Estimation Techniques For Sensor Less Speed Control Of Im

IEEE ISIE 2006, July 9-12, 2006, Montreal, Quebec, Canada

Estimation Techniques for Sensorless Speed Control of Induction Motor Drive Pavel Brandstetter, Martin Kuchar, David Vinklarek

VSB-Technical University of Ostrava, Department of Power Electronics and Electrical Drives, Czech Republic pavel.brandstetterWvsb.cz Abstract-Rotor position and speed sensors are required for vector control of induction motor. These sensors are sources of trouble, mainly in hostile environments, and their application reduces the drive robustness. The cost of the sensors is not also negligible. All the reasons lead to development of different sensorless methods for rotor position and mechanical speed estimation in electrical drives. The paper deals with the speed estimators for applications in sensorless induction motor drive with vector control, which are based on application of Kalman filter and artificial neural network.. The development and DSP implementation of the speed estimators for applications in sensorless drives with induction motor are described in the paper.

INTRODUCTION

I.

In modern control techniques for induction motor with high dynamic requirements the speed transducer such as tachogenerator, resolver or mainly digital shaft position encoder are used to obtain speed information. These sensors are sources of trouble, mainly in hostile environments. The main reasons for the development of sensorless drives are: 0 reduction of hardware complexity and cost 0 increased mechanical robustness higher reliability working in hostile environments decreased maintenance requirements Removing rotor position sensors or mechanical speed sensors from a control structure of electrical drive leads to socalled sensorless electrical drive, which naturally requires another sensors for the monitoring of stator currents and voltages (fig. 1).

C--0-i.E-R--T,E-R-

k,

CONVERTER

CONV ER'l'R

=0

a

1-

I

I.-

:= %--

I I :,:,,:z.x .,

SYSTEM

_ =U.9_

X ,_

B u _

I>

EMMMMMMM=

Fig. 1. Application of estimation techniques for sensorless electrical drive

1-4244-0497-5/06/$20.00 C 2006 IEEE

The estimation methods can be classified into conventional, based on mathematical model of the electrical motor, or based on artificial inteligence (Al). Conventional types of speed estimators can be classified into open loop estimators, MRAS and observers (Kalman, Luenberger). In general open loop speed estimators use monitored stator voltages and stator currents. These estimators have accuracy problems, mainly at low speeds and they are dependent on knowledge of motor parameters. For non-linear systems (in this case induction motor) the extended Kalman filter has to be used [6]. Fuzzy logic, artificial neural networks, genetic algorithms and their combinations are considered in the field of artificial intelligence. The speed estimator based on the artificial neural network does not depend on a knowledge of electrical motor parameters. It is further shown that accurate estimates can be obtained in situation of varying load without the need for explicit load monitoring [1]. II. CONTROL STRUCTURE OF INDUCTION MOTOR DRIVE

Control structure of vector controlled drive is shown in fig.2. Measured stator currents (Block of Current Transducers BCT) are transformed from stationary reference frame [oc, ] into reference frame oriented on the rotor flux space vector [x, y], that is done in Block of Vector Shift 2 (BVS2). Output of this block are real stator currents iS,, iy, which are feedback signals to the current controllers Ri, Ri,y The decoupling rotation voltage components uxe, uye, which are evaluated in Block of Decoupling Circuit (BD), are added to the outputs of mentioned controllers. The inverse shift from reference frame oriented on the rotor flux linkage space vector to stationary reference frame is done in Block of Vector Shift 1 (BVS1). The signals from this block are inputs to the Block of ANNbased Vector Pulse-Width Modulator (ANN-PWM) (referred in [5]). Last mentioned block ensures right switching of six IGBT in Frequency Converter (FC). Controller Ru processes a control error between computed and reference value of stator voltage space vector modulus. The real value of this modulus is computed from values u,* uS *in block of Vector Analyzer (VA). It is necessary to determine the oriented angle y, which is used in BVS1, BVS2. The angle is evaluated in the Block of Evaluation of Oriented Quantities (BEOQ). During training stage of ANN needful rotor position (angle c) is obtained by means of Block of Estimation of Rotor Position (BERP).

