Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

A High Performance Decoupling Control Scheme for Induction Motor with Modified Adaptive Neural Rotor Flux Estimator Manoj Datta1

Mohammed Golam Sarwer1 Md. Abdur Rafiq 1

B. C. Ghosh1

1

Department of Electrical & Electronic Engineering, Khulna University of Engineering & Technology, Khulna-920300Bangladesh. Tel: +880-41-769271-333, Fax: +880-41--774403, E-mail:[email protected].

presence of speed and load torque variations, a rather radical idea that intensifies coupling has been proposed.

Abstract In the high performance operation of a vector controlled induction motor, current and flux control in decoupled control is a very important problem. However, the conventional decoupling scheme does not perform well when there is sudden loading or change in speed. In the case of conventional decoupling control scheme the physical, the physical operation of the induction motor is difficult to understand from the block diagram. This is because, in the conventional block diagram, the dimension of the summing point has no physical meaning. Here, a new state equation based decoupling controller that is combination of feed forward coupling compensation and PI type decoupling is proposed. In this proposed controller, all branches of the summing point have voltage dimension. A great advantage of this controller is the robustness to the motor load torque and speed variations. Hence, the proposed scheme looks suitable to the practical applications. Through simulation results, it is shown that the proposed controller achieves the desired performance.

Keywords: Decoupled Control, Vector Control.

Induction

Motor,

State

Equation,

Introduction Recently, induction motors are suitable for high performance operation due to low voltage drop in the leakage inductances. In the high performance applications of induction motor with the field orientation control, the coupling problem between q axis and d axis current and flux causes a serious problem for fast response. In most field orientation control of an induction motor drive system, the overall performance is directly related to the performance of the current control. Therefore, it is very important to decouple the coupling term for better performance. Recently, various decoupling methods have been proposed, for example, hysteresis regulator [3], stationary frame PI regulator [5], synchronous frame PI regulator [5], multivariable state feedback regulator [2], and internal model control regulator [4]. Since the conventional decoupling controls show poor performances in the

In this paper, two additional PI controllers [6] are employed with the new state equation based decoupling controller [7] to compensate the coupling terms. This new decoupling controller helps to understand the physical operation of the motor and all the branches of the summing point have voltage dimension which is absent in the conventional decoupling controller. More over rotor flux estimation with the help of modified adaptive neural integrator and rotor flux angle estimation by load angle calculation [8] under perfect field orientation is employed. Through simulation, the performances of the proposed controller are observed and found satisfactory.

Conventional Induction Motor Block model The dynamics of induction motor in synchronously rotating d-q frame [1] for cage rotor is given such that

V ds   R s + PL s V   ωe Ls  qs  =   0   PL m    ( ω 0    e − ω r ) Lm PLm ωe Lm R r + PLr (ω e − ω r ) Lr

− ω e Ls Rs + PLs − (ω e − ω r ) Lm PLm − ω e Lm

  PL m  − (ω e − ω r ) Lr   R r + PL r 

*

ids    iqs  idr    iqr 

(1)

Here, the meanings of the variables are as follows.

Vds , Vqs : d axis and q axis stator voltage (V); ids , iqs : d axis and q axis stator current (A); idr , iqr : d axis and q axis rotor current (A); Rs , Rr : stator and rotor resistances (O); Ls = L1 + Lm , Lr = L2 + Lm ; Ls , Lr : stator and rotor inductances (H); Lm : mutual inductance (H); L1 , L2 : stator and rotor leakage inductance; ω e : electrical angular speed (rad/s); ωr : rotor angular speed (rad/s); ωsl : slip speed (ωe − ωr ) ; P : operator d / dt ; The output equation and mechanical state equation are given as follows, respectively

Te = pLm ( iqs idr − i dsi qr )

(2)

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005 Pω r = ( p(Te − Tl ) − B ω r ) / J

(3)

Here, the meanings of the variables are as follows. Te : electrical torque (Nm); Tl : load torque(Nm); J : moment of inertia (kg-m2); B : damping coefficient (Nms/rad); p : number of pair of poles.

