Adaptive Neuro Fuzzy Based Dynamic Simulation of Induction Motor Drives Dr. A. Jaya Laxmi Associate Professor, Dept. of EEE, Jawaharlal Nehru Technological University, College of Engineering, Kukatpally, Hyderabad-500085, Andhra Pradesh, India
[email protected]
P. M. Menghal Faculty of Degree Engineering, Military College of Electronics & Mechanical Engineering, Secunderabad, 500 015 Research Scholar, EEE Dept., JNTU, Anantapur-515002, Andhra Pradesh, India prashant_menghal@ yahoo.co.in Abstract— In the industrial sector especially in the field of electric drives & control, induction motors play a vital role. Without proper controlling of the speed, it is virtually impossible to achieve the desired task for a specific application. Basically AC motors, such as Induction Motors are of Squirrel-Cage type. They are simple, reliable, low cost and virtually maintenance-free electrical drives. Based on the inability of conventional control methods like PI, PID controllers to work under wide range of operation, artificial intelligent based controllers are widely used in the industry like ANN, Fuzzy controller, ANFIS, expert system, genetic algorithm. The main problem with the conventional fuzzy controllers is that the parameters associated with the membership functions and the rules depend broadly on the intuition of the experts. To overcome this problem, Adaptive Neuro-Fuzzy controller is proposed in this paper. The comparison between Conventional PI, Fuzzy Controller and Adaptive neuro fuzzy controller based dynamic performance of induction motor drive has been presented. Adaptive Neuro Fuzzy based control of induction motor will prove to be more reliable than other control methods.
Keywords- Adaptive Neuro-Fuzzy controller, PI Controller, Fuzzy Logic Controller(FLC), Sugeno Fuzzy Controller, Hebbian learning algorithm
I. Rs Rr Lm Lls Llr ωr Llr Rr ψqs ,ψds ψqr , ψdr iqs , ids iqr , iqr vqs , vds vqr , vqr p θ ωa J
NOMENCLATURE
The stator resistance. The rotor resistance. The magnetizing inductance of the motor. The stator leakage inductance. The rotor leakage inductance. The slip frequency is the frequency of the actual rotor current. The rotor leakage inductance referred to stator side. The rotor resistance referred to stator side. q-axis and d-axis components of stator flux. q-axis and d-axis components of rotor flux. q-axis and d-axis components of stator current. q-axis and d-axis components of rotor current. q-axis and d-axis components of stator voltage. q -axis and d-axis components of rotor voltage. Number of poles. The angular position of the rotor. Reference frame rotating speed. Moment of inertia (kg/m2).
Te Tl e (k) r (k) y (k) Δe(k) Δu(Ri)
Electrical torque. Load torque. Control error. Reference signal. Output signal. Changed error. The crisp Δu value corresponding to the maximum membership degree. II.
In
INTRODUCTION
most of the industries, induction motors play very important and that is the reason they are manufactured in large numbers. About half of the electrical energy generated in a developed country is ultimately consumed by electric motors, of which over 90 % are induction motors. For a relatively long period, induction motors have mainly been deployed in constant-speed motor drives for general purpose applications. The rapid development of power electronic devices and converter technologies in the past few decades, however, has made possible efficient speed control by varying the supply frequency, giving rise to various forms of adjustable-speed induction motor drives. In about the same period, there were also advances in control methods and Artificial Intelligence (AI) techniques. Artificial Intelligent techniques mean use of expert system, fuzzy logic, neural networks and genetic algorithm. Researchers soon realized that the performance of induction motor drives can be enhanced by adopting artificialintelligence-based methods. Since the 1990s, AI-based induction motor drives have received greater attention. Among the existing control technologies, intelligent control methods, such as fuzzy logic control, neural network control, genetic algorithm, and expert system, have exhibited particular superiorities. Artificial Intelligent Controller (AIC) could be the best controller for Induction Motor control. Over the last two decades, researchers have been working to apply AIC for induction motor drives [1-6]. This is because that AIC possesses advantages as compared to the conventional PI, PID and their adaptive versions. Since the unknown and unavoidable parameter variations, due to disturbances, saturation and change in temperature exists; it is often difficult to develop an accurate system mathematical model. High accuracy is not usually of high importance for most of the
induction motor drive. During the operation, even when the parameters and load of the motor varies, a desirable control performance in both transient and steady states must be provided. Controllers with fixed parameters cannot provide these requirements unless unrealistically high gains are used. Therefore, control strategy must be robust and adaptive. As a result, several control strategies have been developed for induction motor drives within last two decades. The main idea for such a hybrid controller is that with a combination of fuzzy logic and neural network, such as uncertainty or unknown variations in plant parameters and structure can be dealt more effectively. Hence, the robustness of the control of induction motor is improved. Conventional controllers have on their side well established theoretical backgrounds on stability and allow different design objectives such as steady state and transient characteristics of the closed loop system to be specified. Much research work is in progress in the design of such hybrid control schemes. Fuzzy controller conventionally is totally dependent to memberships and rules, which are based broadly on the intuition of the designer. This paper tends to show Adaptive Neuro Fuzzy controller has edge over fuzzy controller. For training the fuzzy, the authors used Sugeno fuzzy controller with two inputs and one output [10-14]. III.
