Study on Adaptive PID Control Algorithm Based on RBF Neural Network

TELKOMNIKA Indonesian Journal of Electrical Engineering
Vol. 13, No. 2, February 2015, pp. 287 ~ 291
DOI: 10.11591/telkomnika.v13i2.6958  287
Received November 3, 2014; Revised December 19, 2014; Accepted January 2, 2015
Study on Adaptive PID Control Algorithm Based on
RBF Neural Network
Qi Xuemei，Zhang Jingdong
School of Transportation and Automobile Engineering, Panzhihua University,
Panzhihua, 617000, China
Abstract
Aim at the limitation of traditional PID controller has certain limitation, the traditionalPID control is
often difficult to obtain satisfactory control performance, and the RBF neural networkis difficult to meet the
requirement ofreal-time control system.To overcome it, an adaptive PID control strategy based on (RBF)
neural network isproposed in this paper. The resultsshow that the proposed controller is practical and
effective, because of the adaptability, strong robustness and satisfactory controlperformance.It is also
revealed from simulation results that the proposed control algorithm is valid for DC motor and also
provides the theoretical and experimental basis.
Keywords: adaptive PID controller, RBF neural network, DC motor
Copyright © 2015 Institute of Advanced Engineering and Science. All rights reserved.
1. Introduction
PID controllers are the most common industrial process controller, its structure is
simple, good robustness and high reliability, and the PID controller is widely used industrial
process control [1].
However, the conventional PID controller has a certain limiting, especially
the controlled object contains a nonlinear and time-varying characteristics,the traditionalPID
control is often difficult to obtain satisfactory control performance [2]. Since the parameters
empirical formula of PID controller is proposed by the Ziegler andNiehols, and the many
methods have been used for the parameter setting of the PID controller. With the development
of intelligent control theory, the intelligent control technology was introduced in PID control by
many scholars, and provided new method means for the PID controltechnology.In recent years,
the artificial neural network has been used in complex process control, and has attracted
widespread attention [3, 4]. Because the neural network has adaptive learning, parallel
processing and the strong ability of fault tolerance.The neural network adaptivePID control
scheme which is locally approximated by the RBFnetworkis adopted in this paper, and in order
to improve the system accuracy, robustness and adaptiveness [5].
2. RBF function
The Radial Basis Function (RBF) is a neural network which was put forward by
J.Moodyand C.Darken in the late 1980s, it is a three layer feed forward network with single
hidden layer (Figure 1), is a kind of local approximation of the neural network. The RBFis a kind
of three layer forward network. The mapping which is from the input to the output is nonlinear,
and the mapping which is from hidden layer space to the output space is linear [6]. It simulates
the neural network structure for the partial adjustment of the human brain and each receiving
domain. RBF is a kind of local approximation network, which has been proved that the any
precision approximates any continuous function. This kind of network characteristics is that it
onlyhas a few output of connection power influence aim at local input space, so that local
approximation network has the advantages of fasterlearning speed [7]. Therefore, the RBF
network can significantly accelerate the learning speed and avoid local minimum problem, which
is suitable for the real-time control.

 ISSN: 2302-4046
TELKOMNIKA Vol. 13, No. 2, February 2015 : 287 – 291
288
Figure 1. Three layer feed forward network with single hidden layer
In the structure of RBF network, 1 2[ , , ]T
nX x x x  is the input vector of network.
Assuming the radial basis vectors of the RBF network is 1 2[ , , ]T
nH h h h  . Where jh
isgaussian basis function:
2
2
exp( ), 1, 2, .
2
j
j
j
X C
h j m
b

    (1)
The j network node of center vector is , 1 2 , ,[ , , ]T
i j j j i j n jC c c c c   . Assuming the
basis width vector of network is 1 2[ , , ]T
mB b b b  , jb is the basis width parameter of node, and
is greater than zero. The weight vector of network is 1 2[ , , ]mW w w w  .The output of the
network is given as:
1 1 2 2( )m m my k wh w h w h w h     (2)
Assuming the ideal output is ( )y k , the performance index function is:
21
( ) ( ( ) ( ))
2
mE k y k y k  (3)
Based on the gradient descent method, the iterative algorithm of output power, node center and
base width parameterare:
( ) ( 1) ( ( ) ( )) ( ( 1) ( 2))j j m j j jw k w k y k y k h w k w k         (4)
2
3
( ( ) ( ))
j
j m j j
j
X C
b y k y k w h
b

   (5)
( ) ( 1) ( ( 1) ( 2))j j j j jb k b k b b k b k         (6)
, 2
( ( ) ( )) j ji
j i m j
j
x c
c y k y k w
b

   (7)
( ) ( 1) ( ( 1) ( 2))ij ij ij ij ijc k c k c c k c k         (8)
Where  is learning rate, is momentum factor.

