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research paper on neuro fuzzy
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Adaptive Neuro Fuzzy Based Dynamic Simulation of Induction Motor Drives
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
Dr. A. Jaya Laxmi
Associate Professor, Dept. of EEE, Jawaharlal Nehru Technological University, College of
Engineering, Kukatpally, Hyderabad-500085, Andhra Pradesh, India [email protected]
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. NOMENCLATURE Rs The stator resistance. Rr The rotor resistance. Lm The magnetizing inductance of the motor. Lls The stator leakage inductance. Llr The rotor leakage inductance. ωr The slip frequency is the frequency of the
actual rotor current. Llr The rotor leakage inductance referred to stator side. Rr The rotor resistance referred to stator side. ψqs ,ψds q-axis and d-axis components of stator flux. ψqr , ψdr q-axis and d-axis components of rotor flux. iqs , ids q-axis and d-axis components of stator current. iqr , iqr q-axis and d-axis components of rotor current. vqs , vds q-axis and d-axis components of stator voltage. vqr , vqr q -axis and d-axis components of rotor voltage. p Number of poles. θ The angular position of the rotor. ωa Reference frame rotating speed. J Moment of inertia (kg/m2).
Te Electrical torque. Tl Load torque. e (k) Control error. r (k) Reference signal. y (k) Output signal. Δe(k) Changed error. Δu(Ri) The crisp Δu value corresponding to the maximum membership degree.
II. INTRODUCTION
In 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 artificial-intelligence-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. 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].
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
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 ( ) (3) 1 ( ) (4)
By substituting the values of flux linkages in the above equations, the following current equations are obtained as: (5)
( ) (6) (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) 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 23 √2 sin ωt By using Parks Transformation, voltages atwo phase in the d-q axes, and are applied toIn order to obtain the stator and rotor currmotor in two phase, Inverse park transformathe last stage [6].
Fig. 2 Induction motor in d-q mode
Fig. 3 Simulated Induction Motor Model in Conv
IV. FUZYY LOGIC CONTRO
The speed of induction motor is adjustcontroller. The following equation is usedfuzzy triangular membership functions:
( , , , ) 0 0 In fig. 4, the membership function of Δe, evalues of each triangle that are applied into shown.
Vqs
Vds
TL
iqs
ids
iqr
idr
Te
Wr
induction motor d-q model
Va
Vb
Vc
teta
Vqs
Vds
abc to d-qPark transformation
1/s
Integrator
Final speed value
0
Constant1
Va
Vb
Vc
AC Source
(14) (15) are transformed to o induction motor. rents of induction ation is applied in
el
ventional Mode
OLLER ed by the fuzzy
d to represent the
(16)
e and three scalar this controller are
Fig. 4 Triangular Me
In Table-I, the fuzzy rules dcontroller are given. The cefollowing ( ) ∑ μ ( , , ,∑ , , , Where, Δu(Ri) is the crisp Δmaximum membership degreoutput from the rule decisioconventional simulated inductFig. 3 is modified by adding FFig. 5. Speed output terminal oan input to fuzzy controller, anmotor the error is maximum, sproduces a crisp value. Thefrequency of sine wave in the sis then compared with triangufiring signals of IGBTs in the of these firing signals also grathe frequency of applied voltag
Fig. 5 Fuzzy Control
Torque
Speed
iqs
ids
iqr
idr
teta
Iabc
Ir-abc
XY Graph
ICONR
To Workspace2
ICONS
To Workspace1
SCON
To Workspace
Scope1
Scope
Speed contrller
Continuous
pow ergui
V
V
T
Va
Vb
Vc
teta
Vqs
Vds
abc to d-qPark transformation
In1
1 4 3 6 5 2
IGBT1
IGBT4
IGBT3
IGBT6
IGBT5
IGBT2
Va
Vb
Vc
PWM ac source
0
Load Torque
1/s
Integrator
NB 1
NS Z
-0.5 -1 0
NB NS Z
0
NB 1
NS Z
-0.05 -0.1 0
NB NS Z
-0.05 0
embership of Δe and e
decision implemented into the enter of area method yields the
) ( ) μ (17)
Δu value corresponding to the e of the fuzzy set that is an
on table for the rule Ri. The tion motor model as shown in Fuzzy controller and is shown in of induction motor is applied as
nd in the initial start of induction so according to fuzzy rules FC en this value will change the speed controller. The sine wave ular waveform to generate the PWM inverters. The frequency
adually change, thus increasing ge to Induction Motor [12].
