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Sliding Mode Tracking Controller For Hydraulic Robot Manipulators With Numerical Analysis

Syarifah Zyurina Nordin1, Haszuraidah Ishak2, J.H.S Osman2
1Department of Mathematics, Faculty of Science

2Department of Mechatronics & Robotics, Faculty of Electrical Engineering

Universiti Teknologi Malaysia

This abstract is concerned with the problems controlling the electrohydraulic robot manipulators. The control of electrohydraulic robot manipulator is challenging due to the dependence of system parameters on variables such as displacement and velocity, on the geometry and inertia of the links, uncertainties associated with gravity, coriolis and centrifugal forces, variations in payload handled by the manipulator, and environmental influences. To overcome these problems, the variable structure control (VSC) strategy will be utilized to overcome the inherent high nonlinearity in their dynamics under centralized frameworks. In the approach, a variant of the VSC known as the Sliding Mode Control (SMC) was adopted to ensure the stability of the system dynamics during the sliding phase and to render that the system insensitive to the parametric variations and disturbances. The performance and robustness of the proposed controller is evaluated through computer simulation by using Matlab and Simulink. The parameter governing the hydraulic robot manipulators have been studied through forth-order Runge-Kutta (RK4) and extrapolation method. The desired state trajectory of the system representing the three joints of a robot have been compared with the corresponding state vector at different time intervals using the above mentioned RK4 and extrapolation method. The system’s error dynamics during sliding mode also have been determined between the desired and corresponding state trajectory. Well composed comparison has been carried out with the aid of the obtained results and graphs. The results prove that the controller has successfully provided the necessary tracking control for the 3 DOF electrohydraulically driven robot manipulator system


Dynamic Geometry: Theory and Practice
Robert L. Pour
Department of Mathematics, Emory & Henry College, Emory, Virginia 24327, U.S.A

This paper gives an overview of the pedagogical foundations supporting the use of software to teach geometry. The “The Van Hiele Model of Geometric Thought” is the principle model. Activities are discussed which demonstrate this model and reinforce the “constructivist” approach to teaching and leaning. Examples are provided using the Software Cinderella. The theoretical basis Cinderella construction is briefly discussed.


Biomechanical Analyses of Two Lumbar Vertebrae Implanted with an Artificial Disc (IVD)
A. K. Mohammed Rafiq & W.H. Wan Mohd Musyris
Biomechanics and Tissue Engineering Research Group (Bio-TEG), Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

Lower back pain is normally related to the degeneration of the spinal intervertebral discs (IVD) due to the natural process of aging. Even though conservative treatments are normally sought after, in some severe cases surgery would be the only solution to alleviate pain and prevent mechanical instability. Lumbar pack pain can be surgically treated either through arthrodesis or arthroplasty. Arthrodesis consists of surgical immobilization or fusion of the joint, whilst arthroplasty consists of implantation of an artificial disc between the vertebrae. The objective of this study was to analyses, using finite element method, the biomechanics of two lumbar vertebrae treated with an artificial intervertebral disc. A three dimensional model of lumbar vertebrae was created from CT datasets of L3. The model was then used to create a two level lumbar segment with a normal healthy IVD. Another model was created where the IVD is replaced with an artificial IVD to simulate total disc replacement (TDR). The artificial IVD consists of two endplates made of metal which is separated by a polyethylene liner with dome structure on both sides to allow rotation of the endplates. The material properties of the bone were obtained from the CT datasets Hounsfield unit, and pressure was applied on the top vertebra. The results showed that the artificial IVD exerted more stress to the vertebrae, reducing the cushioning effect of an intact healthy IVD. The differences observed between the biomechanics of surgically treated and intact IVD were associated with the geometrical and surgical features of the devices.


