RDU 080314

THE DEVELOPMENT OF EMBEDDED INPUT SHAPING TECHNIQUES FOR

VIBRATION CONTROL OF FLEXIBLE MANIPULATOR SYSTEM

(PEMBINAAN TEKNIK PEMBENTUKAN INPUT TERBENAM UNTUK

KAWALAN GETARAN BAGI SISTEM FLEKSIBEL MANIPULATOR)

MOHD ASHRAF BIN AHMAD

AHMAD NOR KASRUDDIN NASIR

NASRUL SALIM PAKHERI

NOR MANIHA ABDUL GHANI

MOHD ANWAR ZAWAWI

NURUL HAZLINA NOORDIN

RESEARCH VOTE NO:

RDU080314

Fakulti Kejuruteraan Elektrik dan Elektronik

Universiti Malaysia Pahang

2010

UMP/RMC/LA.IIO7

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PUSAT PENGURUS$T PENYELIDIKAN (RMC)

BORANG PENGESAHANI.APORAN AKHIR PEIVYELIDIKAN

TAJUK PROJEK: THE DEVELOPMENT OF EMBEDDED INPUT SHAPING TECHNIQUESFOR VIBRATION CONTROL OF FLEXIBLE MANIPULATOR SYSTEM

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ABSTRACT

THE DEVELOPMENT OF EMBEDDED INPUT SHAPING TECHNIQUES FOR

VIBRATION CONTROL OF FLEXIBLE MANIPULATOR SYSTEM

(Keywords: Embedded system, input shaping, vibration control)

This project presents investigations into the applications and performance of

embedded input shaper in command shaping techniques for vibration control of a

flexible manipulator. A constrained planar single-link flexible manipulator is considered

and the dynamic model of the system is derived using the assume mode method. An

unshaped bang-bang torque input is used to determine the characteristic parameters of

the system for design and evaluation of the input shaping control techniques. In order to

investigate real-time implementation of the controllers, the embedded input shaping is

programmed in PIC microchip and tested to the flexible manipulator model in Matlab.

The investigation results of the response of the manipulator to the shaped inputs are

presented in time and frequency domains. The performance of the controllers in real-

time are investigated in terms of the level of vibration reduction and time response

specifications.

Key researchers : Mohd Ashraf Ahmad, Ahmad Nor Kasruddin Nasir, Nasrul Salim

Pakheri, Nor Maniha Abd. Ghani, Mohd Anwar Zawawi, Nurul Hazlina Noordin

E-mail : mashraf@ump.edu.my

Tel. No. : 094242070

Vote No. : RDU080314

iii

ABSTRAK

PEMBINAAN TEKNIK PEMBENTUKAN INPUT TERBENAM UNTUK

KAWALAN GETARAN BAGI SISTEM FLEKSIBEL MANIPULATOR

(Kata Kunci: Sistem terbenam, pembentukan input, kawalan getaran)

Projek ini mempersembahkan penyelidikan berkenaan aplikasi dan tahap

kecekapan teknik pembentukan input terbenam untuk kawalan getaran bagi system

fleksibel manipulator. Sebuah sistem fleksibel manipulator satu cabang telah

dikenalpasti dan system model dinamik telah diterbitkan menggunakan kaedah mod

anggapan. Satu input bang-bang tanpa pembentukan telah digunakan untuk menentukan

ciri-ciri sistem parameter untuk mereka dan menilai teknik kawalan pembentukan input.

Bagi menyelidik perlaksanaan masa sebenar kawalan tersebut, pembentukan input

terbenam telah di programkan di dalam mikrocip PIC dan di uji terhadap model fleksibel

manipulator di dalam Matlab. Hasil penyiasatan sambutan manipulator tersebut terhadap

pembentukan input telah dipersembahkan dalam domain masa dan domain frekuensi.

Tahap kecekapan kawalan dalam masa sebenar telah disiasat dan difokus kepada

pengurangan tahap getaran dan spesifikasi sambutan masa.