and magnetizing inductance (Llr = Lr + Lm). From the equivalent circuit of the induction motor in d-q frame, the model equations are derived. The flux linkages can be achieved as: 1
(1)
1
(2)
1
(
)
1
(
)
(4)
By substituting the values of flux linkages in the above equations, the following current equations are obtained as: (5) )
(
(6)
DYNAMIC MODELING & SIMULATION OF INDUCTION MOTOR DRIVE
The induction motors dynamic behavior can be expressed by voltage and torque which are time varying. The differential equations that belong to dynamic analysis of induction motor are so sophisticated. Then with the change of variables the complexity of these equations decrease through movement from poly phase winding to two phase winding (q-d). In other words, the stator and rotor variables like voltage, current and flux linkages of an induction machine are transferred to another reference model which remains stationary[1-6].
(3)
(7) )
(
(8)
Where ψmq and ψmd are the flux linkages over Lm in the q and d axes. The flux equations are written as follows: (9) (10) (11) In the above equations, the speed ωr is related to the torque by the following mechanical dynamic equation as: 2 (12)
Fig. 1 d q Model of Induction Motor
In Fig.1 stator inductance is the sum of the stator leakage inductance and magnetizing inductance (Lls = Ls + Lm), and the rotor inductance is the sum of the rotor leakage inductance
then ωr is achievable from above equation, where: p: number of poles. J: moment of inertia (kg/m2). In the previous section, dynamic model of an induction motor is expressed. The model constructed according to the equations has been simulated by using MATLAB/SIMULINK as shown in Fig. 2 in conventional mode of operation of induction motor. A 3 phase source is applied to conventional model of an induction motor and the equations are given by: √2
(
)
(13)
2 3
√2
(14)
sin ωt (15) √2 a transformed to By using Parks Transformation, voltages are two phase in the d-q axes, and are applied too induction motor. In order to obtain the stator and rotor currrents of induction motor in two phase, Inverse park transformaation is applied in the last stage [6].
NS
NB
PS
Z
PB
1
-0.1
-0.05
0
NS
NB
0.1
0.05
Z
PS
0.1
PB
1
-1
0
-0.5
0.5
1
1.5
Fig. 4 Triangular Meembership of Δe and e
In Table-I, the fuzzy rules decision d implemented into the controller are given. The ceenter of area method yields the following
( ) Fig. 2 Induction motor in d-q modeel ICONS To Workspace1
iqs
iqs
ids
ids
iqr
iqr
idr
idr
Te
teta
Vqs Va
Va
Vb
Vb
Vc
Vc
Iabc
Vqs Vds Vds
AC Source
Ir-abc
teta
abc to d-q Park transformation
Scope1 ICONR
TL
To Workspace2
0
Wr
Constant1
Speed
induction motor d-q model
Final speed value 1/s
Torque XY Graph
Integrator
SCON
Scope
To Workspace
Fig. 3 Simulated Induction Motor Model in Convventional Mode
IV.