 i1  P  = i2 

1 L I  1  0 

I − PLm  I

 0    R I  − s 1    0 I  L2 

I J − ω e Lm  I  J

0  L1J − ωe   Rr I   0

J  0 + ωr  J   Lm J

0  L2 J 

0   i1  V1    +  Lr J   i 2  V 2   (5)

Equation (1) can be simplified and rewritten as

 i1  1   Ls Rs I P  =  −  i2  A  − Lm Rs I

− Lm R r I  J − ωe A  Ls R r I  0

 − L2 J − L L J   i1   Lr I m r  + ωr  m +    L L J L s Lr J   i 2   − Lm I  m s

0 J 

− Lm I  V1   Ls I  V2   (4)

i ds  idr  1 0  1 − 1 where I =   , J = 1 0  , i1 = i  , i 2 = i  , 0 1      qs   qr  V V  ds   dr  0 V1 =   , V 2 =   =   , A = L1 L2 + ( L1 + L2 ) Lm . V qs   Vqr  0

V1    0

 Lr I  − L m I

− Lm I  +  Ls I  +

1 As

ωr

1 Js

Te

+ p B

-

- +

In many cases of the vector control, the rotor flux λ 2 ( = [λ dr λ qr ] t ) is used as the state variable. When the relation

the rotor flux and the current (λ 2 = Lm i1 + L r i 2 ) is used, the state variable [ i1 λ2 ]t is expressed as

between

 i1   I λ  = L I  2  m i1    i2 

- -  Ls Rs I − Lm Rr I     − Lm Rs I Ls Rr I  J 0  ωe A   0 J   − L2 J ωr  m  Lm Ls J

In equation (5) the terms bound by {} are related to the voltage. Compared to the conventional state equation (4), the operator P remains on the right hand side of equation (5). Therefore, it is called “the extended state equation.”

− Lm Lr J   L s Lr J 

pLm (iqsidr − idsiqr )

Tl

Figure 1. Block diagram of induction motor using conventional state equation From equations (2), (3), and (4), a matrix block diagram of the induction motor using conventional state equation can be obtained as shown in Fig. 1. In this block diagram, no branches of the summing point have voltage dimension, and therefore the physical meaning of the block diagram cannot be easily understood. Hence, this block diagram is not helpful to understand the physical operation of the machine.

New State Equation A new state equation in which all branches of summing point having the dimension of voltage is proposed. To obtain such equation, the operator P concerning the mutual inductance Lm is remained on the right hand side. The state equation (4) can be written as

0  i 1  Lr I  i 2 

(6)

Contrarily, the state variable [i1i 2 ]t is expressed as

i1   LI i  = − m I  2   Lr

0  i 1  1  I Lr λ2 

(7)

From equations (5), (6), and (7), a matrix block diagram of the induction motor using extended state equation can be obtained as shown in Fig. 2. Here the equations (2) and (3) are omitted. In this block diagram, all branches of the summing point have the dimension of voltage. Thus, it is easy to understand the physical operation of the machine. V1    0

+ +

- - - -

1 L I  1  0  

 0  1 1 s I L2 

 I  Lm I

[A]

Rs I   0

[B]

I pLm  I

[C ]

[D] [E ]

L J ωe  1  0

0   Rr I 

 I  Lm − L I  r

i1    i2 

0   L2 J 

J ω eL m  J  0 ωr  Lm J

I  I

 i1    λ 2  0  1  I L r 

0   Lr I 

J  J 0   Lr J 

Figure 2. Block diagram of induction motor using extended state equation From Fig. 2 the extended state equation can be written as:

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

 1 I  i1   L1 P  =   λ 2   Lm I  L1 L I − PLm  2  L2 I

 0  1  Lr  Lr I  L2 

  R s Lr I −   − R r Lm I 

0  Rr I 

Lm J  0   i1  0 + ωr     Lr J  0 L  r J  λ2 

I  AJ − ωe  I  0

V   +  1  V2  

di σ Ls ds = − Rs ids + ω eσ Ls iqs + Vds dt

(9)