154

Then the position is determined by integration of estimated rotor speed. BEOQ is based on so-called current model (referred in [2]). Ru

The state covariance matrix P is obtained in prediction part of the algorithm. After fulfilment actual measurement it is then corrected. The covariance matrices Q, R is necessary experimentally set up. The model of the Kalman filter is in fig. 3. One of the parts of Kalman filter is a single step extrapolator based on system model. This extrapolator predicts estimation of the state variable vector x. The measurement model then transforms the prediction of estimation to the prediction of measurement. This prediction is compared with real measured values. The obtained difference is then used to correct the actual prediction of estimation.

Ris,

Ri

sin y

cos y im

(D(k+l1,Itk/ k, u k/ k) S~lm siny

-

Fig. 3. Model of the Kalman filter

COS y

i,.

i3p

Fig. 2. Control structure of sensorless vector controlled induction motor drive

Controller RQm processes a control error between estimated Qm and reference value Qm* of mechanical speed. III. APPLICATION OF KALMAN FILTER FOR SPEED ESTIMATION

A closed loop estimator is called an observer. A representation of the observed plant classifies the observer. The deterministic observer comprises the deterministic plant model while the stochastic type comprises other plant model representations. The Kalman filter, which is a special class of a Luenberger observer (deterministic type), derived to meet a particular optimality stochastic condition. The Kalman filter provides an automatic design procedure thus relieving many of the design decision associated with the explicit design of the Luenberger observer [6]. The Kalman filter has two forms - basic and extended. The extended Kalman filter (EKF) can be used for non-linear systems. This means that model of the plant is extended by extra variables, in our case by mechanical speed. The Kalman filter allows to obtain no measured state variables (rotor speed oim, components of rotor flux vector 4YRa, YVRP) with usage measured state variables (components of stator current space vector isw, isp) and as well statistics of noise and measurements (covariance matrix of state vector P, covariance matrix of system noise vector Q, covariance matrix of measurement noise vector R).

The notation of matrices is following: matrix A-state matrix, matrix B-matrix of inputs, matrix C-matrix od outputs. Matrix C defines measurement's relations to the state variable. The mathematical model of induction motor is very complicated. There are many of different models described in literature. It is advantageous to use the model, which is expressed in stationary reference frame [oc, f] because the overall quantum of equations is reduced. The general model of the induction motor can be written as:

155

dx

(1)

Ax + Bu

dt

Measurement model provides prediction of measurement: y

=

(2)

Cx

The previous system of equations must be discretized with aspect of implementation on digital signal processor (DSP). Generally, these equations can be rewritten as: x(k + 1)

=

Adx(k) + Bdu(k)

(3)

y(k) = Cx(k) (4) The symbol k denotes k-th sampling instant. Then the discretized system matrix Ad, discretized input matrix Bd and discretized output matrix Cd will be: Ad

=

exp[AT]

I + AT

+

(AT)2 2

(5)

Bd |[exp(AT)]. Bdcr

BT

0

Cd

ABT)

+

By considering the measurement noise vector w(k) (with its covariance matrix R) the equation will be: (15) y(k) = Cx(k) + w(k)

(6)

2

(7)

=C

Now, the following steps have to be perform in order to obtain optimal estimation ( x is estimated value of state vector, x is predicted value of state vector):

The complete motor model with extra equation for rotor speed (extra variable for EKF) can be written as: (8) LhRR

Lh

LRKL

LRKL

KR

2 ~~T

1-RT KL

KR -T

0

Lh -

LRKL

KL Lh

Ad

0

OMT

TR Lh

0

P(k + 1)

Dk+1

Bd

O'

KL

1

(9)

° °

0

K(k+1)

[iSa (k)

ls/(k) u(k)

=

X4oRa(k)

KR

=

Rs

Lh 2

RR

LR

Rf8(k)

S (k)

uS/i (k)]