Key researchers : Mohd Ashraf Ahmad, Ahmad Nor Kasruddin Nasir, Nasrul Salim

Pakheri, Nor Maniha Abd. Ghani, Mohd Anwar Zawawi, Nurul Hazlina Noordin

E-mail : mashraf@ump.edu.my

Tel. No. : 094242070

Vote No. : RDU080314

iv

TABLE OF CONTENTS

CHAPTER TITLE Page

TITLE PAGE i

ABSTRACT ii

TABLE OF CONTENTS iv

LIST OF TABLES vi

LIST OF FIGURES vii

LIST OF APPENDICES ix

CHAPTER 1 INTRODUCTION 1

1.1 Introduction 1

1.2 Objective 3

1.3 Scope of project 4

1.4 Problem statement

5

CHAPTER 2 LITERATURE REVIEW 7

2.1 Introductions 7

2.2 Review of dynamic modeling system 8

2.3 Review of input shaping method 8

2.4 Summary 11

CHAPTER 3 METHODOLOGY 12

v

3.1 Overview 12

3.2 The flexible manipulator system 14

3.3 Modeling of the flexible manipulator 16

3.4 Positive input shaping 18

3.5 Hardware design 22

3.5.1 Microcontroller module 22

3.5.2 FTDI module

25

CHAPTER 4 RESULTS AND DISCUSSION 27

4.1 Implementation 27

4.2 Unshaped bang-bang torque input 28

4.3 Positive input shaper 32

4.4 PIC embedded with positive input shaper 39

4.5 Comparative assessment 41

4.5 Summary 48

CHAPTER 5 CONCLUSION AND RECOMMENDATION 49

5.1 Conclusion 49

5.2 Recommendation 50

REFERENCES 51

APPENDIX A 53

APPENDIX B 60

APPENDIX C 63

APPENDIX D 64

APPENDIX E 67

APPENDIX F 80

vi

LIST OF TABLES

TABLE NO. TITLE PAGE

4.1 Rise time and settling time of unshaped bang-bang torque

input

36

4.2 Rise time and settling time of positive with different order

derivative

36

4.3 Rise time, settling time and overshoot for hub-angle in

embedded positive input shaping

45

vii

LIST OF FIGURES

FIGURE NO. TITLE PAGE

3.1 The block diagram input shaping control configuration 13

3.2 Block diagram input shaping control configuration for next

session

14

3.3 Description of flexible manipulator 15

3.4 PIC18 memory bus structure 23

3.5 Internal architecture of PIC18 24

3.6 Connection between FTDI and PIC microcontroller 25

3.7 The overview of FTDI RS232RL basic breakout board 26

3.8 FTDI schematic diagram 26

4.1 Input shaping control configuration block diagram 28

4.2 Illustration of input shaping technique 28

4.3 Unshaped bang-bang torque input for time domain 29

4.4 Unshaped bang-bang torque input for PSD of the end point

acceleration

29

4.5 Response of the flexible manipulator to the unshaped bang-

bang torque input

30

4.6 Unshaped bang-bang torque input and shaped bang-bang

torque with positive ZV, ZVD, ZVDD shapers.

33

4.7 End-point displacement in time domain 34

viii

4.8 PSD of unshaped and shaped bang-bang torque input 35

4.9 End-point residual in time domain 35

4.10 Response of the flexible manipulator to the shaped with

PZV, PZVD, PZVDD

36

4.11 Rise and settling time of hub angle response using positive

inputs shaping

38

4.12 Comparison graph of result in embedded positive input

shaping and matlab simulation

39

4.13 PSD of embedded positive input shaping and matlab

simulation with different order of derivation

42

4.14 End-point acceleration of embedded positive input shaping

and matlab simulation in different order of derivation

44

4.15 Comparison in embedded positive input shaping and

matlab simulation with different order of derivation for

hub-angle

46

4.16 Rise and settling time of the hub-angle using maltab

simulation and embedded positive input shaping

47

ix

LIST OF APPENDICES

APPENDIX TITLE PAGE

A Software development source code 53

B PIC18LF14K50 Datasheet 60

C PIC18LF14K50 Block diagram 63

D PIC programmer tools PICkit2 user’s guide 64

E Conference Proceedings 67

F Equipment Submission Form and Preliminary IP

Screening Form

80

CHAPTER 1

INTRODUCTION

1.1 Introduction

Flexible manipulator is finding an increasing number of applications especially

in automation and manufacturing industries. Robots that were once used to pock and

place work pieces are now being used in more complex tasks such as assembling and

working at unmanned places.

Flexible robot manipulators exhibit many advantages over rigid robots; they

required less material, are lighter in weight, consume less power, require smaller

actuators, are more maneuverable and transportable, have less overall cost and higher

payload to robot weight ratio. However, the control of flexible manipulator to achieve

and maintain accurate positioning is challenging. Due to the flexible nature of the

system, the dynamic are significantly more complex. Problem arises due to precise

positioning requirements, system flexibility which leads to vibration, the difficulty in

2

obtaining an accurate model of the system and non-minimum phase characteristics of the

system. In this respect, a control mechanism that accounts for both rigid body and elastic

motion of the system is required. If the advantages associated with lightness are not to

be sacrificed, accurate models and efficient controllers have to be developed.