L σ Ls = −R s i qs + ω eσLs i qs − ω e m λdr + Vds dt Lr

(1 − L2m / Ls Lr ) ; With the rotor flux oriented control scheme, it is obtain in the steady state that λdr = Lm i ds . Therefore, the current dynamic equations in the steady state are given by di σ Ls ds = −R s i ds + ω eσLs i qs + Vds dt

dt

* V ds +

-

-

+

PI 2

ωeσLs Rs + sσL s ω eL s Rs + sσL s

+

PI 4 ?

-

PI 3 * V qs

g qq =

PI1 1 + ( PI12 + PI 3ωeσ Ls ) Rs + σLs s ( R s + σ Ls s ) 2 ω e Ls ( Rs + σLs s) ω e Ls ( R s + σLs s)

+ PI 2

2

2

− PI 3

1 , R s + σLs s

1 . R s + σ Ls s

In order to nullify g dq and g qd , PI2 , PI3 need to be chosen such that

PI 2 = PI3 =

ωe Ls PI1 Rs + σLs s

(14)

ωeσLs PI1 Rs + σLs s

(15)

* * The command voltages Vds and Vqs are calculated by

(12)

Vds +

1 1 ) 2 + 2PI 1 , R s + σLs s R s + σLs s

(11)

= − R s iqs + ω eσ Ls ids + Vds

PI1 ?

1 )2 R s + σ Ls s

PI 1 1 , + ( PI12 + PI 2ω eσLs ) R s + σ Ls s ( R s + σ Ls s ) 2

g qd = PI 1

λdr , λqr : d axis and q axis rotor flux linkages (H); λr : rotor flux linkage (H); σ : total leakage coefficient

*

(13)

g dd =

(10)

Here, the meanings of the variables are as follows.

di qs

+ ( PI 2 PI 3 + PI12 )(

g dq = −PI 1

di qs

iqs

g qd i *ds    g qq i *qs 

where, ∆ = 1 + ω e Ls (ω eσ Ls + σPI 2 + PI 3 )(

The rotor flux oriented control is achieved by letting λqr = 0 and λdr = λr = constant. Then the current dynamics equations (1) yield

i*ds +

i ds  1  g dd i  =  g  qs  ∆  dq

(8)

Proposed Decoupling Controller Using PI Type Decoupling and Extended State Equation

σ Ls

decoupling controller uses two additional PI controllers for eliminating the coupling terms. Note from Fig. 3. that PI 1, PI4 are the normal d-q axis PI controllers, respectively, while PI2, PI3 are the additional PI controllers for decoupling. It is assumed that PI1 and PI4 are designed identically. Now it is obtained from Fig. 3. that

ids 1 ? Rs + sσL s

* Vds = ( K p1 +

* Vqs = ( K p1 +

K i1 * )(i ds − i ds ) s

(16)

K i1 * )(i qs − i qs ) s

(17)

?

ωeσLs

And,

the

compensation

voltages

Vdsc

and

Vqsc

for

decoupling are calculated by Vdsc Vqsc

-0.4 + + + V qs

ωeLs

* V ds = ( K p1 +

1 ? Rs + sσL s i qs

Induction Motor

Figure 3. The equivalent block diagram of the proposed PI controller In the high performance range, the coupling terms are dominant over Rs ids , Rs iqs . The proposed PI type

=

ω eσ Ls * V qs R s + σLs s

* V qs = ( K p1 +

=

K i1 ω eσ Ls ) (i *qs − i qs ) s R s + σLs s (18)

K i1 ω eσ Ls ) (i *ds − i ds ) s R s + σLs s

ω eσLs * V ds R s + σ Ls s

(19)

