Induction Motor Model with ANFIS Joycer Osorio
Arturo Molina
Pedro Ponce
David Romero
Tecnológico de Monterrey Campus Ciudad de México
[email protected]
Tecnológico de Monterrey Campus Ciudad de México
[email protected]
Tecnológico de Monterrey Campus Ciudad de México
[email protected]
Tecnológico de Monterrey Campus Ciudad de México
Abstract—In this paper is presented the analysis of an induction motor in terms of its torque, load conditions and motor speed. An induction motor model is developed to study the motor speed and its torque responsiveness for different load requirements, for this is developed a constitutive law, which links electrical and physical parameters. An Adaptive Neuro-Fuzzy Inference System (ANFIS) model is then used to test the different load characteristics of the induction motor in study. Keywords- ANFIS, Artificial Neural Networks, HEV, AC motors, vector control, induction motor and electric machines. I.
INTRODUCTION
The implementation of Artificial Intelligence (AI) control techniques for automotive applications has reached important design levels, in order to avoid negative environmental and economic impacts. Nowadays, the problems that affect the environment have a serious impact over humanity, e.g.: acid rain, greenhouse effect, respiratory failures, chronic diseases, and even cancer. The current technology in the autoindustry has a lot of fault on this problem. Since some years ago, one of the most important solutions in the industrial and academic research areas has been the implementation of new energy sources in order to decrease the levels of pollution. It is known that one of the biggest pollution sources in the world comes from the gas vehicles emissions. For this reason many different solutions have been proposed with the intention to obtain vehicles with fewer gas emission and optimal rates of fuel consumption. Different university research teams, autoindustry and other groups involved in the vehicle development performance area have been working in the improvement of the Engine Control Unit (ECU) to achieve higher power engine performance and fewer gas exhaust emission, better control techniques, innovation of power train systems and design of new hybrid vehicle concepts. In this way, several research works have been developed about AI systems for automotive applications. Hybrid Electric Vehicles (HEVs) application is one of the most important areas where induction motors are used in order to improve vehicle performance, since these electric machines have attractive advantages in terms of low costs, less robustiveness, and higher speeds and efficiency rather than other motor/generator machines. The analysis of induction motor models and the characterization of their common parameters are the main objective of this paper. Next, some research works related to advanced control strategies applied to HEV and other vehicle applications are presented as a short report on the state-of-the-art.
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In 2005, M. Mohebbi and M. Charhgard [1] developed a control strategy based on an Adaptive Neuro-Fuzzy Inference System (ANSI) model that was applied to parallel hybrid electric vehicles. The objective was to adjust the throttle in the combustion engine to achieve the maximum output torque of the vehicle while minimizing fuel consumption used by the internal combustion engine. The inputs of the system were the desired torque and the battery pack SOC (State of Charge). The results showed a very good response of the vehicle with the ANFIS model proposed in comparison with Mohebbi´s previous work [2] where it was implemented a fuzzy control system to achieve the same objective proposed with the ANFIS model [1]. Another control strategy was proposed by Zhang Weige et al [3]; they developed a fuzzy-neural network control for the air fuel ratio of a Compressed Natural Gas (CNG) engine and achieved a gas exhaust emission reduction. The control strategy was applied in a Proportional Integral (PI) controller and the results obtained showed close values to the target air fuel ratio (λ) of 1.5, giving a good engine performance. In this paper is presented an induction motor load characterization. To accomplish this, authors have implemented an intelligent control technique called: Adaptive Neuro-Fuzzy Inference System (ANFIS) that combines the benefits of an artificial neural network with the benefits of a fuzzy inference system in a single model. This structure allows having two intelligent approaches achieving good reasoning in quality and quantity: the fuzzy reasoning and the network calculation [4]. This paper is structured in five sections. In section II, the analysis of an ANFIS model is presented in order to understand clearly how its algorithms work. In section III, the induction motor model in study is introduced. In section IV, is detailed an ANFIS model for the different induction motor loads characteristics. Finally, conclusions are presented, where the results obtained from the induction motor model and the ANFIS model are discussed. II. ANFIS MODEL An ANFIS model combines the artificial neural network’s benefits with the fuzzy inference system’s profits in a single model. This kind of model has become very popular due to its characteristics such as: fast and accurate learning, and the capacity of data management [5]. The main objective of an ANFIS is to optimize fuzzy system’s parameters (in the way to obtain accurate answer to the problem) through a learning algorithm implementation and a set of inputs and outputs, which are responsible of the learning process. Two important ANFIS actions for its operation mode are: 1) a fuzzy inferences system is built, 2) the membership function parameters are
2 adjusted by a hybrid training algorithm, which combines gradient descent and the least-square method. The least-squares method is actually the major driving force that leads to fast training, while the gradient descent serves to slowly change the underlying membership function that generates the basic functions for the least-squares method [6]. This type of adjustment allows the fuzzy system to learn the data set that we are providing. The adaptive neuro-learning works in a similar form as a neural network. The technique of the adaptive neuro-learning provides a procedure of fuzzy modeled to learn information about a set of data [7]. The Fig. 1 shows the general structure of ANFIS.
