A modeling method of SRM based on RBF neural networks

A Modeling Method of SRM Based on RBF Neural

Networks

Shufen Qi

College of Automation and Electronic Engineering Qingdao University of Science and Technology

Qingdao, Shandong Province, China

qsf16@http://wendang.chazidian.com

Abstract—This paper presents a modeling method of Switched Reluctance Motor (SRM) based on the Radial Basis Function (RBF) Neural Networks. By analysing measuring data and nonlinear characteristics of SRM, the modeling of SRM is designed with Gaussion Function. The simulated results show that the proposed model has better capability of generalization and correctly represents the characteristics of SRM compared with traditional method of local linearization or BP Neural Networks, which is more significative to real-time control for SRM.

Keywords-SRM; RBF Neural Networks; Modeling

Hui Kong

College of Automation and Electronic Engineering Qingdao University of Science and Technology

Qingdao, Shandong Province, China

Kong_hui2009@http://wendang.chazidian.comArtificial Neural Network (ANN) techniques have grown rapidly in recent years [3]. Extensive research has been carried out on the application of artificial intelligence. Radial Basis Functions emerged as a variant of artificial neural network in late 80’s. However, their roots are entrenched in much older pattern recognition techniques as for example potential functions, clustering, functional approximation, spline interpolation and mixture models. Due to their nonlinear approximation properties, RBF neural networks are able to model complex mappings [4].

This paper investigates the use of RBF neural networks for the modelling of the magnetic nonlinearity of the SRM. Since this method does not require any prior information I. INTRODUCTION

regarding the SRM system apart from the input and output

An important characteristic of the SRM drive is its inherent

signals, it is quite simple and cost effective. The modelling

nonlinearity. The inductance of the magnetic circuit is a

method in this paper departs significantly from previous

nonlinear function of both phase current and rotor position [1].

modelling method by the authors, in which the magnetisation

In addition, the system handles energy most efficiently when

curves are represented by functions of flux linkage against

the energy conversion cycles are made as square as possible,

rotor position, rather than current. In the paper, first, magnetic

maximising the ratio of energy converted to energy input. This

nonlinearity of the SRM is presented, then RBF neural

leads a particularly difficult problem because of their

network approach to the modelling of the SRM is presented.

complicated magnetic circuit, which operates at varying levels

RBF neural network training requirements are discussed next

of saturation under operating conditions. Square energy

and finally, the models are verified through comparisons with

conversion cycles are created by driving the motor into

experimentally measured results.

magnetic saturation and bring the energy handling requirements of inverter into closer alignment with the energy

II. MAGNETIC NONLINEARITIES OF THE SRM conversion characteristics of motor. This can results in reduced

switch requirements and energy savings. The recirculated A cross section of 8/6 SRM is shown in Fig. 1, in which energy in a drive with an applied voltage requires current flow both the stator and the rotor are salient poles. The stator and acts to increase the inverter and motor losses that winding consists of a set of coils, each of which is wound on accompany the current flow. Some relevant papers proposed a one pole. The reluctance of the flux path between the two quite successful method to model the flux linkage as a function diametrically opposite stator poles varies as a pair of rotor of current and rotor position. This method has been modified poles rotates in and out of alignment. Since inductance is by several others. And some authors have also proposed a inversely proportional to reluctance, the inductance of a phase method to provide analytical expressions for the flux linkage winding is a maximum when the rotor is in the aligned and current for every rotor position within a single summary position and a minimum when the rotor is in the non-aligned equation. In contrast to the above methods, there have been position. The rotor teeth tend to align with an energized phase many attempts to generate the necessary static magnetisation in order to minimize the reluctance path [1]. curves by Finite Element Analysis (FEA) [2]. Recently, the

The production of torque of the SRM depends upon the authors have reported an application of RBF neural networks

stator current magnitude regardless of the direction [5]. The for modelling of the magnetic nonlinearity of the magnetisation

magnetic torque of SRM is a kind of reluctance torque. The curves.