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

This PI type decoupling is not sufficient to achieve high performance decoupling control. So, another decoupling method based on the extended state equation (5) is adopted with the PI type decoupling. In the matrix block diagram of Fig. 2. , the matrices [C], [D] and [E] have vector J, which means the existence of the coupling between d-q axis. Therefore, in order to cancel this coupling matrix elements (1, 1) and (1, 2), equivalent respective elements of opposite sign are added to the output of the PI type decoupling controller. Since element (1, 1) of matrix [C] does not exist, coupling between d-q axis due to leakage inductance L1 is cancelled. Since elements (1, 1) and (1, 2) of matrix [D] do not exist, steady state coupling terms between d-q axis due to the mutual inductance Lm are cancelled [7], [8]. In Fig. 2., the matrix [B] signifies the transient state transformer coupling. Since elements (1, 1) and (1, 2) of matrix [B] do not exist, transient state transformer coupling of the stator circuit is cancelled. After canceling all the coupling terms, the matrix block diagram of the induction motor can be obtained as shown in Fig. 4.

Rotor Flux and Rotor Flux Angle Estimator Rotor Flux & Rotor Flux Angle Estimation Using Adaptive Neural Integrator: The main problem of the integration in flux estimation as used in high performance electrical drives is the presence of dc biases, which affect the accuracy of the flux estimation. In particular dc drifts are always present in the signal before it is integrated, which causes the integrator to saturate with a resulting inadmissible estimation error. Moreover, a dc bias also appears at the output of the integrator because of the initial conditions. Then it is necessary to remove the dc components of the signals both before and after they are integrated. An adaptive filter (ADALINE) as presented in [9] used as a notch filter to cut off the dc component adaptively. Fig. 6 shows the adaptive integrator with two identical neural notch filters before and after the pure integrator [9]. Ts z −1

+

e

wk V1    0

+

+ + +

+

J ω eL m  0

I I  pLm   0 0 

+ J  0

1  I  L1 -  0 -  - -

 0  1 1 s I L2 

[A]

 I   Lm I

 I  Lm − L I r 

 Rs I   0

0   Rr I 

I I  pLm   I I  [C ] L1J 0  ωe   0 L 2J   [D] J J  ωe L m   J J  [E ]  0 0  ωr   Lm J Lr J 

0 1 Lr

  I 

i1    i2 

[B]

L J ωe  1  0

0  0

i1   ∧ i2   I  Lm I − 

Lr

[I

 ∧  I  λ 2 Modified adaptive neural rotor  Flux estimator

0 1 Lr

0] [i1 ]

Figure 4. Decoupling control using extended state equation After the decoupling control using extended state equation, the block diagram of the current control of induction motor can be obtained as shown in Fig. 5. i *ds

+

PI1

* V ds +

V ds

-

* V qs

*

iqs

ω eσLs PI2 Rs + sσL s V dsc

+

PI 4

* V ds

PI3

εk

yk

-1

Neural filter 1

λ

yk εk

Neural filter 2

Figure 6. Neural filter based integrator. The learning law of the neural adaptive filter is based on the algorithm suggested in [9], in which the flux-linkage λ is obtained from back e.m.f e (k ) by an integrat ion method accomplished by programmable cascaded low-pass filter (PCLPF) implement by a hybrid neural network consisting of a recurrent neural network (RNN) and a feed-forward artificial neural network (FFANN). A simple modification is done on the algorithm proposed in [9]. In the modified algorithm presented in this paper, rotor flux is estimated from both back emf e(k ) and change of back emf ∆e (k ) . This change of back e.m.f is not taken as an input in the algorithm suggested in [9]. By considering the change of back e.m.f ∆e (k ) as an input to the RNN, the flux estimation is improved largely. An equivalent RNN is then proposed which results in the following matrix equation:

λ1(k +1)  W11 0  λ1(k)  W13 W14 λ (k +1) = W W  λ (k) +  0 e(k) +  0 ∆e(k) (20)  2   21 22  2      where λ is the rotor flux, W11 ,W 21 , W22 , W13 and W14 are the weights of the RNN, which is shown in Fig. 7. z-1

ids

z-1

W11+ W13 + +W

(a) d axis stator current

* V qs +

V qs

+ ω eL s Rs + sσL s Vqsc

1 ? Rs + sL1

-1

 i1    λ2 

0   Lr I 

+ wk

1 ? Rs + sL1

λ1( k )

14

iqs

e ∆e

W + 21 W 22 + W11W13W14W 21W 22

λ 2 (k )

(b) q axis stator current

Figure 5. Block diagram of current control. (a) d axis stator current and (b) q axis stator current.