, ,
μ (
,
∑
, ,
)
( )
(17)
μ
,
Where, Δu(Ri) is the crisp Δu value corresponding to the maximum membership degree of the fuzzy set that is an output from the rule decisioon table for the rule Ri. The conventional simulated inducttion motor model as shown in Fig. 3 is modified by adding Fuzzy F controller and is shown in Fig. 5. Speed output terminal of o induction motor is applied as an input to fuzzy controller, annd in the initial start of induction motor the error is maximum, so s according to fuzzy rules FC produces a crisp value. Theen this value will change the frequency of sine wave in the speed s controller. The sine wave is then compared with trianguular waveform to generate the firing signals of IGBTs in the PWM inverters. The frequency of these firing signals also graadually change, thus increasing the frequency of applied voltagge to Induction Motor [12].
FUZYY LOGIC CONTRO OLLER
Continuous pow ergui
The speed of induction motor is adjusted by the fuzzy controller. The following equation is usedd to represent the fuzzy triangular membership functions: 0 ( , , , )
∑
IGBT1 IGBT4 IGBT3 IGBT6 IGBT5 IGBT2
Va
iqs
Va
ids
ids
iqr
iqr
idr
idr
Te
teta
Iabc
stator current Scope
Vqs Vb
Vb
Vc
Vc
V Vds
PWM ac source
Vds
Ir-abc
teta
abc to d-q Park transformation
(16)
iqs V Vqs
T TL
Torque Scope
0
d-q to abc Park transformation
Wr
Load Torque 1 4 3 6 5 2
induction motor d-q model Integrator
In 1
0 In fig. 4, the membership function of Δe, e and three scalar values of each triangle that are applied into this controller are shown.
1/s Speed Scope
Speed contrller Feedback Divide
1710 U(k) Reference
1
Fuzzy controller
Fig. 5 Fuzzy Control Induction Motor Model
rotor current Scope
Scope1
1
In1
Out1
Vtri then IGBT5 is ON & IGBT2 is OFF When Vcontrol3 < Vtri then IGBT5 is OFF & IGBT2 is ON The above logics are applied to generate firing signals applied to speed controller block as shown in Fig. 6.The output of the PWM inverter is shown in Fig. 8.
t>T
End Fig. 9 Flow Chart of Fuzzy Simulation Process
,
The ANFIS model is shown in Fig. 10. It states that if the cross product of output and input is positive, then it results in increase of weight, otherwise decrease of weight. Fig. 11 shows ANFIS layout.
TABLE I. MODIFIED FUZZY RULE DECISION
Δe
e
V.
PB
NB ZZ
NS NS
ZZ NS
PS NB
PB NB
PS
PS
ZZ
NS
NS
NB
ZZ
PS
PS
ZZ
NS
NS
NS
PB
PS
PS
ZZ
NS
NB
PB
PB
PS
PS
ZZ
ADAPTIVE NEURO FUZZY CONTROLLER
AC motor drives are used in multitude of industrial and process applications requiring high performances. In high performance drive systems, the motor speed should closely follow a specified reference trajectory regardless of any load disturbances and any model uncertainties. In the designing of a controller, the main criteria is the controllability of torque in an induction motor with good transient and steady state responses. With certain drawbacks, PI controller is able to achieve these characteristics. The main drawbacks are (i) The gains cannot be increased beyond certain limit. (ii) Non linearity is introduced, making the system more complex for analysis. With the advent of artificial intelligent techniques, these drawbacks can be mitigated. One such technique is the use of Fuzzy Logic in the design of controller either independently or in hybrid with PI controller. Adaptive NeuroFuzzy Inference System(ANFIS) replaces the draw-backs of Fuzzy Logic Control and Artificial Neural Network. Adaptive neuro fuzzy combines the learning power of neural network with knowledge representation of fuzzy logic. Neuro fuzzy techniques have emerged from the fusion of Artificial Neural Networks (ANN) and Fuzzy Inference Systems (FIS) and have become popular for solving the real world problems. A neuro fuzzy system is based on a fuzzy system which is trained by a learning algorithm derived from neural network theory. There are several methods to integrate ANN and FIS and very often the choice depends on the applications. In this paper, the inputs will be e(k) and Δe(k)[12,15,17,35]. A first-order Sugeno fuzzy model has rules which are as follows: • Rule1: If x is A1 and y is B1, then f1 = p1x + q1y + r1 • Rule2: If x is A2 and y is B2, then f2 = p2x + q2y + r2 In the Sugeno model if-then rules are used, and output of each rule is linear combination of inputs plus a constant value. The learning algorithm applied to this model is Hebbian. This method is feed forward and unsupervised and the weights will be adjusted by the following formula:
(
)
(
)
(18)
Fig.10 Neuro Fuzzy Controller
Fig. 11 ANFIS layout
In layer 2 of ANFIS layout, the triangular membership function is same as that of the fuzzy controller model. The output of layer 2 is given by:
,
,
(19)
Layer 3 indicates the pro (product) layer and its output is product of inputs, which is given by:
( ).
