The application of NARX neural networks in identification electric drive control system

This paper deals with an identification model control system using recurrent neural networks to estimate the angle main mirror in azimuth moving of large radio telescope electric servo drive. The architectural approached to design recurrent neural networks based on “Nonlinear Auto Regressive with Exogenous inputs – NARX models” is analyzed. It is convenient to apply this design in the field of prediction and modeling control system.

THE APPLICATION OF NARX NEURAL NETWORKS

IN IDENTIFICATION ELECTRIC DRIVE CONTROL SYSTEM

Nguyen Duc Thanh1, Doan Van Thuy1, Tran Huu Phuong2*

Abstract: This paper deals with an identification model control system using

recurrent neural networks to estimate the angle main mirror in azimuth moving of large radio telescope electric servo drive The architectural approached to design recurrent neural networks based on “Nonlinear Auto Regressive with Exogenous inputs – NARX models” is analyzed It is convenient to apply this design in the field

of prediction and modeling control system During computer simulation, the performances of neural network identification model with different parameters are compared in the working of electric drive control systems In this work, designing, training, testing of neural networks identification model are carried out by Matlab/ SIMULINK environment

Keywords: Large radio telescope; System identification; Artificial neural networks; Model NARX

1 INTRODUCTION

System identification techniques are fundamental methods in theory of automatic control systems System identification in control engineering is the process to design a model mathematical description F uˆ ( ) adequate fitted plant structure F u( ) based on known input vector u( )k and observed output vector y( )k from the real plant system, with k1, 2,, N (fig 1)

ˆ

where e is mean square error (MSE), defined by the norm  ; yˆ ( )k Fˆ( )u is output vector of identification model; u( )k is vector allowable control input signal

ˆ ( )

F u

( )

F u

( )k

u

(k 1)

y

ˆ (k 1)

y

e

Fig 1 System identification

The process of identification model F uˆ ( ) depends on collecting data, note that the experiment should be constructed, such that the data collected adequately describes the process The process should be subjected to a sufficient number of inputs, so that an accurate relationship between input and output can be obtained Finally, validating the identification model involves assessing how well the model replicates the observed data From a historical point of view, before the 1980s, identification of dynamic systems used linear parametric autoregressive (AR), moving-average (MA) and autoregressive moving-average (ARMA) models introduced by Box and Jenkins These models are linear and are not able to cope with certain non-stationary signals, and signals whose mathematical model is not linear In recent years, artificial neural networks (ANNs) have

been known as powerful mathematical computational tools, well approach to control technical object ANNs can be classified in two typical tasks, one of which is the choice of optimal structure of the ANNs and the other is building an effective learning algorithm which they use for weight updates [3] In the field of system identification, a model control process in the form of ANNs is developed to estimate (forecast) the output values

in the future

2 THE NARX NEURAL NETWORKS IDENTIFICATION

In traditional system identification, model structure must be defined a prediction to estimate all required system parameters In case of large radio telescope servo drive, defining a predictive model is difficult to implement With ANNs, it is capable of identifying underlying relationship between the given input and output data Fig 2 is an ANNs identification system is used in this paper We propose a modern approach architectural ANNs based on “Nonlinear Autoregressive models with Exogenous inputs - NARX model”, which are therefore called NARX recurrent neural networks in series-parallel mode [2] Such networks can be expanded by nonlinear equation as following

ˆ

ˆ ( k  1)  F u k u k ( ), (  1), , ( u k  d ) , ( ), ( y k y k  1), , ( y k  d ), ,

where F u yˆ ( , ) is input-output conversional function performed by the ANNs; d 1 is input

tapped delay line; d 2 is output tapped delay line

The NARX model for approximation of a function F u yˆ ( , ) can be implemented in many ways, but the simpler seems to be by using a feedforward neural network with the embedded memory As is shown in fig 2, the plant produces output y k ( 1) and it is approximated by output of identification model y k ˆ( 1) with a one-step-ahead prediction because of the series-parallel configuration Plant and identification model have the same input u k( ) In this work, u k( ) is angular azimuth axis data, y k ( 1) is angle encoder output data on the main mirror of the antenna, y k ˆ( 1) is predictive value of the output in the ANNs mode, e k ( 1) is predictive error which y k ( 1) is compared with y k ˆ( 1)

( )

u k

( 1)

y k 

ˆ( 1)

y k 

1

z

1

z

1

z

1

z





( 1)

e k 

 ( 1)

u k 

1

( )

u kd

2

( )

y kd

( 1)

y k 

Fig 2 Schematic diagram NARX model in series-parallel mode

Let’s regard an experiment of using NARX model to design an identification model in process of estimation angle main mirror in azimuth moving of the large radio telescope