Biological Classifiers for Problem Solving
Siti Maryam Shamsuddin
Soft Computing Research Group, Research Management Center,

Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

The structure of HUMAN BODY (cells, emotion, perception, etc) and living organism have inspired the creation of human intelligence, and sparks a lot of research in solving complex problems. These nature creations have introduced the concept of Biological Inspired Computing (BIC) by the Scientist. BIC is an area of investigation that draws upon methaphors or theoretical models of biological systems in order to design computing machines that could allow the creation of new machines with promising characteristics, such fault-tolerance, self replication, reproduction, evolution, adaptation and learning, and growth. BIC plays a significant role in the area of pattern recognition in a variety of engineering, and scientific disciplines such a biology, psychology, medicine, marketing, computer vision, artificial intelligence, and remote sensing. In this paper, we present few examples of in-house BIC techniques that have been implemented in the areas of Computer Science. These include the enhancement of identifying the individuality of document authors, abnormality of stock market behavior with Artificial Immune System (AIS), and hyper sausage neuron that uses the principle of homology-continuity to take optimal cover of distribution of one kind of samples in feature space in Biomimetic Pattern Recognition.

Keywords: Biologically Inspired Computing; Artificial Immune System; Brain-Inspired System; Biomimetic Pattern Recognition.


Newton-Kaczmarz Methods for Reconstruction of Electrical Impedance Tomography with Multiple Measurement Data: A Numerical Result
Agah D. Garnadi
Department of Mathematics, Institut Pertanian Bogor, Indonesia

We report numerical results on reconstruction of Electrical Impedance Tomography from multiple measurement data. The basic algorithm for reconstruction we use Newton-Kaczmarz, as a combination of Iteratively Regularized Gauss Newton algorithms which is have a good theoretical behavior for non-linear inverse problem; and projection method, i.e. Kaczmarz methods, to reduce memory requirement during reconstruction. We utilize two-level refinement from coarse to finer triangulation to reduce segmentation effect in the case of coarse triangulation. The triangulation refinement fully adapted using a-posteriori error estimation.


Students’ Approach on Delivering A Simple and Alternative Euclidean Division Algorithm
Mohd Sulhi1, Azniah2, Noraishiyah2, Tuan Salwani2 & Siti Mistima2
1Student, Industrial Automation and Networking Section;

2Mathematics Unit, General Studies Section; Universiti Kuala Lumpur Malaysia France Institute

Section 14, Jalan Teras Jernang 43650 Bandar Baru Bangi, Selangor Darul Ehsan, Malaysia

Consider the two polynomials defined by and where . If we divide by , i.e. , then, there exist a quotient and remainder; denoted by and respectively. This can later be written as . This relationship is found by using long division algorithm or factor theorem. However, there exists an alternative algorithm called Euclidean Division Algorithm (EDA). This is not to be confused with Euclidean Algorithm where it is used to find the greatest common factor of two natural numbers or two polynomials. The EDA is a special set of algorithm used in determining the result of two polynomials dividing each other. In other words, EDA is an alternative method to that of a long division. This method later develops the remainder and the factor theorem. The algorithm presented in this paper is quite different to that to the algorithm of long division; however, it produces the same result if the long division method was used. There have been numerous proofs on verifying that the EDA works properly. However, this paper will discuss the alternative proof on EDA in a simple and not-so-complicated language. Examples on implementing the EDA method as prescribed in this paper are also included.

Keywords: Euclidean Division; EDA; Factor Theorem and Long Division


Cardinality of the Sets of Solution to Congruence Equation Associated with a Seventh Degree Form
Siti Hasana Sapar & K.A Mohd Atan
Laboratory of Theoretical Mathematics, Institute for Mathematical Research,

Universiti Putra Malaysia

The exponential sum associated with is defined as

where the sum is taken over a complete set residues modulo and let be a vector in the space with Z ring of integers and be a positive integer, a polynomial in with coefficients in Z.

The value of has been shown to depend on the estimate of the cardinality, the number of elements contained in the set where is the partial derivative of with respect to .

This paper will give an explicit estimate of for polynomial in of degree seven based on the p-adic Newton polyhedron technique associated with the polynomial. The seventh degree polynomial is of the form

The estimate obtained is in terms of the p-adic sizes of the coefficients of the dominant terms in.