Figure. 1. An ANFIS’s General Structure
The associated parameters to the membership functions change during the learning process. In Fig. 1, the points with circular shape represent fixed points and the points with square shape represent adjustable points. The adjustments are calculated due to a vector, which is denominated gradient. This vector is useful to know how are approximating the results of the ANFIS outputs with the real outputs. Once the gradient is obtained, many routines of optimization were applied to adjust the parameter to minimize the error [8]. It is important to take into account that two different rules cannot share the same membership function, although the number of rules is the same that the number of membership functions of the output. To illustrate Sugeno type rules having outputs which linear combination of their inputs are:
Fundamentally, ANFIS is a graphical network representation of Sugeno-type fuzzy systems, endowed with neural learning capabilities. In this section, it is detailed how an ANFIS algorithm works. In the next sections, are presented an induction motor model and the ANFIS model developed for testing its different load characteristic. This allows us to understand the importance of an induction motor model and its different loads characteristics with the implementation of an ANFIS model. III. INDUCTION MOTOR MODEL In the industry, induction motors are broadly used for industrial drives applications. One of the most implemented methods to control industrial drives is based on vector control, which consists on control AC machines as DC machines by means of a decoupled control of the rotor flux magnitude and the torque-producing current [9].
One issue related to vector control implementation is the difficulty in obtaining an accurate model of induction motor, owing to the variation of induction motor parameters, such as resistance, inductance and time constant among others. This is an important reason by which is necessary to study and analyze induction motor models. Induction motors are classified based on their characteristics. One of them is based on their rotor type, that is: (1) Squirrelcage rotor: for this kind of induction motors the rotor is completely isolated. (2) Slip-ring rotor: current is provided to the rotor directly through electrical contacts called commutators and slip rings. Also these motors can be classified based on its number of phases, that is: (a) Three- phase induction motor, (b) Twophases induction motor, and (c) One-phase induction motor. Several characteristics of AC machines are attractive for industrial implementation rather than DC machines, to mention a few: AC motors are cheaper than DC motors; AC motors have higher performance in terms of efficiency and speed than DC motors. Nevertheless, DC motors have the characteristic to be controlled by techniques simplest than control techniques implemented to AC motors, this give to DC motors a good part in industrial applications. However, as was mentioned above, for AC motors have been developed control techniques to facilitate controlling them. In order to know better an induction motor performance for different loads and under certain parameters, it is developed and evaluated an induction motor model. A. Induction Motor Parameters The induction motor parameters used to develop the model are:
P= 4 (Number of poles)
Rs= 1.06 (Stator resistance)
Rr= 3.54 (Rotor resistance)
Xm= 230.808 ( Magnetizing impedance [Ohms])
Xls= 7.815 (Stator side leakage impedance [Ohms])
Xlr= 7.815 (Rotor side leakage impedance [Ohms])
we= 377. (Base electrical frequency [rads/s] )
J= 0.089 ( Rotor inertia )
B1= 0 ( Load damping coefficient)
vds= 380 ( D axis stator voltage )
vqs=380 ( Q axis stator voltage)
vqr= 0 (D axis rotor voltage)
vdr= 0 ( Q axis rotor voltage)
TL= 0 ( Load torque, initial condition)
With the initial parameters defined, next the induction motor simulation is presented.