direction of rotation is irrelevant to direction of current and

978-1-4577-0321-8/11/$26.00 ©2011 IEEE

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elements. Because of structure of SRM and the nonlinearity of magnetic circuit, both the inductance of winding and the flux linkage are a nonlinear function of current and rator position. SRM models are generally made up of three parts: the electrical model, torque characteristics and mechanical model. The electrical circuit for one phase of SRM is shown in Fig. 2. Applying Kirchhoff voltage law and ignoring hysteresis, eddy current and the mutual inductance between the windings thus voltage given by (1) [6].

v=ir+

dψi,θ (1) dt

However, one of most important purpose of measuring flux linkage of SRM is to analyse characteristics of the torque. We can work out the torque characteristics on the basis of the flux linkage characteristics as shown by (2) (3) (4).

?W' (2) ?θi=const

T=

W'=

³ψ(θ,i)di (3)

i

‘T’ is electromagnetic torque. ‘W'’ is magnetic field coenergy.

The expression formula of the torque can be figured out by substituting (3) in (2) as follows:

T=

?§i

(4) ¨³0ψ(θ,i)di·¸

¹i=const?©

Where ‘v’ is voltage across phase winding

‘i’ is phase current

‘r’ is resistance of the phase winding ‘? ’ is flux linkage. ‘θ’ is rotor angle.

In addition, the torque characteristics is a influencing

A group of actual measurement data given in Tab. I was measured through a experiment and the SRM we use in this experiment is a 4-phase 8/6 motor. In Tab. I, ‘i’ is phase

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considered in various scientific fields. The Gaussian activation function for RBF networks is given by:

φj(X)=exp[?(X?μj)T¦-j1(X?μj)] (5)

For j = 1,…, L, where X is the input feature vector, L is the number of hidden units, ? and ?? are the mean and the covariance matrix of the jth Gaussian function.

The output layer implements a weighted sum of hidden-unit outputs:

ψ(X)=¦λjk?j(X) (6)

j=1

L

measured every 5° angle of rotor in a cycle. The actual

measurement data show that the flux linkage is a monotone increasing function when the rotor angle changes from 0° to 30° and is a monotone decreasing function when the rotor angle changes from 30° to 0°. The flux linkage curves are drawn based on the measuring data and shown in Fig. 3. Based on the general equation of SRM and the actual measurement data, the model of SRM is designed by using the gradual approaching method of Artificial Neural Network modeling.

III. NEURAL NETWORK MODELLING OF THE SRM Ability and adaptability to learn, generalisation, less information requirement, fast real-time operation and ease of implementation have made ANNs popular in the last few years. ANNs have been applied in many areas. Dynamic system modelling, identification and control using ANNs are particularly very promising. As a result of that, the modelling of SRM has been employed using the RBF neural network, which is the most popular algorithm in the arena of neural networks [3].

A. RBF Neural Networks

RBF are embedded in a two layer neural network, where each hidden unit implements a radial activated function. The output units implement a weighted sum of hidden unit outputs. The input into an RBF network is nonlinear while the output is linear [7]. Due to their nonlinear approximation properties, RBF networks are able to model complex mappings, which perceptron neural networks can only model by means of multiple intermediary layers [8].

In order to use a Radial Basis Function Network we need to specify the hidde unit activation function, the number of processing units, a criterion for modeling a given task and a training algorithm for finding the parameters of the network. Various functions have been tested as activation functions for RBF networks. Mixtures of Gaussians have been

For k = 1,…M, ?jk where are the output weights, each corresponding to the connection between a hidden unit and an output unit and M represent the number of output units. The weights ?jk show the contribution of a hidden unit to the respective output unit.