Control of machines that exhibit flexibility becomes important when designers

attempt to push the state of the art with faster and lighter machines. Many researchers

have examined different controller configurations in order to control machines without

exciting resonances. However, after designing a good controller, the input commands to

the closed-loop system are “desired” trajectories that the controller treats as disturbances.

Often these “desired” trajectories are step inputs or trajectories that the machine cannot

rigidly follow. The considered vibration control schemes can be divided into two main

categories: feed forward and feedback control technique.

Active vibration controls of slewing flexible structures, such as the flexible

robotic manipulator system, have experienced rapid growth in recent years. Most of the

attention has been focused on eliminating vibrations that result in the structure when

control applied. The vibration of flexible manipulator or system often limits speed and

accuracy. The vibration of such manipulator or system is usually caused by changes in

the reference command or from external disturbance. If the system dynamics are known,

Commands can be generated that will cancel the vibration form the system’s flexible

modes. Accurate control of flexible structures is an important and difficult problem and

has been an active are of research book.

This paper presents investigations into the application and performance of input

shaping control schemes with positive input shapers for vibration control of a single-link

flexible manipulator. Moreover this paper provides a comparative assessment of the

performances of these schemes. The results of this work will be helpful in designing

3

efficient algorithms for vibration control of various systems. The Zero Vibration (ZV)

shaper is the basic shaper, and constraint the vibration to zero at the modeling frequency.

To increase robustness to parameter variations, the order of derivative or higher, of

residual vibration constraints of ZV shaper is also constrained to zero to yield what are

known as Zero Vibration Derivative (ZVD) shaper. In this work, input shaping with

positive input shaping (ZV to ZVDD) is considered. The dynamic model describing the

motion of the flexible manipulator is derived using the assume mode method.

Experimental exercises are performed within the flexible manipulator simulation

environment. First, to obtain the characteristic parameter of the system, the flexible

manipulator is excited with a single-switch bang-bang torque input. Then the input

shapers are designed based on the properties of the manipulator and used for

preprocessing the input, so that no energy is fed into the system at the natural

frequencies. Performances of the developed controller are assessed in term of level of

vibration reduction, time response specifications and robustness to errors in vibration

frequency. Experimental results in time and frequency domains of the response of the

flexible manipulator to the unshaped input and shaped inputs with positive are presented

and discussed.

4

1.1 Objective

The objective of this study:

i. To develop an embedded input shaping for vibration control of a flexible

manipulator system.

ii. To study the dynamic characteristic of the flexible manipulator in order to

construct the control method for vibration reduction.

iii. To investigate the performance of higher derivative order of input

shaping.

1.2 Scope of project

The scope of project is divided into 6 parts. The first part is study the dynamic

model. In this part, we are using the assume mode method. Assume mode method looks

at obtaining approximate modes by solving the partial differential equation (PDE)

characterizing the dynamic behavior of the system. The goal in the modeling of a

flexible manipulator system is to achieve an accurate model representing the actual

system behavior. This is very important part of the research in order to design a good

controller for the system.

The second part is developed the positive input shaping algorithm. These project

present investigations into the application and performance of input shaping control

schemes with positive input shapers for vibration control of a single-link flexible

5

manipulator. In third part of project are simulation studies. Simulation is performed with

bang-bang torque and smooth displacement driven maneuvers. Validation of a dynamic

model for use in experimental work is an important step before implement the controller.

PIC controller study is one of the parts in the project scope. PIC controller will

be designed and programmed algorithm with bang – bang input and positive input

shaping with different derivative orders. The fifth part of the project scope is analyzing

the results. Performances of the shapers are examined in terms of level of vibration

reduction and time response specifications. The performance of the positive input

shapers with different derivative order will be investigated and the results are examined

in comparison to the unshaped bang-bang torque input for similar input level in each

case. The last part is verifying the simulation results. The results of the simulation will

be compared and analyzed with the results of embedded positive input shaping using

PIC for vibration control of flexible manipulator.