(∆ )
(20) th
Layer 4 represent Norm and it calculates the ratio of i firing strength to sum of all firing strengths. The obtained output is normalized firing strength, which is given by:
(21)
∑
Layer 5 is an adaptive node with functionality as follows:
( ( )
(∆ )
)
(22)
That pi, qi, ri are consequent parameters, which are initially are set to 0.48, 0.25 and 1 respectively. Then they are adaptively adjusted with Hebbian learning algorithm. Layer 6 calculates the output which is given by :
∑ ∑
(23)
Fig.12 shows the overall structure of Adaptive Neuro-Fuzzy model. Continuous
iqs
pow ergui
IGBT4 IGBT3 IGBT6 IGBT5 IGBT2
iqs
Torque-Speed Characteristics with Conventional Controller
20
Vqs Va
Va
Iabc
ids
ids
iqr
iqr
idr
idr
Te
teta
stator current Scope
Vqs Vb
Vb
Vc
Vc
15
Vds
PWM ac source
Vds
Ir-abc
teta
abc to d-q Park transformation
TL
Torque Scope
0
d-q to abc Park transformation
Wr
Load Torque
10 rotor current Scope
T or qu e
IGBT1
whereas in adaptive neuro fuzzy and FLC, no oscillations occur in the torque response before it finally settles down as shown in Fig. 15. Good torque response is obtained with adaptive neuro fuzzy controller as compared to conventional and FLC at all time instants and speed response is better than conventional controllers and FLC. There is a negligible ripple in speed response at Adaptive neuro fuzzy controller in comparison with conventional controller and FLC under dynamic conditions which is shown in Fig.14. Modeling and simulation of Induction motor in conventional, fuzzy and adaptive neuro fuzzy are done on MATLAB/SIMULINK. Fig. 16 show the stator currents and rotor currents of 3 different controllers under dynamic conditions.
5
1 4 3 6 5 2
induction motor d-q model 1/s
In 1
Integrator
Speed Scope
0
Speed contrller Feedback Divide
1710
-5 0
U(k) Reference
200
400
600
800
1000
1200
1400
1600
1800
Speed
1
Fig.13 (a) Torque –Speed Characteristics with Conventional Controller
Fuzzy controller
Torque-Speed Characteristics with Fuzzy Controller 140
Fig.12 Adaptive Neuro-Fuzzy Controller Simulation model
100 80
SIMULATION RESULTS & DISCUSSION
60 T or q u e
A complete simulation model for inverter fed induction motor drive incorporating the proposed FLC and adaptive neuro fuzzy controller has been developed. The dynamic performance of the proposed FLC and Adaptive neuro fuzzy based induction motor drive is investigated. The superiority of the proposed adaptive neuro fuzzy controller is proved by comparing the response of conventional PI with FLC speed controller based IM drive.The results of simulation for induction motor with its characteristics are listed in Appendix 'A' as given below: Fig.13, 14 and 15 show the torque–speed characteristics, torque and speed responses of conventional, FLC and adaptive neuro fuzzy controller respectively. It appears the rise time drastically decreases when fuzzy controller is added to simulation model and both the results are taken in same period of time. In Fuzzy based simulation, it is apparent from the simulation results shown in Fig. 13(b) and Fig 13 (c), torque-speed characteristic converges to zero in less duration of time when compared with conventional Controller, which is shown in Fig. 13(a). Adaptive neuro fuzzy controller has no overshoot and settles faster in comparison with FLC and conventional controller. It is also noted that there is no steady-state error in the speed response during the operation when adaptive neuro fuzzy controller is activated. In conventional controller, oscillations occur,
40 20 0 -20 -40 -60 -200
0
200
400
600
800 Speed
1000
1200
1400
1600
1800
1600
1800
Fig.13 (b) Torque –Speed Characteristics with Fuzzy Controller Torque-Speed Adaptive Neuro Fuzzy Controller 120 100 80 60 T orq u e
VI.