FFANN ωr

Figure 7. Block diagram of the integration algorithm

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

After estimating rotor flux, the rotor flux angle can be calculated as:

Under perfect field orientation control, if this load angle is subtracted from stator current angle (the angle between α axis and stator current), then the rotor flux angle from load angle calculation can be obtained as:

∧

λ βr

θ flux = arctg ∧ λ ar where θ flux

(21)

θload = arctg

is the rotor flux angle from rotor flux

∧

Simulation Results

Rotor Flux Angle Estimation by Load Angle Calculation:

Simulation studies have been conducted in order to establish the functionality of the proposed control scheme. The simulated induction motor is 3φ , 220 V, 1 hp. The model parameters for this motor are Pp = 2 , Rs = 1.798

For control of the presented system, it is essential to know the value of rotor flux angle. The use of the variables “instantaneous imaginary power” and “instantaneous real power” provides a simplification of the control system. Akagi in [10] provide these new definitions of instantaneous powers in three phase circuits based on instantaneous voltage and current values

p = vα siαs + vβsi βs

(22)

q = vβsiα s − vas i βs

(23)

ohm, Rr = 0 .825 ohm, Ls = Lr = 0. 08323 henry, L1 = L2 = 0.0071 henry, and Lm = 0.07613 henry. The motor load inertia and friction coefficient have been chosen to be J = 0.02095 kg-m2, and B = 0.002 N m-sec/rad, respectively. Figures 9 and 10 shows the estimated a axis rotor flux by the proposed methods and the algorithm in [9] respectively. The proposed technique is effective to reduce the phase difference. Similar results were found for ß axis rotor flux.

Haithem Abu-Rub presented a method to find load angle from the above calculated p and q in [8]. The average values of powers P and Q are obtained by filtering p and q using a first order filter. Taking into account the differential equations of stator current and rotor fluxes, the load angle (the angle between rotor flux and stator current ) is obtained as:

Fig. 11 (a, b, c, d, e, f and g ) shows a comparative plots of speed response, d, q axis stator currents, stator current, d, q axis rotor fluxes, and rotor flux angle estimation with the algorithm [9] and proposed methods for conventional decoupling controller and proposed decoupling controller in a speed control mode. In this speed control mode, there is a change in the command speed from 0 to 250 rad/s at 2 second and from 250rad/s to 0 at 5 second and again from 0 to 250 rad/s at 9 second. From the figures, it is clearly observed that proposed decoupling controller gives more satisfactory results than that of the conventional one.

  L2  L L L  L L   R L ωr  r P−Rs r +Rr m is2+ r  r Q−1− m  s r ωeis2 Lr   Lr Lm  LsLr  Lm  Lm  Lm  δ = arctg L  R L  L2  L L  L L   ωr  r Q−1− m  s r ωei2s  − r  r P−Rs r +Rr m is2 Lr   Lm  LsLr  Lm  Lr Lm  Lm (24) * 1 i ds + Lm

PI1

* Vds

ω *r

+ - ωr

PI

V ds

+ -

* V qs

i*qs +

PI 2

PI 4

V qs

+

* V ds

PI 3

?

∧

λr

ω eL s Rs + sσL s Vqsc

? ?

?

ANN Based Flux Estimator

? ?

? ?

? ?

   L Ri  ω sl Calculation ω sl = m r∧qs   Lr λ r  

? V a-ß a I i Vb N b IM ? to Vc V ic a-b-c

?

?

θ flux

-

-

ia

Vα s d-q ? to a-ß V βs ?

