Page 1

A HYBRID TECHNIQUE FOR

FREQUENCY DOMAIN

IDENTIFICATION OF SERVO SYSTEM

WITH FRICTION FORCE

SHAIK.RAFI KIRAN,

Research Scholar,

JNTUniversity College of Engineering,Anantapur

Dr.S.SIVA NAGARAJU,

Assoc Professor,

JNTUniversity College of engineering,Kakinada

Dr.S.VARADARAJAN

Assoc Professor,

SVUniversity College of engineering,Tirupathi

Abstract

The system identification process in servo system with frictional force seems to be a complex task because

of its non-linear nature. For such non-linear systems, a good choice is system identification in frequency

domain. However, most of the techniques are manual and are inappropriate for determination of system

parameters. This makes system identification ineffective for servo systems with frictional force. To

overcome this issue, a hybrid technique is proposed in this paper. The proposed technique exploits neural

network and genetic algorithm to determine the system parameters of servo systems with friction. In the

proposed technique, the target parameters are determined from the transfer function derived for the

system. Subsequently, the system parameters are identified by a process formed by blending the neural

network and genetic algorithm techniques. Prior to performing the identification procedure, back

propagation training is given to the neural network using a pre-examined dataset. Then with the

combined operation of neural network and genetic algorithm, the system parameters that are closer to

the target parameters for the servo system with frictional force are determined. The technique is

implemented and compared with the existing frequency domain identification technique. From the

comparative results, it is evident that the proposed technique outperforms the existing technique.

Keywords: Frequency domain, servo system, friction, identification, system parameters

1. Introduction

System identification process uses measured input-output to estimate a model for capturing system

dynamics [11] [16]. Extracting mathematical models from physical systems is the objective and process of

system identification [2] [4]. System identification models can be constructed for diverse stages and the control

system can be supported by optimally choosing their outputs [1]. Recently, several applications such as acoustic

echo cancellation, channel equalization, biological system modeling and image processing have shown great

interest in nonlinear systems identification [3].

Some nonlinearity exists in hydraulic servo systems because of friction force [8]. Due to the capability

of servo systems to serve huge driving forces and quick responses they are commonly employed in the position

control of friction [6]. In high precision systems that achieve high-resolution movements by commonly

employing transmission mechanisms, position dependent friction occurs [7]. Hence, friction has an influence on

all regimes of operations of a servo system [9].

Friction is one of the most significant drawbacks in high precision servo systems [5]. The frictional

force may be defined as the resistance experienced by a substance in moving on top of another [12] [14]. The

Shaik.Rafi Kiran et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462Vol. 3 No. 3 March 20112020

Page 2

friction force depends on the velocity and period of contact [13]. The influence of friction force on servo-

systems is remarkable particularly at low velocity motion [15].

Generally, the frequency domain model of nonlinear systems can be represented using transfer function

[17]. A waveform is analyzed with regard to the diverse frequency components existing in the waveform by the

frequency domain method [18]. The output of nonlinear system can be constructed using the frequency domain

analysis of linear system [10]. The output frequency component is different from the input frequency component

for nonlinear system [20]. Frequency domain system identifications assume the input and output signals to be

periodic or time restricted within the observation time [19].

In most of the works, frequency domain identification of servo system with friction force is controlled

by the transfer function. The control techniques of such plants are ineffective, because the transfer function

target parameters of the plant are determined at random and the friction force is manually selected. So the

determined parameters are inappropriate and selection of friction force takes considerable time. To overcome

this issue, in this paper, we propose a hybrid technique for servo system identification in the frequency domain.

The rest of the paper is organized as follows. Section 2 gives a brief review of the recent research works and

Section 3 discusses about the model of a servo system. Section 4 details the proposed technique with required

mathematical and pictorial illustrations. Section 5 discusses about the implementation results and Section 6

concludes the paper.

2. Recent Research Works: A Review

A plenty of research works that deals with system identification are available in the literature. Among

them, a handful of significant works are reviewed briefly in this section.

Madhusudan Singh et al. [21] have discussed the significant issue of using neural network for the

identification and control of nonlinear dynamical systems. Based on the neural network model, they have

created a method to compute the system parameters for the derivation of system dynamics of non linear system

in an easier manner compared to other techniques invented so far. The updated parameters of the system to tune

the controller suitably have been obtained using a learning algorithm. Moreover, through simulated results, the

system stability obtained by their method has been shown to be superior to that obtained by other available

networks.

J. Fernandez de Canete et al. [22] have discussed that the graphical programming language, LABVIEW

has its roots in automation control and data acquisition. They have offered a powerful toolset based on artificial

neural networks (ANN) for process identification and control of nonlinear systems utilizing this platform. A lab-

scale distillation column DELTALAB DC-SP has been monitored and controlled by employing this tool. Both,

high speed of response and null stationary error have been provided by the proposed control scheme for

variations in set points and dual composition control respectively. Moreover, the proposed control scheme has

confirmed its robustness in the existence of externally forced disturbances.