3 B. Induction Motor Model Development The induction motor model is referred to the equivalent circuit on Fig. 2. [
Figure 2. Equivalent Circuit Model
The parameters in the right part of the circuit are the rotor parameters that have been referred to the stator through the ideal transformer in the machine model. The dynamic equations of the induction motor can be described from the flux equation of the stator phase as, bs and cs (see Fig. 3) and the spatial vector of the stator flux [10], which is defined as: ̅
(1)
The right part of the equation (1) represents the contribution of each phase. This equation can be physically interpreted as the spatial vector magnitude and direction of the net stator flux sinusoidal distribution. In the same way, it can be represented the spatial vector of the rotor flux: ̅
(2)
Expressions (1) and (2) represent the net stator and rotor flux in the reference frame. In order to define the induction motor model, the stator and rotor flux must be discomposed in their orthogonal components. The stator and rotor flux can be expressed as: [
]
[
][
]
In order to define the stator and rotor flux in an orthogonal coordinates, it is used Park’s transform [11], so the transformation is:
[
]
[ [
]
]
It is possible to note that the induction motor model has two subsystems, stator and rotor, so the Park’s transform presented above is applied to the rotor too, so that the matrix equations for the stator and rotor in orthogonal coordinates are: (4) (5) In the equations (4) and (5) the variables and represent the transformation matrix (e.g. Park’s transform) for the stator and rotor respectively. These are defined as and , whrere and are the angle rotation for the stator and rotor respectively. In order to obtain the simulation equations the following step is to define the stator voltage in the new orthogonal frame. That is:
] (3)
The matrix equation presented is in terms of stator, rotor and common inductances and stator and rotor currents. The impedances in (3) are defined as: Now, using the differentiation product rules is defined the stator and rotor voltages, so finally we have: [
Where and are the impedances that links the stator winding with the rotor winding. The impedances and are the stator and rotor leakage respectively, they are defined as:
]
[ [ In the equation (3) the impedance is referred to the common impedance among the stator and rotor, it is defined as:
] ]
For the rotor the equation is: [
]
4 Synthetizing the equations for the stator and rotor are:
Stator
Each component (d, q and o) is defined: (6) (7)
Figure. 3. Rotor Speed, TL = 0
Rotor
Each component (d, q and o) is defined: (8) (9)
It is important to mention that the rotor’s voltages equations and are equal to zero for a squirrel cage machine. From the equations (6)-(9) the voltages and fluxes are defined for the stator and rotor in a unified reference frame. Therefore, it is multiplied those equations by the vector obtaining the motor model in a stator frame.
Figure. 4. Electromagnetic Torque, TL= 0
(10) (11) (12) (13) Finally, in order to have the complete set of equations to model an induction motor. It is taking into account the mechanical implications, that is: (14) Where P was defined in the subsection A. The electrical rotor speed is defined as:
Figure. 5. Electromagnetic Torque vs. Motor Speed, TL= 0
The second simulation is to evaluate the results in terms of electromagnetic torque, speed and the relation among torque and speed, when it is applied different load torque values to the induction motor. This is shown in Fig. 6 and 7.
(15) The induction motor model is completed. The equations (10)-(13) represent the stator and rotor voltages components, and the equations (14) and (15) represent the electromagnetic torque and rotor speed. C. Simulation The simulations presented in this section are based on the model developed in the sub-sections before. First, it is evaluated the initial conditions, that is, when it is not applied any load torque. The results for this condition are presented in Fig. 3, 4 and 5.