On Higher Order Analogues of the RSA Cryptosystem
Mohamad Rushdan Md. Said
Institute for Mathematical Research, University of Putra Malaysia,

43400 Serdang, Selangor, Malaysia.
In this paper, we investigate and review public-key cryptosystems which are derived from higher order linear recurrence relation which are based on the Lucas function. The RSA scheme is based on hard mathematical problem, the intractability of factoring large integers. This application of a hard mathematical problem to cryptography revitalized efforts to find more efficient methods to factor. The first motivation to develop a new cryptosystem analogous to RSA is the possibility that the higher order analogues are more secure than the RSA. The explicit formulation involves a generalization of the Euler Totient function, which underlie the algebra of the RSA cryptosystem.
Keywords: Public-key Cryptosystem; Quartic Polynomial; Resolvent Cubic Polynomial; Lucas Sequence; Euler Totient Function.


Effect of Control on the Onset of Marangoni-Bénard Convection with Uniform Internal Heat Generation
Norfifah Bachok, Norihan Md Ariffin & Fadzillah Md. Ali
Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia.

The effect of control on the onset of Marangoni-Bénard convection in a horizontal layer of fluid with internal heat generation heated from below and cooled from above is investigated. The resulting eigenvalue problem is solved exactly. The effects of control are studied by examining the critical Marangoni numbers and wave numbers. It is found that the onset of Marangoni-Bénard convection with internal heat generation can be delayed through the use of control.


Modeling of Concentration and Capacity Profile of Solid Diffusion in Lithium-Ion Cell
Siti Aishah Hashim Ali
Institute of Mathematical Sciences, Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

In the effort to produce high performance batteries, mathematical model has become a vital tool in helping batteries developers to understand the behavior of the battery systems during charge, discharge and relaxation. In this work, a mathematical model of a lithium-ion (Li+) cell under the solid phase diffusion limitation is presented. The model equation is used to derive the Li+ concentration and the capacity profiles under galvanostatic discharge. Two cases are being considered. In first case, the active material is considered to be thin film of thickness 2 (where  >> the height of the film) with both sides exposed to the electrolyte, while in the second case, the active material is

considered to be spherical of radius R.


Maximum Density Effects on G-Jitter Induced Free Convection between Vertical Plates Heated and Asymmetrically
Sharidan Shafie1, Norsarahaida Amin1 & Ioan Pop2
1Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

2Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania.

The effect of g-jitter induced free convection in the fluids at the temperature of the maximum density in microgravity is considered. The problem is studied under a simple system consisting of two heated vertical parallel infinite flat plates held at constant but different temperatures. The governing equations are solved analytically for the induced velocity and temperature distributions. Graphical results for the velocity profile of the oscillating flow in the channel are presented and discussed for various parametric physical conditions such as the wall temperature parameter, and oscillating frequency, . It has been found that these parameters affect considerably the velocity of the flow.


Analysis of a Dengue Disease Transmission Model without Immunity
Yusuf Yaacob
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia,

81310 Skudai, Johor Malaysia

A transmission model for dengue fever is discussed in this paper. Restricting the dynamics for the constant host and vector populations, and also with no immunity to the disease, the model is reduced to a two-dimensional planar system. In this model the endemic state is stable if the basic reproduction number of the disease is greater than one. For a relatively small series of outbreaks of the disease in population sufficiently large for the number of susceptible to remain effectively constant, the model is reduced to a population model for the group of infectives.


Time-Dependent Generation Of Fluid Motion Along A Channel By A Traveling Magnetic Field
Mohd Noor Saad
Department of Mathematics, Faculty of Science, University Putra Malaysia,

Serdang, Selangor, Malaysia
A two dimensional multi Fourier-component magnetic field is moved at a uniform velocity along a closed channel filled with an incompressible conducting fluid. Induced currents in the fluid interact with the field to give a Lorentz force which drives fluid motion. Under the assumption of small magnetic Reynolds number and a small magnetic interaction parameter the time-dependent fluid flow is investigated. In the case of a two Fourier-component source an analytical expression for the source term is derived and it is shown that for effective stirring the width of the channel has to be at most equal to the wavelength of the applied magnetic field. For the case of multi-Fourier component source numerical methods were used and it is shown that four vortices could be obtained