Induction Motor Model
d-q to abc Park transformation
stator current Scope
rotor current Scope
iqs
ids
iqr
idr
teta
Iabc
Ir-abc
Vqs
Vds
TL
iqs
ids
iqr
idr
Te
Wr
induction motor d-q model
Torque Scope
Speed Scope
Feedback
Reference
U(k)
Fuzzy controller
Divide
1710
1
PS PB
0.5 1 1.5
PS PB
PS PB
0.05 0.1 0.1
PS PB
0.05 0.1 0.1
Fig. 6 Fuzzy Logic Speed Controller
As discussed earlier, the crisp value obtained from Fuzzy Logic Controller is used to change the frequency of gating signals of PWM inverter. Thus the output AC signals obtained will be variable frequency sine waves. The sine wave is generated with amplitude, phase and frequency which are supplied through a GUI. Then the clock signal which is sampling time of simulation is divided by crisp value which is obtained from FLC. So by placing three sine waves with different phases, one can compare them with triangular waveform and generate necessary gating signals of PWM inverter. So at the first sampling point the speed is zero and error is maximum. Then whatever the speed rises, the error will decrease, and the crisp value obtained from FLC will increase. So, the frequency of sine wave will decrease which will cause IGBTs switched ON and OFF faster. It will increase the AC supply frequency, and the motor will speed up. Fig. 6 shows Fuzzy logic speed controller block. The structure of PWM inverter is shown in Fig 7. The inputs to these blocks are the gating signals which are produced in speed controller block. The firing signals are applied to IGBT gates that will turn ON and OFF the IGBTs according to the following logics.
Fig. 7 PWM inverter circuit
When Vcontrol1 > Vtri then IGBT1 is ON & IGBT4 is OFF When Vcontrol1 < Vtri then IGBT1 is OFF & IGBT4 is ON When Vcontrol2 > Vtri then IGBT3 is ON & IGBT6 is OFF When Vcontrol2 < Vtri then IGBT3 is OFF & IGBT6 is ON When Vcontrol3 > 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.
Fig. 8 (a) IGBTs gating signals
Fig. 8 (b) PWM inverter output The flow chart of simulation of fuzzy logic controller is shown in Fig. 9
Fig. 9 Flow Chart of Fuzzy Simulation Process
6
2
5
5
4
6
3
3
2
4
1
1
Triangle
In1 Out1
Sin wave2
In1 Out1
Sin wave1
In1 Out1
Sin wave
Scope1
<=
<=
<=
NOT
NOT
NOT
1
In1
t = t + Δt
Start
Reading the initial values and assigned values of the
variables
Generating Vabc and then Vdq0
Solving the differential equations to find the flux linkages , , , , ,
Calculating the currents , , , Calculating the torque and the
angular speed
t > T
End
TABLE I. MODIFIED FUZZY RULE DECISION
Δe
NB NS ZZ PS PB
e
PB ZZ
NS NS NB 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
V. 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 Neuro-Fuzzy 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)
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.
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) Layer 4 represent Norm and it calculates the ratio of ith 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.
Fig.12 Adaptive Neuro-Fuzzy Controller Simulation model
VI. SIMULATION RESULTS & DISCUSSION 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,
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.
Fig.13 (a) Torque –Speed Characteristics with Conventional Controller
Fig.13 (b) Torque –Speed Characteristics with Fuzzy Controller
Fig.13 (c) Torque –Speed Characteristics with Adaptive Neuro Fuzzy
Controller
Speed contrller
d-q to abc Park transformation
stator current Scope
rotor current Scope
Continuous
pow erguiiqs
ids
iqr
idr
teta
Iabc
Ir-abc
Vqs
Vds
TL
iqs
ids
iqr
idr
Te
Wr
induction motor d-q model
Va
Vb
Vc
teta
Vqs
Vds
abc to d-qPark transformation Torque Scope
In1
1 4 3 6 5 2
Speed Scope
IGBT1
IGBT4
IGBT3
IGBT6
IGBT5
IGBT2
Va
Vb
Vc
PWM ac source
0
Load Torque
1/s
Integrator
Feedback
Reference
U(k)
Fuzzy controller
Divide
1710
1
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que
Torque-Speed Characteristics with Conventional Controller
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Fig. 14 (a) Torque Response of Conventional Controller
Fig. 14(b) Torque Response of Fuzzy Controller
Fig. 14(c) Torque Response of adaptive neuro fuzzy controller
Fig.15 (a) Speed Response of Conventional Controller
Fig. 15(b) Speed Response of Fuzzy Controller
Fig. 15(c) Speed Response of adaptive Neuro Fuzzy Controller
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x 106
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SP
EE
D
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Fig. 16(a) Stator & Rotor Currents of Conventional Controller
Fig. 16(b) Stator & Rotor Currents of Fuzzy Controller
Fig. 16(c) Stator & Rotor Currents of Adaptive Neuro Fuzzy Controller
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
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 Rr = 0.816 Xls = 0.754 Xlr = 0.754 Xm = 26.13 p = 4 J = 0.089 rpm = 1710
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January 2012.
0 0.5 1 1.5 2 2.5
x 106
-100
-50
0
50
100
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TIME
0 0.5 1 1.5 2 2.5 3
x 105
-400
-300
-200
-100
0
100
200
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Time
Sta
tor
& R
otor
Cur
rent
s
Current responses with Fuzzy Controller
0 0.5 1 1.5 2 2.5 3
x 105
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tor
& R
otor
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rren
ts
Current responses With Adaptive Neuro Fuzzy Controller
Stat
or &
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or C
urre
nts
Current responses of Conventional Controller