Figure. 6. Rotor Speed Results for different TL
5
(
)
(15)
Where: T: Generated torque T0: Friction torque TN: Nominal torque
: Nominal speed : Motor speed Figure. 7. Electromagnetic Torque Results for different TL
D. Analysis of Results A 4 poles squirrel cage induction motor was modeled and simulated. The results obtained from the simulations give the idea of how response an induction motor in front different load torques conditions. First the simulation was run without any load torque and the result for the rotor speed was a curve with a linear part until yield a constant speed. The torque response depicted in Fig. 4 consists in a transitory and stable parts, the first one depicts the motor dynamic behavior at the motor starter with oscillations over the starting torque. On the other hand the second simulation was run for different load torque values. It is possible to note from Fig. 6, that if the load torque increases then the rotor speed yielded decrease. The results obtained were logical and coherent with the simulation conditions. However, one important condition to take into account is the variables and , which are the angles picked for the Park’s transformation. For the induction motor model presented these variables were defined as: ,
m: Variation factor The possible motor characteristics responses are [10]: Independent response: for m= 0, the generated torque no dependent on the speed. It is a characteristic of cranes and pumps. Linear response: for m=1, the generated torque has a lineal relation with the motor speed. It is characteristic o generator with independent excitation. Parabolic response: for m= 2, the generated torque has a square relation with the motor speed. It is characteristic of centrifugal pumps. Decreasing response: for m= -1, the generated torque has an inversely proportional relation with the motor speed. Figures 8 to 11 represent each mechanical characteristic.
: rotor position ∫
These angles depend on our decision, but the choice made for this simulation gave good results and allow us to understand better a motor induction response for different load torque conditions.
Figure. 8. Independent Response
IV. MOTOR MECHANICAL CHARACTERISTICS In section III and induction motor model was developed and simulated in order to know its mechanical response for different load torque conditions. But, how load conditions affect or characterize an electric machine? To response to this question is studied and analyzed different load characteristics of electric machines. In order to simulate different load characteristics an ANFIS model is developed, also the ANFIS model presented in this section lets us estimate speed-torque responses for different conditions. A. Speed-Torque Characteristic Response To develop the ANFIS model is important first to estimate an equation that allow us to know the different torque conditions in terms of the motor speed. Therefore, the following mathematical equation is defined:
Figure. 9. Linear response
6
Figure. 14. Linear response, ANFIS approach Figure. 10. Parabolic Response
Figure. 15. ANFIS Result Figure. 11. Decreasing Response
B. ANFIS Simulation In order to achieve the ANFIS model is established the following parameters: T0: 1200 TN: 1300
Parabolic Response - Parameters: 5 triangular MFs Linear output 2000 epoch
: 1500
The results obtained are presented in the following figures Independent Response - Parameters: 11 Triangular MFs Linear output 3000 epoch
Figure. 16. Parabolic Response: ANFIS Approach
Figure. 12. Independent Response: ANFIS Approach Figure. 17. ANFIS Result
Decreasing Response - Parameters: 21 triangular MFs Linear output 5000 epoch Figure. 13. ANFIS Result
Linear Response - Parameters: 3 triangular MFs Linear response 1000 epoch
7
Figure. 18. Decreasing Response: ANFIS Approach
C. Analysis of Results The results obtained from each simulation illustrate how closer the ANFIS approach to the reference is. This development allows us to design a control implementation capable to control a motor under the load conditions established. Also, it was possible to note the difficulty to set the optimal ANFIS parameters. From Fig. 12 and 13 is possible to note the variations within a 0.004 of amplitude, which means a good approach for the independent response. From the decreasing response in Fig. 18 is possible to note how closer the ANFIS approach to the response is. For the last response the parameters were set at 21 triangular membership functions, linear output and 5000 epoch. It is possible to imply, the high number of membership functions and iterations required to reach a good response from the ANFIS system.