70-m parabolic antenna dia70-meter (the RT-70 antenna) In [1], [4], we introduced aug70-mented mathematical model of electric servo drive of the RT-70 antenna in system of four-mass branched elastic model with concentrated parameters This model is written in discrete-time state-space with sampling interval Ts, as

( 1) ( ) ( )









with coordinates

ω1 M21 ω2 M32 ω3 M42 ω4 i m 3T



where ω , ω , ω , ω1 2 3 4 are speeds of each mass; Mm, M21, M32, M42 are moment’s motor and moments elastic between masses; im is current motor; y ( ) k  φ3 is vector output (angle main mirror in azimuth moving of the RT-70 antenna) In position loop has discrete model predictive controller based on Laguerre functions [5] (MPC-Laguerre regulator) Structural diagram of the RT-70 antenna electrical servo drive control system is shown in fig 3 and its parameters are described in detail in [4] This structure includes the Discrete State Space Plant, the MPC-Laguerre Predictive Controller block, the NARX Neural Network-NNET block, and the Graph

Fig 3 Scheme of the RT-70 antenna servo control system in Simulink

In this experiment, we carried out a computation by using the Neural Network Time Series Tool to design standard NARX architecture NARX model uses a feedforward neural network to approximate the function F u yˆ ( , ) A diagram of the resulting network

is shown below (fig 4), where a two-layer feedforward network is used for the approximation This implementation also allows for a vector ARX model, where the input and output can be multidimensional In the hidden layers, the nonlinear sigmoidal activation functions are taken, whereas in the output layer, the linear activation function is used During the training procedure, the backpropagation method is applied

Fig 4 Architecture of the NARX neural network in Neural Network Time Series Tool

3 SIMULATION RESULTS

In this considered case, ANNs are used to estimate the angle main mirror in azimuth moving of the RT-70 antenna electrical drive The optimal output signal of MPC-Laguerre

position regulator, angle encoder output data of main mirror and external disturbance (wind flow) such as "white noise" are chosen as input signals of these ANNs structure The angle main mirror in azimuth moving varies in the range from 0 '' to

36000 ''(arcseconds) with resolution is 2 '' The duration of model simulation is 30 minutes The drive system of the RT-70 antenna suffers under wind disturbance with its average flow speed is 10 m/s Amplitude of external disturbances was taken equal to 10%

of maximum useful value signal The number of training data ANNs is 180 000 samples The simulations are carried out using the Matlab/SIMULINK R2016a with sampling interval T s 102 sec

To investigate the influence of input parameters to the quality estimation accuracy of angle main mirror, the different input parameters of ANNs are composed and will be change in 3 variants The changed parameters are following:

1) the predictive horizon of MPC- Laguerre regulator, N p; 2) training function; 3) tapped delay line, d  d1  d2; 4) structure of the NARX model with different numbers of neurons at hidden layers

First, we select 3 values predictive horizon of the MPC-Laguerre regulator [5] and test them in separately each:

1) N  p 30; 2) N  p 106; 3) N  p 68

Then, to test quality of identification model, we give 3 training functions backpropagation:

1) trainscg – scaled conjugate gradient backpropagation; 2) trainbr – Bayesian regularization backpropagation; 3) trainlm – Levenberg - Marquardt backpropagation

The different input vectors of ANNs are composed of the actual and tapped delay line: 1) when d 1, the NARX model is described in the form

ˆ

ˆ ( k  1)  F u k u k ( ), (  1), φ ( ), φ ( k k  1)

2) when d 2, the NARX model is described in the form

ˆ

ˆ ( k  1)  F u k u k ( ), (  1), ( u k  2), φ ( ), φ ( k k  1), φ ( k  2)

3) when d 3, the NARX model is described in the form

ˆ

ˆ ( k  1)  F u k u k ( ), (  1), ( u k  2), ( u k  3), φ ( ), φ ( k k  1), φ ( k  2), φ ( k  3)

The following, structures of the NARX model with different number neurons in hidden layers are tested:

1) x  2 1 (7); 2) x  4 1 (8); 3) x 10 1 (9)

where the number ANNs model input nodes x depends on the kind of input vector

according to (4) – (6)

After the composing with 3 variants, the ANNs identification models are trained and tested we obtain the following diagrams: servo tracking position responses of the RT-70 antenna, corresponding to angle main mirror set point p 20 '' and the MSE estimation angle graphs between the reaction of the plant and the output of identification model