Shaik Rafi Kiran et al. [23] have described the system identification use of the discrete wavelet

transform (DWT). A test excitation that also serves as the analyzing function for the DWT of the output of the

system under test (SUT) has been used to achieve identification of the (SUT). Any signal that yields an

orthogonal inner product in the DWT at some step size other than unity has been used as excitation by the

method. They have preferred to use the wavelet scaling coefficients with a step size of 2 as excitations. Yet, a

multirate problem which necessitates to ‘over sample’ the SUT output has been introduced, because the system

impulse or frequency response can then be calculated only at half the existing number of points of the sampled

output sequence. Some of the numerous advantages of the proposed method over available methods have

included the utilization of simple, easy to create excitation and prevention of singularity problems and the

(unbounded) buildup of round-off errors that can happen with accepted methods. Compared to traditional

system identification methods, the identification of diverse finite and infinite impulse response systems by the

proposed system has been proved to be considerably superior by extensive simulations.

Mao Xin-tao et al. [24] have analyzed a pneumatic rotary position servo system in which a rotary

cylinder is controlled by an electro-pneumatic flow proportional valve. Feed forward compensation pole-

placement self-tuning strategy has been adopted to improve the dynamic performance of the system. The

controller because of its superior ability to assess the system parameters in real-time has been capable of

enhancing the system performance and reducing the impact of factors that have not been taken into account in

the system models. Thus the robustness of parametric anti disturbance of the controller system has been good.

The starting stage controlled system output has not been stable because of the impact of the initial parameters of

Shaik.Rafi Kiran et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462 Vol. 3 No. 3 March 20112021

Page 3

the controller system. On account of the convergent tendency of the adaptive control system parameters, the

output of the system has a tendency to be stable in the steady working state. The proposed method has other

merits such as fast convergence and high efficiency.

Chee Khiang Pang et al. [25] have developed a modal parametric identification method for linear-time-

invariant flexible mechanical systems to assess residues, damping ratios, and natural frequencies of resonant

modes. Two consequent least squares error optimization principle in modal summation structure has been

utilized to optimize the coefficients and residues of the transfer function model. Experimental frequency

responses measured by a laser doppler vibrometer from a commercial dual-stage hard disk drive has been used

to prove the proposed methodology. Their results have confirmed that the proposed system identification

algorithm was both effective and robust in estimating the modal parameters of adjustable mechanical constructs

in mechatronic systems.

Kemao Peng et al. [26] have proposed a modeling and compensation of friction and nonlinearities of a

conventional voice-coil-motor (VCM) actuator employed in popular HDDs, and an improved nonlinear control

technique based design of an HDD servo system. Their contribution has been two-fold: first by inspecting the

configuration and structure of the original system thoroughly and by means of a careful analysis of its physical

influence along with its time-domain and frequency- domain responses they have obtained a comprehensive

model for the VCM actuator encompassing friction and nonlinear characteristics. Then they have used an

improved blended nonlinear feedback (CNF) control method with a simple friction and nonlinearity

compensation strategy to design a servo system for the hard drive. The important role of the enhanced CNF

technique has been to eliminate the uncompensated part of friction and nonlinearities without compromising the

overall tracking performance. Their method has been shown to be very effective and successful by simulation

and experimental results for both the modeling and the servo design. Specifically, their experimental results

have shown that the conventional proportional-integral-derivative (PID) control has been outperformed by the

improved CNF control in settling time by 76%. They have believed that other servomechanism problems could

be solved by adopting this approach.

Nuij et al. [27] have proposed a novel measurement method based on non-parametric frequency

domain that permits obtaining the stick to gross sliding transition of a mechanical system with dry friction. The

method has extended the Sinusoidal Input Describing Function theory (SIDF) to Higher Order Describing

Functions. The magnitude and phase of the higher harmonics in the periodic response of the non-linear system

has been related to the magnitude and phase of a sinusoidal excitation using the obtained Higher Order

Sinusoidal Input Describing Functions (HOSIDF). Both the classical Frequency Response Function (FRF)

technique and the newly developed HOSIDF technique have been used to analyze a non-linear mechanical

system with dry friction. The third order SIDF has clearly displayed the stick/sliding transition of the system in

case the FRF technique failed to identify it. The pre-sliding displacement of the system has been determined

from the third order SIDF. Information about the resonance frequency of the system caused by the friction-

induced stiffness has been generated using the first order SIDF. The friction force that must be presented in the

stick-phase has been evaluated from the pre-sliding displacement and the friction-induced stiffness. Force

measurements validation has shown outstanding conformity.