120
40 20 0 -20 -40 -60 -200
0
200
400
600
800 Speed
1000
1200
1400
Fig.13 (c) Torque –Speed Characteristics with Adaptive Neuro Fuzzy Controller
Torque response of Conventional Controller
Speed response of Conventional Controller
20
1800 1600 15
1400 1200 S P E ED
T orq u e
10
1000 800
5
600 400
0
200 -5
0
500
1000
0 0
1500
0.5
1
1.5
2.5 x 10
Fig.15 (a) Speed Response of Conventional Controller
Fig. 14 (a) Torque Response of Conventional Controller Torque response of Fuzzy Controller
6
Speed response of Fuzzy Controller
140
1800 1600
100
1400
80
1200
60
1000 S peed
T orq u e
120
40
800
20
600
0
400 200
-20
0
-40
-200
-60
2
Time
Time
0
0.5
1
1.5 Time
2
2.5
Fig. 14(b) Torque Response of Fuzzy Controller
0
0.5
1
1.5 Time
3 x 10
5
2
2.5
3 x 10
Fig. 15(b) Speed Response of Fuzzy Controller
5
Speed response of Adaptive Neuro Fuzzy Controller 1800
Torque response of Adaptive Neuro Fuzzy Controller 120
1600 100
1400 80
1200 60
1000 T orq u e
S peed
40
800
20
600 0
400
-20
200
-40 -60
0 0
0.5
1
1.5 Time
2
2.5
Fig. 14(c) Torque Response of adaptive neuro fuzzy controller
3 x 10
5
-200
0
0.5
1
1.5 Time
2
2.5
Fig. 15(c) Speed Response of adaptive Neuro Fuzzy Controller
3 x 10
5
Current responses of Conventional Controller
the control system will decrease the rising time more than expectation and it proves adaptive neuro fuzzy controller to perform better than FLC and Conventional controller. APPENDIX 'A' The following parameters of the induction motor are chosen for the simulation studies: V = 220 f = 60 HP = 3 Rs = 0.435 Xls = 0.754 Xlr = 0.754 Xm = 26.13 Rr = 0.816 p=4 J = 0.089 rpm = 1710
150
Stator & Rotor Currents
100
50
0
-50
-100 0
0.5
1
1.5
2
2.5
TIME
x 10
REFERENCE
6
Fig. 16(a) Stator & Rotor Currents of Conventional Controller
[1]
Current responses with Fuzzy Controller 300
[2]
200
[3] Stator & Rotor Currents
100
[4]
0
[5]
-100
-200
[6]
-300
-400
0
0.5
1
1.5 Time
2
2.5
3 x 10
5
[7]
Fig. 16(b) Stator & Rotor Currents of Fuzzy Controller
[8]
Current responses W ith Adaptive Neuro Fuzzy Controller 300
Stator & Rotor Currents
200
[9]
100
[10]
0
-100
[11] -200
-300
0
0.5
1
1.5 Time
2
2.5
3 x 10
[11]
5
Fig. 16(c) Stator & Rotor Currents of Adaptive Neuro Fuzzy Controller
[12]
VII. CONCLUSION In this paper, simulation results of the induction motor are presented in conventional, fuzzy control and Adaptive neuro fuzzy based models. As it is apparent from the speed curve in two models, the fuzzy controller drastically decreases the rise time, in the manner which the frequency of sine waves are changing according to the percentage of error from favorite speed. The frequency of these firing signals also gradually change, thus increasing the frequency of applied voltage to Induction Motor. According to the direct relation of induction motor speed and frequency of supplied voltage, the speed also will increase. With results obtained from simulation, it is clear that for the same operation condition of induction motor, fuzzy controller has better performance than the conventional controller. By comparing Adaptive neuro fuzzy model with FLC model, it is apparent that by adding learning algorithm to
[13] [14] [15] [16] [17] [18]
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