1.3 Problem statement

Manipulator arms have traditionally been designed to have rigid links to ensure

stable and reliable control. Minimum vibration and good positional accuracy are

achieved by maximizing the stiffness of the system. Normally heavy material is used,

because to design a stable system. Due to the heavy material is used, its course the rigid

link manipulator are usually large and massive. As a consequence, such robots are

usually heavy with respect to the operating payload. The drawbacks of this large and

massive robot manipulator are limitation of the operation speed, the increase of the size

of actuators and higher energy consumption.

6

Flexible manipulator is exhibit several advantage over the disadvantages of rigid

link manipulator. However, flexible manipulator also occur several problems, example

difficult to maintain the accurate positioning and the dynamic are highly non-linear and

complex. This problem arise due to precise positioning requirements, system flexibility

leading to vibration, the difficulty in obtaining accurate model of the system and non-

minimum phase characteristics of the system. If the advantages associated with lightness

are not to be sacrificed precise models and efficient control strategies for flexible

manipulators have to be developed.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

One of the present challenges in the reduction of the vibration in flexible

manipulator is in determining the desired input pattern with minimum vibration. The

vibration is a concern of virtually every engineering discipline and mechanical engineers

continually face the problem of vibration because mechanical systems vibrate when

performance is pushed to the limit. The typical engineering solutions to vibration are to

design stiff systems. Add damping to flexible system, or develop a good controller.

Input shaping is another possibility for vibration that can supplement methods.

8

2.2 Review of dynamic modeling of flexible manipulator system

An investigation into the dynamic modeling of flexible manipulator systems with

different mechanical structures and actuation mechanisms is presented by J.M.Martins,

Z.Mohamed, and M.A Botto [1]. Dynamic models of the system are developed based on

the assumed method considering linear displacements, quadratic displacements and the

finite element method. Simulation and experimental exercise are performed with bang-

bang torque and smooth displacement driven maneuvers is shown. By using the assumed

modes approach, one can find the transfer function between the torque input and the net

tip deflection. This is the approach currently used by most researches (David Wang and

M. Vidyasagar). David Wang and M.Vidyasagar shown that, when the number of modes

is increased for more accurate modeling, the relative degree of the transfer function

becomes ill-defined. This can greatly affect the performance of a controller designed

using this model. An alternate approach is proposed which uses the rigid body

deformation minus the elastic deformation as the output [2].

2.3 Review of input shaping method

Input shaping improves response time and positing accuracy by reducing residual

vibrations in computer controlled machines. The method requires only a simple system

model consisting of simple estimates of the natural frequencies and damping ratio. Input

shaping is implemented by convolving a sequence of impulses an input shaper, with a

desired system command to produce a shaped input that is then used to drive the system.

9

An early form of input shaping was the use of posicast control by smith (1958)

[3]. This technique breaks a step of certain amplitude into two smaller steps, one which

is delayed in time. The result is a reduced settling time for the system. optimal control

approaches have also been used to generate input profiles for commanding vibratory

systems. Junkins et al.(1986) and Chun et al. (1985) have also made considerable

progress towards practical solutions of the optimal control formulation for flexible

systems [4]. Gupta and Narendra (1980), and Junkins et al. (1986) have included some

frequency shaping terms in the optimal formulation [5]. Farrenkopf (1979) has

develpred velocity shaping techniques for flexible spacecraft [6]. Swigert (1980)

demonstrated that torque shaping modeling decomposes into second order harmonics

oscillators [7].

Mohamed and Tokhi (2003) have presented experimental investigations toward

the development of feed-forward control strategies for vibration control of a flexible

manipulator using command shaping techniques based on input shaping, low-pass an

bang-pass filtering. An unshaped bang-bang torque input is used to determine the

characteristic parameter of the system for designed based on the natural frequencies and

damping ratios of the system. The performance and effect of number of impulse

sequences (two-impulse and four-impulses) and filter orders are assessed, in term of

level of vibration reduction at resonance modes, speed of response, robustness and

computational complexity [1].

An approach is commend-shaping techniques known as input shaping has been

proposed by singer and co-workers which are currently receiving considerable attention

in vibration control. Since its introduction, the method has been investigated and

extended. The method involves convolving a desired command with a sequence of

impulse known as input shaper. The shaped command that results from the convolving is

used to drive the system.