The hybrid training process facilitates the convergence to the tolerance error and made the design process faster. From the experience acquired in the development process done in this work, some inferences are listed: To develop an ANN or ANFIS controller the desired plant outputs and its corresponding inputs must be clear. In the design process of controllers based on ANFIS or ANN, the most difficult part is to define how many neurons are needed for the system and the correct set of values for the training process. The definition of these parameters is often an iterative process. This paper establishes a relevant study of electric machines performance under certain operational conditions. This work represents a first approach of electric machines modeling in terms of electrical and mechanical parameters, with the aim to understand motor speed and torque response for different power requirements. Thus, other developments will be presented in futures works in order to yield greatest improvement in power control systems of HEV. REFERENCES [1]
M. Mohebbi, M. Charkhgard and M. Farrokhi. Optimal Neuro-Fuzzy Control of Parallel Hybrid Electric Vehicles, Proc. IEEE Conf. on Vehicle Power and Propulsion, 2005, 26-30.
[2]
M. Farrokhi and M. Mohebbi. Optimal fuzzy control of parallel hybrid electric vehicles, Proc. International Conf. on Control, Automation and Systems, Kintex, Gyeonggi-Do, Korea, 2005.
[3]
Zhang Weige, Jiang Jiuchun, Xia Yuan and Zhou Xide. CNG Engine Air-Fuel Ratio Control Using Fuzzy Neural Networks. Proc. 2nd International Workshop on Autonomus Decentralized System, IEEE, 2002, 156-161.
[4]
M. Aliyari Schoorehdeli, M. Teshnehlab and A. K. Sedigh. A Novel Training Algorith in ANFIS Structure, Proc. IEEE Conf. American Control Conference, Minneapolis, MN, 2006, 1-6.
[5]
Tsoukalas, Lefteri H, Fuzzy and neural approaches in engineering (New York: Wiley, c1997).
[6]
Jyh-Shing Roger Jang. Input Selection for ANFIS Learning, Proc. 5th IEEE International Conference on Fuzzy Systems, 1996. 1493-1499.
[7]
Ponce, P., Inteligencia Artificial con Aplicaciones a la Ingeniería, Alfaomega, Primera edición, 2010.
[8]
Jyh-Shing Roger Jang. ANFIS: Adaptive- Network-Based Fuzzy Inference System, International Journal of Transactions on systems, man, and cybernetics-PartC: Applications and reviews, IEEE, 23(3), 1993, 665-685.
[9]
Jovanovic, M.G and Betz, R.E, “Effects of uncompensated vector control on synchronous reluctance motor performance”, IEEE, Inter. Journal of Energy Conversion, Vol. 14 (3), 2002.
V. CONCLUSION According to load torque conditions established for the induction motor model were obtained the results in terms of motor torque and speed. Now, projecting these results in real operation conditions is possible to imply that induction motor or industrial drives speed response depending on the load torque requirements. Also, stator and rotor electrical parameters like inductances, resistances, number of poles among other; take an important part in the desire motor performance. Hence, a motor selection depends on certain implications (e.g. power required, application specifications, etc.), which are directly linked to electrical parameters. Thus, the constitutive law (10) presented in the induction motor model relates electrical and physical parameters in order to estimate the motor torque allowing to us variant load torque and see the induction motor response in terms of torque and speed. With the induction motor model defined in the first part of this paper. The second part relates mechanical responses in terms of load characteristics with an intelligent technique; this in order to develop an ANFIS model that allow us to estimate different load characteristics of electric machines. The advantages of the ANFIS model developed in this paper are; accuracy, simplicity and the capability to design a better controller with fewer resources. However, several variables need to be set in order to reach the desired control performance. Also from the results obtained, it is possible to note: The training process takes a considerable time but when the training results are implemented the system maintains its stability and works faster.
[10] Ponce, P & Sampé, L., J., Maquinas Eléctricas y Técnicas modernas de control. Alfaomega, 2008. [11] Cusido, J.; Rosero, J. A.; Ortega, J. A.; and García, A. L. Romeral, Induction Motor Fault Detection by using Wavelet decomposition on dq0 components, IEEE International Symposium on Industrial Electronics, 2006, pp. 2406-2411.
