MEP 2006, 7-11 November 2006, Guanajuato, Guanajuato, México. DESIGN AND IMPLEMENTATION OF A SELF-TUNING CONTROL. USING ARTIFICIAL ...
MEP 2006, 7-11 November 2006, Guanajuato, Guanajuato, México.
DESIGN AND IMPLEMENTATION OF A SELF-TUNING CONTROL USING ARTIFICIAL NEURAL NETWORKS OF SECOND ORDER Mario A. Ibarra-Manzano1, Dora L. Almanza-Ojeda1, Andrés Hernández-Gutiérrez1, Juan P. Amezquita-Sánchez1 and Luis F. López-Martínez1. 1
Facultad de Ingenería Mecánica, Eléctrica y Electrónica (FIMEE) Guanajuato University. Av. Tampico #912, Col. Bellavista Salamanca, Gto., México. Phone: 464-6480911, Fax: 464-6472400 e-mail: {ibarram, luzdora, ahernandez}@salamanca.ugto.mx
Abstract-In this works we present the design and implementation of a self-tuning control using artificial neural networks of second order. The control is implemented as an embedded system through a Digital Signal Process (DSP). This system uses a digital control of closed loop proportional, derivative and integral (PID) self-tuning by artificial neural networks. In this works furthermore is presented a practical application by controller the velocity angular of a motor. Keywords: self-tuning control, artificial neural networks, second order, embedded system.
INTRODUCTION The automatic control has been an important issue in the development of engineering and science, due to, it has converted in important and integral part of most of industrial and fabrication process [1]. Current advances in theory and practice about automatic control give more facilities to get an optimal behavior among dynamics systems, to increase its productivity, to minimize several repetitive handled operations among others routine activities[2]. The main applications of automatic control can be divided in the follow blocks: a) control used to make products, e.g. the industrial control or the movement control, among others, b) control which is integrated in the product, e.g. control of a car or an airplane, or hard disk motor control. Current applications of modern control theory include systems out of engineering field, such as biologic, biomedical, economic and socioeconomic systems [1]. The intelligent control has been the start point and it has produced significant advances in control theory [3]. The intelligent control is used when action applied is complex or the control process has uncertain. There are three main tendencies of this control, the neural network control, fuzzy logic control and classic artificial intelligent [3]. Neural network is based on to use the neuronal techniques in order to obtain better performance than current techniques. The design and theory of Artificial Neural Network (ANN) has had a significant advance during latest 20 years. Many of this progress are due to the signal processing [4]. The no-lineal features and the capability of ANN to learn about its environment in supervised and unsupervised way, also its property which let to be universal approximate, made ANN, an excellent solution to hard signal processing problems and specially problems in pattern recognition [4]. Since the point of view of signal process, it is necessary to develop an appropriated compression of the ANN basic structures and also to understand how does it impacts to 1-4244-0628-5/06/$20.00 ©2006 IEEE
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different algorithms and signal processing applications. A design problem of ANN consists of to identify the neural structure which can be used to solve real problems, among others which are still under develop or have difficulties during their use [4]. An important problem, during signal processing applications, is to understand the essential of the problem in order to use the most appropriate structure in each case. Also, it is important to evaluate performance, robustness and the relation between velocity and effectiveness in the signal processing systems, furthermore, to develop methodologies in order to use ANN with signal processing algorithms. And finally, another important problem is how to evaluate the ANN models, training algorithms and how to identify the best ANN structure for solving the problem [4].
NEURAL MODEL The k-th neuron from L-th layer of second order ANN is showed in Figure 1, this neuron uses equation (1) and equation 2, as net function and activation function respectively [5]. As we can see, the second order ANN has inputs and its combinations, and a multi-layer perceptron has only inputs, this is the main difference between them [6]. X1X1
Wk11 X1X2 Wk12 . . . Wkij XiXj . . WkNM . XN XM
Σ f(u ) L k
L
Zk
L
θk
Figure 1: Model of a second order neural network. N
N
L L −1 L −1 ukL = ∑∑ wkij zi z j + θ kL
(1)
zkL = f (ukL )
(2)
i =0 j =0
As in most of ANN, the knowledge of this model is located in its synaptic weights [5]. The learning algorithm used by this model, is a modified back propagation algorithm [7], first step of this algorithm consist to calculate the gradient of the neuron by equation (3), as second step consist to update synaptic weight by equation (4), where η1, η2 and μ are first and second order learning factor and momentum respectively, finally update skew by equation (5).
δ k (l ) = [d k (l ) − zk (l )] f ' (uk (l )) M
M
l =1
l =1
(3)
[
wkij (t + 1) = wkij (t ) + η1 ∑ δ k (l ) zi z j + η 2 ∑ δ k (l ) zi z j + μ wkij (t ) − wkij (t − 1)
]
(4)
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M
θ k (t + 1) = θ k (t ) + ∑θ k (l )
(5)
l =1
IMPLEMENTED MODEL There are several aspects of a neural control; one of them is the optimization of the control models by neural network techniques. A neural control model implementation is showed in Figure 2, which is constituted by a proportional integral and differential control (PID) and to tune by a second order ANN. The PID control uses three adjustment constants, which are calculated by using the second order ANN. As input, ANN uses the error, which represents the difference between expected velocity and real velocity. This difference and the current output of the system are entered in the ANN and with this, it is possible to obtain the three adjustment constants. The neural structure makes PID control more stable and with a better answer. The neural structure, used in this system, has three layers with two neurons in the input layer, three neurons in hidden layer and three neurons in output layer. The activation functions used are: sigmoidal to first two layers and a lineal function for the third layer. ANN Expected velocity + _
AC Motor
PID control
Sensed velocity
Encoder
Figure 2: Model of the control system.
The neuronal model is implemented in the control of AC motor, by using a Digital Signal Processing (DSP) as an implementation system, an encoder as an angular velocity sensor and a power stage by synchronized pulses. The input system is the sensed velocity by encoder. The control algorithm delivers a level of comparison which is used by Pulse Weight Modulate (PWM) technique. This level of comparison let to PWM controls the revolutions of the motor.
CONCLUSIONS The ANN development gives us new ideas for to solve problems and for to make better systems. The second order ANN presents better performances than multi-layer perceptron, because of a second order ANN has a no-lineal net function and perceptrons uses a lineal one. Nevertheless, a no-lineal function is more complex, so that, it needs more computing time. The implemented system shows an optimum answer, it has a better rise time, setting time and steady state error. This system is embedded which means that it is independent of the programming platform.
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REFERENCES 1. Katsuhiko Ogata. Modern Control Engineering. Prentice Hall, Inc. 4ª. Edition. 2002. 2. William Bolton. Control Engineering. Addison Wesly Longman Limited. 2ª. Edition. 2001. 3. Mohammad Teshnehlab and Keigo Watanabe. Intelligent Control Based on Flexible Neural Networks. Kluwer Academic Publishers. Netherlands. 1999. 4. Yu Hen Hu y Jenq-Nenq Hwang. Handbook of Neural Network Signal Processing. CRC Press. 2002. 5. López-Aligue, Francisco, Acevedo-Sotoca, Isabel, Valle, Montserrat, Jaramillo-Moran, Miguel,”A General Higher Order Neural Model”, IEEE International Conference of Neural Networks, Vol. 3, 1994, p. 1525-1526. 6. Young, S., Downs, T., “Generalisation in Higher Order Neural Networks”, Electronics Letters, Vol. 29, No.16, 1993, p. 1491-1492. 7. Lippman, Richard P., “An Introduction to Computing with Neural Nets”, IEEE ASSP Magazine, Abril 1987, pp. 45, 49.
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