TELKOMNIKA ISSN: 2302-4046 
Study on Adaptive PID Control Algorithm Based on RBF Neural Network (Qi Xuemei)
289
Jacobian matrix algorithm is as follows:
1 1
2
1
( )( )
( ) ( )
m
jm
j j
j j
c xy ky k
w h
u k u k b

 
 
 (10)
Where 1 ( )x u k .
3. Design of Adaptive PID Controller Based on the BRF Neural Network
There are many function form of RBF neural network, Gauss function was selected
inthis article as the hidden layer node function according to its unique advantages [8]. Based on
the RBF neural network, the adaptive PID control system structure is as shown in Figure 2.
Neural network adaptive PID controller adjusts the connection weights of neural network NN
and the three parameters of PID according to the square error of the given input and system
outputas the objective function [9]. The PID controller is applied to the controlled object, and
makes the system output close to the given input of system.
Figure 2. Adaptive PID Controller based on the BRF neural network
The control error of PID controlleris given as following:
( ) ( ) ( )error k rin k yout k  (11)
The three inputs of PID is given following as:
(1) ( ) ( 1)xc error k error k   (12)
(2) ( )xc error k (13)
(3) ( ) 2 ( 1) ( 2)xc error k error k error k     (14)
Control algorithm is given as:
( ) ( 1) ( )u k u k u k    (15)
( ) ( ( ) ( 1)) ( )
( ( ) 2 ( 1) ( 2))
p i
d
u k k error k error k k error k
k error k error k error k
   
    
(16)
Where , ,p i dk k k arethe proportion, integral and differential parameters respectively.
The tuning index of neural network is selected as:
21
( ) ( )
2
E k error k (17)
The gradient descent method is used for adjustment of , ,p i dk k k .

 ISSN: 2302-4046
TELKOMNIKA Vol. 13, No. 2, February 2015 : 287 – 291
290
( ) (1)p
p p
E E y u y
k error k xc
k y u k u
  
    
     
    
(18)
( ) (2)i
i i
E E y u y
k error k xc
k y u k u
  
    
     
    
(19)
( ) (3)d
d d
E E y u y
k error k xc
k y u k u
  
    
     
    
(20)
The
y
u


can be obtained by the identification of neural network.
4. Simulation
In this section, using the PID control principle based onRBF neural networkmakes
simulationfor DC motor in MATLAB. Parameters of the system for simulation are:KP=0.3,
KD=0.3, KI=0.1,the transfer function of the DC motor is:
2
103
( )
15
G s
s s


(21)
Where the sampling time is 2ms, the input signal is step signal, network hidden layer
neurons number is m = 6.The Figure 3 shows the square wave response curve without the
adaptive setting PID control strategy based on RBF neural network. The Figure 4 shows the
square wave response curve with the adaptive setting PID control strategy based on RBF
neural network. The Figure 5, Figure 6 and Figure 7 reflect the process of PID parameter
adjustment. From the simulation curve we can see that the adjusted online PID controller based
on the RBF neural network has good control effect, and the control effect comparing simple
PIDis greatly improved. This shows that aim at the controlled object which has nonlinear and
time-varying parameter, the algorithm has trace ability and anti-interference ability.
Figure 3. The step signal without the adaptive
settingPID based on RBF NN
Figure 4. The step signal with the adaptive
setting PID based on RBF NN

TELKOMNIKA ISSN: 2302-4046 
Study on Adaptive PID Control Algorithm Based on RBF Neural Network (Qi Xuemei)
291
Figure 5. The adaptive setting curve of ki Figure 6. The adaptive setting curve of kp
Figure 7. The adaptive setting curve of kd
5. Conclusion
In this paper, based on RBF neural network adaptive PID control strategyis proposed
for the DC motor. The results show that the proposed controller is practical and effective,
because of the adaptability, strong robustness and satisfactory control performance. RBFNeural
network adaptive PID controller achieved good control effect. It is also revealed from simulation
results that the proposed control algorithm is valid for DC motor and also provides the
theoretical and experimental basis, and the controller is a kind of practical engineering.
References
[1] Li Lixiang, Peng Haipeng, Wang Xiangdong. PID parametertuning based on chaotic ant swarm.
Chinese Journal ofScientific Instrument. 2006; 27(9): 1104-1106.
[2] KH Ang, G Chong, Y Li. PID Control System Analysis, Design and Technology. IEEE Trans. on
Control SystemTechnology. 2005; 13(4): 559-576.
[3] Li Yuying, Wen Qiaoyan, Li Lixiang, Peng Haipeng, Zhu Hui. Improved chaotic ant swarm algorithm.
Chinese Journal of Scientific Instrument. 2009; 30(4): 733-737.
[4] ZHI Hui-qiang, YANG Zeng-jun, TIAN Liang. AComparative Study on BP Network and RBF Networkin
Function Approximation. Bulletin of Science andTechnology. 2005; 21(2):193-196.
[5] Xia Hong. A fast identification algorithm for box-coxtransformation based radial basis function neural
network. IEEE Transactions on Neural Networks. 2006; 17(4): 1064-1069
[6] ZHAN Li, SUN Peng, CHEN Wen-bai. Control of SwingUp and Stabilization of an Inverted Pendulum
System. Computer Simulation. 2006; 23(8): 289-292
[7] CONG Shuang, ZHANG Dong-jun, WEI Heng-hua.Comparative Study on Three Control Methods of
theSingle Inverted-Pendulum System. SystemsEngineering and Electronics. 2001; 23(11): 47－49
[8] Zhang Jingdong, Wen Guang, Wei Yongqiao, Yin Guofu. RBF Neural Network PID for Bilateral Servo
ControlSystem. TELKOMNIKA. 2013; 11(9): 5200-5209
[9] Liu Jinkun. MATLAB Simulation with Advanced PID Control. Publishing House of Electronics Industry,
Beijing. 2011.

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