Decoupled Control using extended state equation (Fig. 4)

ω eσLs Rs + sσL s V dsc * V qs

(25)

The block diagram of overall control system for induction motor is shown in fig. 8.

∧

estimation, λ ar , and λ βr are the estimated α and β axis rotor flux.

λ*r

ibs −δ ias

i ds

a-ß to iqs d-q

θ load

θ load Calculation

Figure 8. Overall decoupling control system for induction motor.

iαs

? ?

i βs

a-b-c to a-ß

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

Estimated

Actual

0.6

0.6

0.4

0.4 a axis rotor flux (WB)

a axis rotor flux (WB)

Actual

0.2 0.0 -0.2 -0.4 + -0.6 2.00

2.05 2.10 Time(s)

2.15

0.2 0.0 -0.2 -0.4 -0.6 2.00

2.20

Figure 9. a axis rotor flux estimated by proposed method.

Estimated

2.05

2.10 Time(s)

100 50 0 0

2

4

6

8

Time (s)

10

12

14

4 3 2 1 0 0

2

4

6

8

Time (s)

(a)

10

12

14

15 10

10

Stator current (A)

150

5

q axis stator current (A)

d axis stator current (A)

Speed (rad/s)

20

15

6

200

5 0 -5 0

2

(b) 7

0.8

6

0

2

4

6

Time (s)

8

10

12

14

Rotor flux angle (rad/s)

0.0

q axis rotor flux (Wb)

d axis rotor flux (Wb)

1.0 0.6

0.3

4

0.4 0.2 0.0 -0.2

Proposed

-0.4 -0.6

Conventional

-0.8 -1.0 0

2

4

6

Time (s)

(e)

6

8

Time (s)

0.9

0.6

2.20

Figure 10. a axis rotor flux estimated by algorithm in[9]

7 250

2.15

8

10

12

14

10

12

5 0 -5 -10 -15 -20 0

14

2

4

6

8

Time (s)

(c)

10

12

14

(d)

Actual ANN Based

5

Load Angle Based

4 3 2 1 0 4.6

4.8

5.0

Time (s)

(f)

5.2

5.4

(g)

Figure 11. Simulation results obtained from the conventional decoupling controller and proposed decoupling controller when speed command varies. (a) Speed response (b) d axis stator current (c) q axis stator current (d) Stator current (e) d axis rotor flux (f) q axis rotor flux. (g) ) Rotor flux angle estimation when command speed varies.

250 200

Speed (rad/s)

Load torque (Nm)

12 10 8 6 4 2 0 0

2

4

Time (s)

6

(a)

8

10

150 100 50 0 0

2

4

Time (s)

6

(b)

8

Time (s) (g)

6

10

5 4 3

Proposed

2

Conventional

1 0 0

2

4

Time (s)

6

(c)

8

10

18 16

q axis stator current (A)

Time (s) (f)

300

(e)

14

d axis stator current (A)

16

14 12 10 8 6 4 2 0 0

2

4

Time (s)

6

(d)

8

10

Proceedings of the International Conference on Intelligent Systems 2005 (ICIS 2005) Kuala Lumpur, 1 – 3 December 2005

20

0.9

1.0

-5 -10 -15 -20 0

2

4

Time (s)

6

(e)

8

10

0.4 0.2 0.0

-0.2

0.3

Proposed

-0.4 -0.6

0.0 0

2

Time (s)

4

6

8

(f)

10

Conventional

-0.8 -1.0 0

2

4

6

Time (s)

8

(g)

10

12

14

Rotor flux angle (rad/s)

0

6

0.6 0.6

q axis rotor flux (Wb)

5

d axis rotor flux (Wb)

10

Stator current (A)

7

0.8

15

5 4 3 2 1 0 2.0

2.2

2.4

2.6

2.8

3.0

Time (s) (h)

Figure 12. Simulation results obtained from the conventional decoupling controller and proposed decoupling controller when load torque command varies. (a) Load torque (b) Speed response (c) d axis stator current (d) q axis stator current (e) Stator current (f) d axis rotor flux (g) q axis rotor flux. (h) Rotor flux angle estimation when load torque varies.