φ φ id

e   Identification estimation errors are shown and compared, according to fig

5 a), b) is the first variant; fig 6 a), b) is the second variant; fig 7 a), b) is the third

variant of the experiment

5.a) Servo tracking position response 5.b) MSE estimation angle main mirror

Fig 5 The first variant of identification results

6.a) Servo tracking position response 6.b) MSE estimation angle main mirror

Fig 6 The second variant of identification results

7.a) Servo tracking position response 7.b) MSE estimation angle main mirror

Fig 7 The third variant of identification results

From the analysis of the obtained estimation errors, it is clearly visible that the type input parameters of ANNs has a big influence on the estimation quality of both servo tracking position responses and MSE estimation angle values main mirror of the RT-70 antenna The system in the first variant with the simplest input parameter (according to (4) and (7)) cannot estimate angle values main mirror accurately The MSE estimation angle main mirror are about 0.5% of the values angle main mirror (fig 5.a and fig 5.b) The MSE estimation error is much better in the third variant (fig 7.a and fig 7.b), especially the ANNs with training function Levenberg - Marquardt backpropagation

4 CONCLUSION

In this paper, the approach to identification systems using NARX model artificial neural networks were presented The performances of servo tracking position response and MSE estimation angle main mirror of the RT-70 antenna control system with different

parameters of identification model were tested Our work determined well validation of the application of using ANNs for identification system of the RT-70 antenna electrical servo control system

REFERENCES

[1] Tran Huu Phuong, Nguyen Duc Thanh, Nguyen Manh Tuan, “Управление электроприводом крупного радиотелескопа с линейно-квадратичным гауссовским регулятором,” Tạp chí Nghiên cứu Khoa học và Công nghệ quân sự,

số 50, xuất bản tháng 2, năm 2018, Tr 28-37

[2] A O Vedyakova, “ Identification under external disturbance conditions using neural networks,” International Journal of Open Information Technologies, vol 2, 2014, №3,

pp 18-22

[3] K S Narendra, K Parthasarthy, “Identification and control of dynamical systems using neural networks,” IEEE Trans Neural networks, vol 1, 1990, P 4-26

[4] Tran Huu Phuong, Belov M P., Tran Dang Khoa, “Model Predictive Controller Based on Laguerre Functions for Large Radio Telescope Servo Control System”, In

2018 IEEE NW Russia Young Researchers in Electrical and Electronic Engineering Conference (ElConRusNW) 2018 P 1003–1007

[5] L Wang, “Discrete model predictive control design using Laguerre functions.”

Journal of Process Control 14, 2004, pp 13-42

TÓM TẮT

ỨNG DỤNG MẠNG NƠ-RON NARX TRONG BÀI TOÁN NHẬN DẠNG

HỆ THỐNG ĐIỀU KHIỂN TRUYỀN ĐỘNG ĐIỆN TỰ ĐỘNG

Bài báo phân tích kiến trúc và mô hình toán của mạng nơ-ron ngược - mô hình NARX Đây là một kiến trúc mạng nơ-ron có thế mạnh trong các bài toán mô phỏng

và nhận dạng các hệ thống điều khiển truyền động điện tự động Trong bài báo, các tác giả đề xuất một phương pháp ứng dụng thuật toán nhận dạng hệ thống điều khiển dựa vào mạng nơ-ron ngược NARX để ước lượng góc quay theo kênh phương

vị của kính thiên văn vô tuyến cỡ lớn Khi thực hiện mô phỏng trên máy tính, các tính chất của mô hình nhận dạng mạng nơ-ron được so sánh qua các chỉ tiêu về quá trình quá độ và sai số của bộ nhận dạng Việc thiết kế, huấn luyện, thử nghiệm mô hình nhận dạng mạng nơ-ron được thực hiện trên môi trường Matlab / SIMULINK

Từ khóa: Kính thiên văn vô tuyến cỡ lớn; Nhận dạng hệ thống điều khiển; Mạng nơ-ron nhân tạo; Mô hình

NARX

Nhận bài ngày 01 tháng 7 năm 2018 Hoàn thiện ngày 10 tháng 9 năm 2018 Chấp nhận đăng ngày 20 tháng 9 năm 2018

Author affiliations:

1 Institute of Military Science and Technology;

2 Saint-Petersburg Electrotechnical University “LETI”, St Petersburg, Russia

*

Corresponding author: thanhnd37565533@gmail.com.