10

A hybrid input shaping method to reduce the residual swing of a simple

suspended object transported by a robot manipulator or the residual vibration of

equivalent dynamics system has been presented by Sadettin et al [8]. However, input

shaping does not deal with vibration exited by external disturbance. Thus, vibration

absorbers and input shaping are designed concurrently to reduce vibration from both

reference command and external sources. The usefulness of this combined approach for

dealing with both external and reference command disturbances is demonstrated through

computer simulation by Fortgang and Singhose ( 2002 ) [9]. Kai and David (1992) have

designed a controller based on the inverse dynamic of the rigid manipulator and have

used a closed-loop shaped-input filter to reduce or eliminate the vibration of the flexible

link and to reject external disturbance [10]. Magee et al.(1997) have combined command

shaping and inertial damping to control small robot that are attached to the end of the

flexible manipulator. Experimental exercises have been demonstrated to prove that

command shaping guarantees that the level of the vibration will be minimized during

complete robot motion [11].

Several investigations have been conducted on input shaping since its original

presentation by Singer and Seering (1989) [12]. A method for increasing the

insensitivity to modeling error has been presented by Singhose et al. (1990) [13]. A new

input shaping method that allows the range of system parameter values is to be weighed

according to the expected modeling errors has been proposed. Comparisons with

previously proposed input shaper designs in term of shaper length, frequency

insensitivity, and expected level of residual vibration are presented by Lucy et al and

Singhose. (1997) [14]. Input shapers can be made insensitive to parameter; however,

increasing insensitivity usually increases system delays. A design process that generates

input shapers with insensitivity to time delay ratios that are much larger than

traditionally designed input shapers is presented by Singhose. Technique for designing

the impulse sequence for two mode system are presented and compared as a function of

mode ratio. Hyde and Seering (1991) have shown the effective input shaping for

multiple mode systems [15].

11

S. S. Gurleyuk and S. Cinal [16] presented an unsophisticated method for tuning

the amplitudes and time locations of a three-impulse sequence input shaper. The method

helps to solve the insufficient constraint equations directly. The impulse amplitudes can

be produced without additional derivative constraints. It is also shown that a more robust

input shaper can be obtained using the new algorithm by S.cinal [16].

A method and device for controlling and damping undesirable movement within

flexible linkage of a robot arm coupled to a movable, controlled joint and attached drive

motor is presented by Warren F. Philips, logan, Utah [17]. The method includes the

steps of providing position displacement and control in accordance with position and

velocity feedback input. A control algorithm develops deflection feedback signals

proportional to the deflection signal and its first two time derivatives, each multiplied by

a gain whose value is selected to reduce further elastic deflection.

2.4 Summary

After considering the review papers on the vibration control of the flexible

system using the input shaping method, most of the methods use observation from the

simulated or experimental dynamic characteristic of the flexible system. Then, using the

dynamic characteristics of the system, the amplitude and the time location of the

impulses are determined to design the shaped input. The shaped input needs to redesign

once the dynamic system changes due to load disturbance changes. Although the shaped

input is quite robust to certain limit of variations in natural frequencies, the system needs

to be re-simulated to observe and determine the new amplitude and the time location of

the impulse sequences.

CHAPTER 3

METHODOLOGY

3.1 Overview

The block diagram of input shaping control configuration is shown in Figure 3.1.

Simulation exercise is performed within the flexible manipulator simulation

environment by using the Matlab7.5® simulation software. Initially, the bang-bang

torque input is excited to the flexible manipulator system to obtain the characteristic

parameter of the system. The dynamic model describing the motion of the flexible

manipulator is derived using the assume mode method. After the investigation of the

bang- bang torque input’s characteristic is done, the flexible manipulator is excited with

the shaped bang-bang input by using positive input shaping technique in the next

procedure. The input shapers are designed based on the properties of the manipulator

and used for processing the input.

13

Shaped

input

Figure 3.1: The block diagram input shaping control configuration.

A significant number of the positive shaper for vibration control has also been

investigated. These include positive zero vibration derivative (PZVD) shaper and

positive zero vibration derivative (PZVDD). Simulation results in time and frequency

domain of the response of the flexible to the unshaped input and shaped input with

positive shaping technique are presented.

Figure 3.2 shows the block diagram of input shaping control configuration for

the embedded implementation. The bang-bang torque input and positive input shaping

algorithm is programmed on the PIC microcontroller. The positive input shaping

technique consists of positive zero vibration (ZV) shaper, positive zero vibration

derivative (ZVD) shaper and positive zero vibration derivative-derivative (ZVDD)

shaper. The PIC board is connected to the computer desktop by interfaced with FTDI

USB serial board. The study is repeated from the initial step by using the positive input

shaping algorithm in PIC. Then, the experimental result with embedded input shaping is

compared with the simulation result.