Fig. 12 (a, b, c, d, e, f, g and h ) shows a comparative plots of applied load torque, speed response, d, q axis stator currents, stator current, d, q axis rotor fluxes, rotor flux angle estimation with the algorithm [9] and proposed methods for conventional decoupling controller and proposed decoupling controller in a speed control mode. In this speed control mode, there is a change in the load torque from 0 to 7 Nm at 3 second and from 7 Nm to 14 Nm at 6 second. From the figures, it is clearly observed that proposed decoupling controller gives better results than that of the conventional one. Fig. 11 (g) and 12 (h) show the actual rotor flux angle, estimated rotor flux angle from ANN based flux observer, and estimated rotor flux angle from load angle calculation. From the figures, it is observed that ANN based rotor flux angle estimation is more accurate than that of the rotor flux angle obtained from load angle calculation.

Conclusion In this paper, a high performance decoupling controller is proposed. This controller compensates the coupling terms with PI action and extended state equation based decoupling. The response of the proposed decoupling controller is quite satisfactory over a wide operating range compared with the conventional one. Many computer simulation results demonstrate that the proposed controller is very robust to the speed variation and sudden loading. Moreover, the speed response of the proposed decoupling controller is very fast. It is believed that the proposed scheme also has a practicality, thus will find many applications.

References [1] Bashudeb Chandra Ghosh “Parameter Adaptive Vector Controller for CSI-fed Induction Motor Drive and Generalized Approaches for Simulation of CSI -IM System” P.hd. Thesis, Department of Electrical Engineering, IIT, Kharagpur, July, 1992.

[2] Dong-Choon Lee, Seung-Ki Sul and Min-Ho Park, “High Perfor-mance Current Regulator for a FieldOriented Controlled Induc-tion Motor Driver”, IAS Conj. Rec., pp.538-544, 1992. [3] D. M. Bord and D. W. Novotny, “Current Control of VSI-PWM Inverters”, IEEE Trans. Ind. Appl . , vol. IA-21, no. 4, pp.562-570, 1985. [4] L Harnefors and Hans-Peter, “Robust Current Control of AC Machines Using the Internal Model Control Method”, IEEE IAS Conj. Rec., pp.303-309, 1995. [5] T. M. Rowan and R. J. Kerkman, “A New Synchronous Current Regulator and Analysis of Current-Regulated PWM Inverters”,IEEE Trans. Ind. Appl . , vol. 1.4-22, no. 4, pp.678-690,1986. [6] Jinhwan Jung and Kwanghee Nam, “A Dynamic Decoupling Control Scheme for High-Speed Operation of Induction Motors” IEEE Trans. On Ind. Elec., Vol. 46, no. 1, pp. 100-110February, 1999 [7] Yoshitaka Kawabata,, Tomoyuki Kawakami, Yoshiki Sasakura, Emenike C. Ejiogu,and Takao Kawabata, “New Design Method of Decoupling Control System for Vector Controlled Induction Motor.” IEEE Trans. On Power Electronics, Vol. 19, No.1, pp. 1-9, January, 2004 [8] Haithem Abu-Rub, Jaroslaw Guzinski, Zbigniew Krzeminski, and Hamid A. Toliyat, “Advanced Control of Induction Motor Based on Load Angle Estimation.” IEEE Trans. on Industrial Electron., vol. 51, no. 1, February, 2004,pp.5-13. [9] Maurizio Cirrincione, Marcello Pucci, Giamsalvo Cirrincione, and Gerard-Andre Capolino “ A new adaptive Integration Methodology for Estimating Flux in Induction Machine Drives.” IEEE Trans. On Power Electronic. Vol. 19, no. 1, January 2004, pp 25-33. [10] H. Akagi, Y. Kanazawa, and A. Nabae, “Generalized theory of the instantaneous reactive power in three – phase circuits,” in Proc. IPEC, Tokyo, Japan, 1998, pp. 1375-1368.