3. Servo System Model

Normally a plant, an actuator and some driving circuits are present in a servo system. The plant is

driven by the actuator and both the components can be modeled as a second order transfer function. However,

the system can be simplified as shown in Fig 1. In such servo system, static friction and coloumb friction are the

two components. Fig 2 shows the modeling of friction force in servo systems in which

friction and

blocks as depicted in Fig 3.

sF and

s F are the static

c F and

c F are the coloumb friction. The system [2] can be decomposed into linear and non-linear

Figure 1: Block diagram of simplified system with friction

Shaik.Rafi Kiran et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462Vol. 3 No. 3 March 2011 2022

Page 4

Figure 2: Velocity versus friction force

Figure 3: Decomposed block diagram of servo system with friction

The plants to be identified are always assumed to be linear by the traditional frequency-domain identification

methods that are based on covariance analysis and Fourier transform. But, this assumption is almost always

invalid because of the presence of friction. Because, a plant can be represented by a linear block that describes

the system dynamics in the feed forward path and a nonlinear block that describes the friction in the feedback

path [2].

4. The Hybrid System Identification Technique

The proposed hybrid technique for frequency domain identification of servo systems with friction incorporates a

blend of GA and neural network. The system identification technique comprises of (i) Determination of target

parameters and (ii) Identification of system parameters. Let

system with friction. From

G s , pole and constant are determined and fixed as target parameters along with

target DC gain and span of coloumb friction force. The target parameters can be represented

as

[ ]

TTTTT

PPPPP

, where,

T

N is the total number of target parameters and

is the

j target parameter. Based on the target parameters, the system parameters are identified using neural

network and GA. To perform this, the technique includes two major stages, namely, training of neural network

and determining system parameters using GA. The stages are described below.

G s be the ideal transfer function of the servo

( 1)

(0)(1)(2)

T

N

( ) j

TP

: 01

T

jN

th

4.1. Training of Neural network

Prior to performing the task of identifying the system parameters, the neural network needs to be trained well

using the BP algorithm. A pre-examined dataset is obtained from [2] and it is used as the training dataset D for

neural network. The dataset D is comprised of input excitation magnitude as input and the system parameters,

poles, constants, DC gain, minimum friction force and maximum friction force. The dataset D can be

represented as

0

1

1

2

1

P

T

N

P

P

m

m

D

(1)

where,

structure of neural network designed as per the dataset is shown in Fig 4.

1

m and

2

m are the higher and lower excitation magnitudes and

jP is the system parameters. The

Shaik.Rafi Kiran et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462 Vol. 3 No. 3 March 20112023

Page 5

Figure 4: The structure of multi-layer feed forward neural network utilized in the proposed technique.

Step 1: Assign arbitrary weights generated in the interval

output layer neurons. Assign unity value weights to each neuron of the input layer.

min max

,

ww

to the hidden layer neurons and the

Step 2: Determine the BP error by giving the training dataset D as input to the classifier as follows

T out

ePP (2)

In Eq. (2),

The elements of

TP is the target output, and the network output

P can be determined from every output neuron of the network as follows

out

P can be calculated as

0121

[

P P P

]

T

outN

PP

.

out

1

H

N

j iji

i

P w y (3)

where,

12

12

1 exp(

) 1 exp(

)

ii

i

ww

y

mm

; 1

H

iN (4)

In Eq. (3)

the

i

H

N is the number of hidden neurons,

jP is the output from

th

j output neuron and

ij

w is the weight of

j link of the network. In Eq. (4),

iy is the output of

thi hidden neuron.

Step 3: Determine the change in weights based on the obtained BP error as follows

.P .

out

we

(5)

In Eq. (5), is the learning rate, usually it ranges from 0.2 to 0.5.

Step 4: Determine the new weights as follows

www (6)

Step 5: Until BP error gets reduced to a least value, repeat the process from step 2. Essentially, the condition to

be satisfied is 0.1

e

.

The network gets well-trained when the process is completed. When the input excitation magnitude is given,

proper system parameters are provided by the well trained network.

4.2. Determining system parameters using GA

GA is one of the popular evolutionary algorithms and it is utilized to determine the optimal system parameters

for a given input excitation magnitude. The processes that are performed to accomplish this are described below.

(i)

Chromosome Generation: Create

p

N

numbers of random chromosomes,

( )

0

( )

1

x

aa

a

Xx

;

0,1,,1

p

aN

in the interval

minmax

,

MM

, in such a way that it would comply with the

condition

( )

0

( )

1

x

aa

x

. i.e.

( )

a

minmax

,

bxMM

;

1,2.

b

where

( )

0

a

x

and

( )

1

x

a

are the two genes of

Shaik.Rafi Kiran et al. / International Journal of Engineering Science and Technology (IJEST)

ISSN : 0975-5462Vol. 3 No. 3 March 2011 2024