In order to model such a mapping we have to find the network weights and topology. Finding the RBF weights is called network training [9]. If we have at hand a set of input-output pairs, called training set, we optimize the network parameters in order to fit the network outputs to the given inputs. The fit is evaluated by means of a cost function, usually assumed to be the mean square error. After training, the RBF network can be used with data whose underlying statistics is similar to that of the training set. On-line training algorithms adapt the network parameters to the changing data statistics. RBF networks have been successfully applied to various of complex nonlinear modeling, thereinto, the modeling of SRM is a good application example.

B. RBF Network used in Modelling

The RBF network used in modelling is shown in Fig. 4 with a block diagram. The training set used a group of actual measurement data given in Tab. I. This structure was used for training and testing processes. After a couple of training, it was found that only one layer network can achieve the mapping task in high accuracy. The both learning and momentum coefficients were 0.004 and the number of epoch was 100 for training. The most suitable network configuration found was 2x6x1.

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knowledge is required (model or equation), reduced mathematical complexity, and faster operation after training. What’s more, this modeling method presented in this paper has reduced the learning time of network and the number of epoch compared to BP neural network. The model can be based for the analysis and design of the control system of SRM.

REFERENCES

[1] Honghua Wang, “Technology of drive control for Switched Reluctance Motors”[M]. Beijing; Pass of Mechanical industry, 1995. (in Chinese)

[2] Rakesh Saxena, Bhim Singh and Yogesh Pahariya. “Measurement of

Flux Linkage and Inductance Profile of SRM” [J]. International Journal of Computer and Electrical Engineering, Vol. 2, No. 2, April, 2010. pp. 389-393

[3] Elmas C, Sagiroglu S, Colak I, et al . “Nonlinear modeling of a switched

reluctance drive based on neural networks.” Proceedings of Fifth International Conference on Power Electronics and Variable-Speed Drives. London LTK. pp. 7-12, October, 1994.

[4] Reay D, Williams B W, “Sensorless position detection using neural

networks for the control of switched reluctance motors.” Proceeding of the 1999 IEEE International conference on control applications, pp. 1073-1077, 1999

[5] Tian Hua and Ching Gua Chen, “Implementation of a Sensorless

Switched Reluctance Drive with Self Inductance Estimating Technique” IEEE Industrial Electronics Conference, pp. 508-513, 2002. (in Chinese)

[6] Liangwen Ji and Jingping Jiang, “Modeling of Switched Reluctance

Motors Based on Radial Basis Function Neural Networks,” Academic journal of electrotechnics, pp.7-11, April, 2001.

[7] Xia C L, Xue M, Chen W and Xie X M. “Flux Linkage Characteristic

Measurement and Parameter Identification Based on Hybrid Genetic Algorithm for Switched Reluctance Motors.” IEEE Conference on Industrial Electronics and applications (ICIEA), Singapore. pp. 1619-1623, 2008

[8] Nakamura K, Fujio S, Ichinokura O. “A method for calculating iron loss

of an SR motor based on reluctance network analysis and comparison of symmetric and asymmetric excitation.” IEEE Transactions on Magnetics, pp. 3440-3442, 2006

[9] RayW F, Erfan F,” A New Method of Flux or Inductance Measurement

for Switched Reluctance Motors”, Proceedings of the 5th International Conferenceon Power Electronics and Variable -Speed Drives[C]. Oct, 1994, London, UK . pp. 137-140. neural networks is shown in Fig 5. In this paper, the flux linkage model is designed by the actual measurement data of SRM and its result is obtained by off-line training. In the applied process, the value of ? can be got by measuring the input valuse of θang i. Then on the basis of (4), the torque can be obtained and the on-line control can be achieved. Fig. 5 shows the variation of flux linkage with current along with RBF neural network results. These results have also demonstrated the strong potential of the RBF neural network applied to the SRM. Fig. 3 shows an actual measuring result obtained by a data acquisition board. Contrasting Fig. 5 and Fig. 3, there is generally good agreement between simulation and experimental results. IV. CONCLUSION Simulation results were verified through experimental results and the modeling of SRM based on RBF neural network was proven to be reasonably accurate. The advantages of the model developed here are that no a priori

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