KL

Ls

2

Lh =

LR

m(k) ]

(18)

TR

LR RR

Adx(k) + Bdu(k) + v(k)

=

(19)

(k + 1)

hT(k+1)+R]

~~~r O

8 x]~

a-[Cd

0

0

0+Li

oo

o

1

01 o

(20)

(21)

Correction of actual prediction of estimation:

(12)

x(k + 1)

=

x(k + 1) + K(k + 1) [y(k + 1)

-(k+1)

(13)

Cdx(k + 1)

[iSa

-

y(k + 1)]

(22)

]

(23) (24)

iS,B ]

y(k + 1) [=Sa

Correction of the covariance matrix of prediction: P(k + 1)

=

P(k + 1)

-

K(k + 1) h(k + 1) P(k + 1)

(25)

The oriented quantities siny and cosy, which determine a position of rotor flux space vector YR are obtained from following equations: ,

The Kalman filter algorithm is very time extended. With reference to practical implementation of the Kalman filter algorithm on DSP is necessary to reduce the discretisation of matrixes Ad and Bd by reason of time heftiness of the algorithm. The second order of term is neglected. The system model with respect of system noise vector v(k) (with its covariance matrix Q) is obtained from the equation: =

=

(11)

Mathematical symbols: isa is components of stator current space vector iss WRu, WR3 components of rotor flux space vector WR Lh magnetizing inductance self stator and rotor inductance Ls, LR stator and rotor phase resistance RS, RR rotor time constant TR COr angular speed of rotor

x(k + 1)

Ad i(k) + Bd u(k)

X=Xk

P(k+1) hT (k+1) [h(k+1) P(k+1)

where

(10)

0

=

h(k + 1) =

(17)

x

Computation of the Kalman filter gain:

_O O_ 0

x(k + 1 k)

=

k

O

I 0 0 0 0 0

Cd

+Q

P(k) .

a^ ax x xk

0 Increment of time counter:

o

o I

T =

(16)

Ad i(k) + Bd u(k)

where

0

x(k)

=

0

TR

I

=

0 The covariance matrix of prediction:

O

T

COMT

T

TR

-x(k + 1)

0

2 LRKL

T

1-

TR

LhRR LRKT

mT

0 Prediction of state vector:

0

6MT

(14)

156

sin

y

'8 Rp

(26)

|V Rf|

Cosy

Ro

=6

(27)

IV. APPLICATION OF ARTIFICIAL NEURAL NETWORK FOR SPEED

performed in one machine cycle. For testing of the estimation methods there was used electrical drive with induction motor First it is necessary to design right structure of the artificial 2,7kW. Entire control system is shown in fig. 5. The core of the system is mentioned DSP ([tC), which neural network (ANN) and it is also important to determine utilizes additional information from other peripherals - Analog such inputs to ANN, which are available in structure of vector to Digital Digital to analog converter (A/D, D/A), Block of control and from which is able to estimate a rotor speed of IM. Switching and Pulses (BSP), Block of Evaluation of Rotor Position It does not exist a recommended method for determination of (BERP). The BSP is needful for right communication with ANN structure, so the final ANN was designed by means of IGBT frequency converter (FC). Block of Voltage a nd Current trial and error. The main goal was to find the simplest neural Transducers (BVCT) is important to get signals of FC voltage network with good accuracy of speed estimation. This is the and stator currents. Block of A/D converter includes fourkey for industry use of ANN's. channel, 12-bit A/D converter. Next part of the control system It has been designed three layer feedforward 8-22-1 ANN is a board of D/A converter for representation of interesting (fig.4) with following inputs: u,,*(k), u,,*(k-1), u,ji*(k), u,jj*(k- quantities. Communication between DSP and PC is ensured by 1), i4a(k), i4a(k-k), if(k), ifl(k-1). The activation functions in serial interface. hidden layer are tansigmoids and output neuron has linear activation function. The network has been implemented in vector control of induction motor and entire drive was simulated in program