Numerical Solutions Of The One-Dimensional Shallow Water Equations
Salemah Ismail1, Zainal Abd. Aziz2, Mohd Nor Mohamad3 & Nazeeruddin Yaacob4

1Center for Mathematical Studies, Faculty of Information Technology & Quantitative Sciences,

Universiti Technologi MARA, 40450 Shah Alam, Selangor , Malaysia

2,3,4Department of Mathematics, Faculty of Science, University Technology Malaysia, 81310 Skudai, Johor, Malaysia
A numerical model of the one-dimensional shallow water equations is developed to simulate the propagation of water waves above slopes of constant inclination. The discretization of the internal grid points is based on the Lax-Richtmyer finite difference scheme. The values of the surface elevation and the fluid velocity at the left and right boundaries are estimated using the left-running and right-running Riemann invariants. The results showed an increase in wave amplitude as waves run into shallower water. The model is then extended to the case of a stepwise change in the water depth.
Keywords: Shallow water equations; Finite difference

Computer Based Assessment in Engineering Mathematics: A Case Study
Maya Pundoor & Ramadas Narayanan
1Lecturer in Mathematics, Curtin University of Technology, Sarawak Campus, Malaysia

2Lecturer in Mechanical Engineering, Curtin University of Technology, Sarawak Campus, Malaysia.
There are different kinds of assessments, which are suitable for Engineering Mathematics. The developments in Computer Based Education have been driven by advances in Instructional Technology and the increased capability of the technology to respond to the needs of students. Ensuring that the assessment methods adopted reflect both the aims and objectives of the course and any technical developments which have taken place is becoming increasingly important, especially as quality assurance procedures require departments to justify the assessment procedures adopted. Here in this paper, the current form of assessment for the subject Engineering Mathematics is described and critically evaluated its effectiveness as a formative and then as a summative form of assessment. An alternative form of assessment to accompany your new instructional approach is devised. The new form of assessment is compared with the old form, in terms of its effect on the students, and its validity as a measure of mastery of the curriculum topic. The new form of assessment is implemented, evaluated as assessment instrument, identified strengths and recommended improvements in the light of new experience.
Keywords: Computer Based Assessment; Engineering Mathematics.


Oblique Stagnation Slips Flow of a Micropolar Fluid
Lok Yian Yian1, Norsarahaida Amin2, Ioan Pop3

1, 2Department of Mathematics, Universiti Teknologi Malaysia,

81310 UTM Skudai, Johor, Malaysia

3Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253, Romania

This paper considers the problem of steady two-dimensional boundary layer flow of a micropolar fluid near an oblique stagnation point on a fixed surface with slip condition. It is shown that the governing partial differential equations admit exact similarity solutions. The resulting nonlinear ordinary differential equations are solved numerically using the Keller’s box method for some values of the governing parameters. It is found that the flow characteristics depend heavily on the micropolar and slip parameters.


The Important of Statistical Orientation for Quality Improvement in Automotive Parts Manufacturing and Supply in Malaysia
Muzalwana Abdul Mutalib
Department of Applied Statistics, Faculty of Economy and Administration, Universiti Malaya

With intense competition at the regional and global marketplaces, issue on quality and cost is no longer a compromise to automotive suppliers. Quality and reliability is the surviving factor for long term participants in the supply chain of major vehicle manufacturers. This paper aims to review the general quality practices of Malaysian automotive suppliers and the deployment of statistical knowledge, training and understanding are the root cause to low statistical application as quality tools and techniques. Well drawn trainings are needed in these areas. While previous studies mainly probe into the Total Quality Management (TQM) implementation as quality framework, this paper highlights the paramount importance of statistical thinking as a roadmap in the pursuit of quality excellence of these Malaysian automotive suppliers. With the need to build up the image of stringent quality automotive parts so as to increase competitiveness, it is apt for the Malaysian automotive suppliers to integrate the statistical tools and techniques such as Statistical Process Control and Designed Experiments into their quality management practice.

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