Input

shaper

The flexible

manipulator

Output

response

Bang-bang

input

PC

simulation

14

Shaped

input

Figure 3.2: The block diagram input shaping control configuration for next session.

3.2 The flexible manipulator system

A description of the single-link flexible manipulator system considered in this

work is shown in Figure 3.3, where {O and {O X Y } represent the stationary and

moving coordinates frames respectively, s represents the applied torque at the hub. E, I,

p, A, r, and represent the Young modulus, area moment of inertia, mass density

per unit volume, cross-sectional area, hub inertia, radius and payload mass of the

manipulator is confined to the {O } plane.

The rotation of {O X Y } relative to frame {O } is described by the angle θ.

The displacement of the link from the axis OX at a distance x is designated as υ (χ, t).

Since the manipulator is long and slender, transverse shear and rotary inertia effects are

neglected. By using the Bernoulli-ruler beam theorem to model the elastic behavior of

the manipulator. The manipulator is assumed to be stiff in vertical bending and torsion,

allowing it to vibrate dominantly in the horizontal direction and thus, the gravity effects

are neglected. Moreover, the manipulator is considered to have constant cross-section

and uniform material properties throughout. This project is using aluminum type flexible

Input

shaper

The flexible

manipulator

Output

response

Bang-bang

input

PIC PC simulation

15

manipulator system as the modeling model. The dimension of this model is

900 19.008 3.2004 , Young Modulus, E is 7 N/ , Area moment of

inertia, I is 5.1924 , mass density per unit volume, is 2710 kg/ and hub

inertia, is 5.8598 kg is considered. A simulation algorithm characteristic

the dynamic behavior of the manipulator has previously been developed using the

assume mode method. This is used in this work as a platform for test and evaluation of

the proposed control approaches.

Figure 3.3: Description of flexible manipulator

16

3.3 Modeling of the flexible manipulator

The modeling of a flexible manipulator is a basic simulation environment for

development and assessment of the input shaping control techniques [18]. A simulation

environment is developed within Simulink and Matlab for evaluation of the control

strategies. In this project, dynamic model of the flexible manipulator is derived using the

assume mode method. The assume mode method with two modal displacement is

considered in characterizing the dynamic behavior of the manipulator incorporating

structural damping.

The kinetic energy of the system should be formulated as equation (3.1), because

the system must consider revolute joints and motion of the manipulator on a two-

dimensional plane.

(3.1)

Where x , and is the beam rotation inertia about the origin

as if it were rigid. The potential energy U of the beam can be formulated as

(3.2)

The potential energy due to gravity is negligible because only motion in the plane

perpendicular to the gravitational field is considered.

To obtain a closed-from dynamic model of the manipulator, the energy

expressions in (1) and (2) are used to formulate the Lagrangian L = T – U. Assembling

17

the mass the stiffness matrices and utilizing the Euler-Lagrange equation of motion, the

dynamic equation of motion of the flexible manipulator system can be obtained as

(3.3)

Where the D, K, M are the damping, stiffness matrices and global mass of the

flexible manipulator respectively. The damping matrix is obtained by assuming the

manipulator exhibit the characteristic of Rayleigh damping. is a vector of external

forces and Q(t) is a modal displacement vector given as

(3.4)

Where is the modal amplitude of the i th clamped free mode considered in the

assume modes method procedure and n represents the total number of assumed modes.

The uncontrolled system can represented as

(3.5)

With the vector and the matrices A and B are given by

(3.6)

By substituting all the values, the parameters of the flexible-link state space model can

be gained as follow,

18

5154.46334002.0014755467.16290

786.7455541.2010257311.08.217000

14.3418681.7010135271.08.61750

100000

010000

001000

7

7A

8429.23

74.1128

24.1173

0

0

0

B

000111C 0D

(3.7)

3.4 Positive input shaping

In this development, the input shaping method is used to reduce vibration in the

flexible manipulator system. This is a feed-forward control technique where by the

system command is convolved with a sequence of impulse to produce a shaped input

that is then used to drive the system.