Matlab and then it has been implemented in real drive controlled by DSP powered by Texas Instruments. Training stage is performed in Matlab using LevenbergMarquardt algorithm. For implementation of neural speed estimator onto real electrical drive it is necessary to obtain such training data, which determine the desired behavior of artificial neural network. The training data set was obtained from real vector Fig. 5. DSP control system controlled induction motor drive. For this purpose 90 000 samples were measured for each of the input and output For implementation of neural speed estimator onto real signals. During training stage it was used 30 000 samples only electrical drive there is necessary to obtain such training data, and it was achieved an error 5 x 10-3 . Another data was used which determine the desired behaviour of artificial neural for testing phase. network. Data acquisition system (DAQ) was developed for fast transfer of training data from DSP system to PC. Data acquisition system is based on CY7C64603 by Cypress Semiconductor's. It is possible to compare computing demands of each types of speed estimators. It is shown in table 1. ESTIMATION

TABLE I

EXECUTION TIMES OF EACH ALGORITHM

Algorithm

Execution time

TMS320C40 [pts]

Vector control of induction motor

Extended Kalman filter ANN speed estimator and rotor position evaluation

Fig. 4. Artificial neural network for speed estimation (8-22-1)

60 370 205

V. DSP IMPLEMENTATION

VI. EXPERIMENTAL RESULTS

The sensorless vector controlled induction motor drive structure including designed speed estimators has been implemented onto digital signal processor TMS320C40, which provides high computing power for presented control. The processor works with 32-bit data in floating-point arithmetic Instruction cycle interval is 50 ns, while most instructions are

In the chapter it will be presented important quantities of the electrical drive with induction motor 2,7kW. Experimental results are obtained when current and speed loops operate using estimated speed and position. For comparison estimated and real speed is used the real value of mechanical speed which is obtained from incremental encoder.

157

Speed estimator with Kalmanfilter The first testing regime is run-up to 400 rpm and reversation to -400 rpm. Experimental results are shown in fig. 6, 7, 8.

A.

1 5.OOV

+-O.O0S

2 5.00V

20O-s

i 5.OOV 2 5.OOV

SnglfI STOP

t4.

27

Fig. 6. Real and estimated mechanical speed, chl Q. = f(t), ch2: Qm_est= f(t), mQ = 60 rpmNV 55.OOV

+-O.05

2 5.OOV

L 5.OOV

tQ1

.

5.OOV I _

2

5.00V

+-O.05

200 -O'

2OOs

Snglf1 STOP

,-

4_.2

2 5.OOV

-O.0Os

20O/

Sngqlf3 STOP

+,2

Fig. 11. Reference and real flux producing components of stator current, chl: isx = f(t), ch2: isx= f(t), mi= 1A/V

Fig. 7. Reference and real torque producing components of stator current, chI: isy = f(t), ch2: isy = f(t), mi lA /V 1

+-O.0Os

Fig. 10. Reference and real torque producing components of stator current, chl: isy = f(t), ch2: isy = f(t), mi = 1A/V Sng9lfi STOP

200S/

.L Stv S

shown in fig. 9, 10, 11. The third testing regime was aimed on dynamic response to load pulse. Experimental results are shown in fig. 12, 13.

j

Sng nlF3 STOI

5.OOV

2 5. OOv

+-O.00s

I ~~~ ~~~~~~ ~~~ ~~~~~~~~~~~~~~~ ~~~

20/ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Snglf3 STOP

,-

1-1

%...

4_.2

2 .1

Fig. 12. Real and estimated mechanical speed, chl Qm = f(t), ch2: Qm_est= f(t), mQ = 60 rpm/V

Fig. 8. Reference and real flux producing components of stator current, chl: isx*= f(t), ch2: isx= f(t), mi lA/V 5.OOV

2

5.OOV

~.

....

