signals are presented including the control variables v1 and v2.

It is noticeable that the proposed speed sensorless control structure works properly with filter. The obtained system is also robust because works properly in nearly whole speed range even if filter is eliminated from the drive. The drive has very similar transients in case pf work with filter and without filter as well. Example of the speed transients comparison for the both cases is presented in Fig. 11.

Fig. 7. Simulation results for sensorless control system.

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0.23 0.45 0.68 0.90 1.13[s] Start time = 0 End time = 1.12500004377216 0.037500001459072[s/div]

Time[s] 00

0.5

1.0

1.5

2.0

C6

[p.u.]0

0.5

1.0

1.5

2.0

C5

[p.u.]-2.0

-1.0

0

1.0

2.0

C4

[p.u.]-1.0

-0.5

0

0.5

1.0

C3

[p.u.]0

0.3

0.6

0.9

C2

[p.u.]0

0.3

0.6

0.9

C1

[p.u.]

Fig. 8. Experimental results – step changes of the motor commanded speed (C1-ωr, C2- rω , C3-te

com, C4- et , C5- rψ , C6-|is|)

0.23 0.45 0.68 0.90 1.13[s] Start time = 0 End time = 1.12500004377216 0.037500001459072[s/div]

Time[s] 00

1.0

2.0

C6

[p.u.]0

0.5

1.0

1.5

2.0

C5

[p.u.]-2.0

-1.0

0

1.0

2.0

C4

[p.u.]-2.0

-1.0

0

1.0

2.0

C3

[p.u.]0

0.3

0.6

0.9

C2

[p.u.]0

0.3

0.6

0.9

C1

[p.u.]

Fig. 9. Experimental results – motor speed and rotor flux changes (C1-ωr, C2- rω , C3-te

com, C4- et , C5- rdψ , C6- comrdψ ).

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-1.0

-0.5

0

0.5

1.0

C6

[p.u.]0

0.5

1.0

1.5

2.0

C5

[p.u.]0

0.5

1.0

1.5

2.0

C4

[p.u.]0

1.0

2.0

C3

[p.u.]0

0.3

0.6

0.9

C2

[p.u.]0

0.3

0.6

0.9

C1

[p.u.]

225 450 675 900 1125[ms] Start time = 0 End time = 1125 37.5[ms/div]

Time[ms] 0-2.0

-1.0

0

1.0

2.0

C6

[p.u.]

-0.30

0

0.30

C5

[p.u.]0

0.3

0.6

0.9

C4

[p.u.]0

0.3

0.6

0.9

C3

[p.u.]-1.0

-0.5

0

0.5

1.0

C2

[p.u.]-1.0

-0.5

0

0.5

1.0

C1

[p.u.]

Fig. 10. Experimental results – motor speed change

(C1-ωr, C2- rω , C3-tecom, C4- et , C5- rdψ , C6- αψ rˆ , C7- com

su α , C8- αsu , C9- comsdi , C10- sdi , C11- v1, C12- v2,).

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Fig. 11. Robustness of the proposed system - speed transients comparison in the experiments for drive with filter and without filter – the control and estimation structure and controller gains were the same.

VIII. CONCLUSIONS When the LC filter is used in speed sensorless control

system, the control structure and observer structure should be changed. The electrical drives without such changes work with limited dynamics, or sometimes do not work in closed loop control.

To assure low cost and reliability of the system, the number of sensors could not be increased. Some additional variables which appear in the control should be calculated. It is possible when the structure of the calculation system will contain LC filter equations.

In the proposed control system, the number of sensors was limited to two current sensors for inverter output current measurement and for one voltage sensors for dc link voltage measurement.

The correctness of the proposed control system was verified by simulations and by experiments.

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