The input shaping method involves convolving a desired command with a

sequence of impulses. The design objectives are to determine the amplitude and time

location of the impulse. A vibratory system of any order can be modeled as

superposition of second order systems with a transfer function:

19

(3.8)

where ω is the natural frequency and ζ is the damping ratio of the system. Thus, the

impulse response of the system can be obtained as:

(3.9)

where A and are amplitude and the time of impulse respectively. Furthermore, the

response to a sequence of impulse can be obtained by superposition of the impulse

response. Thus, for N impulse, with , the impulse response can be

expressed as

(3.10)

where

and

where and are the amplitude and times of the impulses

20

The residual single mode vibration amplitude of the impulse response is obtained

at time of the last impulse, as

(3.11)

where

(3.12)

To achieve zero vibration after the last impulse, it is required that both and

in equation (3.11) are independently zero. Furthermore, to ensure that the shaped

command input produces the same rigid body motion as the unshaped command, it is

required that the sum of amplitudes of the impulse is unity. To avoid response delay, the

first impulse is selected at time . Setting the derivatives to zero is a derivative to

zero is equivalent to producing small changes in vibration corresponding to the

frequency changes. The order of derivatives of and and set them to zero.

For the case of avoid the problem of large amplitude impulses, each individual

impulse must be less than one to satisfy the unity magnitude constraint. Hence by setting

and in equation (3.11) to zero, . And solving this yields to a two

impulse sequence with parameters such as

21

(3.13)

where

(3.14)

The robustness of the input shaper to error in natural frequencies of the system

can be increased by setting = 0, where is the rate of change of with

respect to . Setting the derivative to zero is equivalent of producing small changes in

vibration with corresponding changes in the natural frequency. Thus, additional

constraints are incorporated into the equation, which after solving, yields three impulse

sequences with parameter as

(3.15)

where K is as in equation (3.14)

The positive ZVDD input shaper is obtained by setting equation (3.11) and ,

to zero and solving with the other constraint equations. Hence a four impulse

sequence can be obtained with the parameters as

(3.16)

22

where K as in equation (3.14)

To handle higher vibration modes, an impulse sequence for each vibration mode

can be designed independently. Then, the impulse sequence can be convolved together

to form a sequence of impulse that attenuates vibration at higher modes.

3.5 Hardware design

In this section, the circuit connection of each module is discussed. The circuit

connection of each module is explained elaborately which include the architecture,

operations, functionality and features of each device. The hardware design is consists of

serial communicator module and Microcontroller module. The system board is designed

based on the requirement of this project.

3.5.1 Microcontroller Module

A microcontroller is as programmable digital component that incorporates the

functions of a central processing unit (CPU) on a single semiconducting integrated

23

circuit (IC). It is much smaller and simplified so that it can include all the function

required on a single chip.

PIC18F14K50 USB Flash Microcontrollers is chosen as embedded tools in this

project. This PIC18 family offers the advantages of namely, high computational

performance at an economical price. It also with the additional of high-endurance, flash

program memory. This PIC microcontroller features a full speed USB 2.0 compliant

interface that can automatically change clock sources and power level upon connection

to host, making it an exceptional device for low power applications. On top of these

features, the PIC18 family introduces design enhancements that make this

microcontroller a logical choice for many high performances, power sensitive

applications. It is very suitable application in this project as an embedded algorithm

function.

This PIC microcontroller contain large number of data storage which is 16kB for

program memory and 768 bytes is for data memory. It is able to embedded a complex

positive input shaping algorithm into program memory of PIC microcontroller. Figure

3.4 shows the relationship between CPU, the bus, and the memory system. Note that

every address bus is unidirectional, which means that data on the address bus goes one

way, from CPU to memory space. On the other hand, the bidirectional data may be

writen to or read from memory.

24

Figure 3.4: PIC18 memory bus structure

Figure 3.5 shows the connection bus of bidirectional between each module,

which is include timer, I/O ports, analog to digital converter, serial port and other

peripherals. The timer in this achitecture can opearate as either a timer or a counter.

There are three ports available in this microcontroller. Some pin of the I/O are

multiplexed with an alternate function form the peripheral features on the device. The

analog to digital converter(ADC) of PIC18 is allow conversion of an analog input signal

to a 10 bit-binary represntation of that signal. PIC18LF14K50 microcontroller include

several other features, such as oscillator selection, interrupts and universal serial bus

peripheral.

25

Figure 3.5: Internal architecture of PIC18

This module is the core module of the project. This module consists of

PIC18LF14K50 and the FTDI chip. The microcontroller contain a full speed, compatible

USB serial interface engine. That allows PIC embedded with positive input shaping

algorithm can be fast communication with USB host. FTDI module is used to interface

device between the USB host and PIC microcontroller. The FTDI module have a

internal power circuit, which able to share power from USB hub to the microcontroller

and FTDI chip. The connection of FTDI and microcontroller is shown in Figure 3.6.