~~~~~~~~~~~........

Snglfj

2O

-O.

~

...

...

...

..

j

STOF

2.OOV

2 2.OOV

-0.0Os

2OO'

Snglfj STOP

..

.........

74i 1

...

Fig 9. Rea anh )

ch: f: Q.

esiae ,-,s

=

mehnia

f

speed,

m: =:0rm :)

2

Fig. 13. Reference and real torque producing components of stator current, chl: isy = f(t), ch2: isy = f(t), mi = 1A/V

The second regime was same as previous but all was done with load. Experimental results are

measurement

158

B. Speed estimator with artificial neural network The first testing regime is run-up to 300 rpm and reversation to -300 rpm. The real value of mechanical speed is obtained from incremental encoder. Experimental results are shown in fig. 14, 15. -so OT

S nql+ T

1 OOT/

drive with load, but ANN speed estimator works correctly even in such situations. It is clear that the network shows its basic ability - generalization. The range of estimated mechanical speed is not anyway limited and it depends on application requirements and corresponding training data.

STnP alu!

5E.OOV 2 5.OOV

-

° 2 5 .-V

0.0

1 00/

Y

100S/

Snglf3 STOP

A

Fig. 14. Real and estimated mechanical speed, chl: Q. = f(t), ch2: Qm_est= f(t), mQ = 60 rpmNV 5.- v

-8O.OS

Fig. 16. Real and estimated mechanical speed,

chl: Q. = f(t), ch2: Qm_est= f(t), mQ = 60 rpmV

SEn1f3 STOP . .

i

~~~~~~~~~~I

5 .uV

-°0.u0 2 5.OOV

1 00/

En91f3 STOPl~~~~~

+11

h

Fig. 15. Real torque and flux producing components of stator current, chl: isy= f(t), ch2: isx= f(t), mi= lA/V

Fig. 17. Real torque and flux producing components of stator current, chl: isy= f(t), ch2: isx= f(t), mi = IAV

The second regime was same as previous but all measurements was done with load. Experimental results are shown in fig. 16, 17.

The sensorless iduction motor drive with the presented mechanical speed estimators gives good dynamic responses and the estimation of the mechanical speed is perfect in steady state and also in transient state. The lowest boundary of fine speed estimation is about 30 rpm.

A

VII. CONCLUSION

ACKNOWLEDGMENT The estimation techniques for sensorless induction motor drive with vector control was presented in the paper. The speed In the paper there are the results of the project 102/05/2080 estimators are based on application of Kalman filter and which was supported by Grant Agency of Czech Republic. feedforward neural network. REFERENCES The Kalman filter is sophisticated algorithm that is suitable for estimation of mechanical speed and rotor flux components. [1] P. Vas, Artificial-intelligence-based electrical machines and drives. Oxford science publication, 1999, ISBN 0 19 859397 X. The main difficulties of Kalman filter are specifying of right Brandstetter, A.C. control drives - modern control methods. VsBcovariance matrices because for many cases the required [2] P.Technical university of Ostrava, 1999, ISBN 80-7078-668-X. statistical information is not available. Of course considerable [3] M. Norgaard, Neural networks for modelling and control of dynamic systems. Springer-Verlag London, 2000, ISBN 1-85233-227-1. design effort is required too. All these reasons lead to a type of Leonhard, Control of electrical drives. Springer - Verlag Berlin, estimator which does not rely on a knowledge of machine [4] W. 1997, ISBN 3-540-59380-2. parameters, which is not computationally demanding, which [5] P. Brandstetter, M. Kuchar, P. Palacky, "Vector Control of Induction Motor Drive using ANN-based VPWM\", Confrence proceedings, 10th requires little design effort and which can produce accurate European Conference on Power Electronics and Applications, Toulouse, estimation of the given system. France, 2003, ISBN 90-75815-07-7. The speed estimator based on the artificial neural network [6] R. G. Brown, P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering. John Wiley & Sons, Inc., Second Ed., 1992. does not depend on a knowledge of electrical motor Fedor, D. Perdukova, J. Timko, "Study of Controlled Structure parameters. During training stage the neural network does not [7] P.Properties with Reference Model", Acta Technica, CSA V 46, 2001, ISSN have any training patterns, which represent a behavior of the 0001-7043.

159