26

Figure 3.6: The connection between FTDI and PIC microcontroller

3.5.1 FTDI RT232RL module

Figure 3.7 shows the overview of FTDI RS232RL basic breakout board. FTDI

chip RS232RL is a type of USB UART interface integrated circuit devices which able to

do asynchronous serial data transfer interface to PIC microcontroller. Since the cost and

the size of circuit board is very limited, so the complete set basic breakout board for the

FTDI FT232RL was chosen. The breakout board is included with the voltage regulator

and clock circuit. It also has TX and RX LEDs that make user to indicate serial traffic on

the LEDs to verify if the board is working or not. The pin out of this board is connected

to microcontroller, such as the power 3.3V, ground, pin RX and pin TX. The schematic

diagram of FTDI breakout board is shown in Figure 3.8.

27

Figure 3.7: The overview of FTDI RS232RL basic breakout board

Figure 3.8: FTDI schematic diagram

CHAPTER 4

RESULTS AND DISCUSSION

4.1 Implementation

The input shapers were designed for pre-processing the bang-bang torque input

and applied to the system in an open loop configuration, as shown in Figure 4.1. These

convolution technique acts like a low pass or band stop filter in the system, thus, cancels

the vibrations in the system. In this work, modeling is done using assume mode method.

The obtained impulse sequences will be combined and convolved with the desired input

(bang-bang torque) to generate a shaped input as shown in Figure 4.2. In this work, the

unshaped and the shaped inputs were designed with a sampling frequency of 1 kHz.

Simulation results of the response of the flexible manipulator to the unshaped input,

shaped input with positive input shapers are presented in this section in time and

frequency domain.

28

Figure 4.1: Input shaping control configuration block diagram.

Figure 4.2: Illustration of input shaping technique

4.2 Unshaped bang-bang torque input.

In this work, the unshaped bang-bang torque input of amplitude ±0.3 Nm is used

as a reference command. The single switch bang-bang torque used as the input to the

system is shown in Figure 4.3. To determine the characteristic of flexible manipulator,

the bang-bang torque input should have positive and negative period to allow the

manipulator to, initially, accelerate and then decrease and eventually, stop at the original

position. The maximum magnitude for the power spectral density (PSD) of the end-point

acceleration for the unshaped bang-bang input in this system as shown in Figure 4.4 is

1128 at 16 Hz and 7758 at 56 Hz.

Input

shaper

Flexible

Manipulator

Bang-bang

torque input

Output

Response

Shaped

input

29

Figure 4.3: The unshaped bang-bang torque input.

Figure 4.4: The unshaped bang-bang torque input for PSD of the end-point acceleration.

30

The hub-angle, hub-velocity, end-point acceleration and end-point displacement

response show that a significant vibration occurs during the movement of the flexible

manipulator. The steady-state hub-angle of 0.66 rad for the flexible manipulator was

achieved within the rise and settling times of 443 ms and 817 ms respectively.

The endpoint acceleration response was found to oscillate between -497.5 m/s² to

704 m/s² whereas the hub-velocity response shows oscillation between -4.336 rad/s and

7.536 rad/s. The final value of the end-point displacement is obtained at 0.6628 rad.

These results were considered as the system response to the unshaped input and will be

used to evaluate the performance of the input shaping techniques. The response of the

flexible manipulator to the unshaped bang-bang torque input is shown in Figure 4.5.

(a) Hub-angle

31

(b) End-point acceleration

(c) Hub-velocity

32

(d) End-point displacement

Figure 4.5: Response of the flexible manipulator to the unshaped bang-bang torque input.

4.3 Positive input shaper

The shaped inputs using positive ZV, ZVD and ZVDD shapers with exact natural

frequency are shown in Figure 4.6. It can be noticed from Figure 4.6 that with higher

number of impulses, more energy is extracted from the original input.

33

(a) Unshaped bang-bang input (b) Shaped with zero vibration

(c) Zero vibration derivative (d) Zero vibration derivative-derivative

Figure 4.6: Unshaped bang-bang torque inputs and shaped bang-bang torque with

positive ZV, ZVD, ZVDD shapers.

Figure 4.7 shows the response at the end-point displacement of the flexible

manipulator system. The transient response of shaped input control is smoother compare

to bang-bang torque input control and further smoother using higher derivative but

slower response. The steady state response of the shaped input control is better than the

bang-bang torque control.

34

The shaped input control performs similar to critically damped and the bang-

bang torque control performs similar to under damped. The oscillation in bang-bang

torque input control delays the system to achieve the desired location accurately.

Figure 4.7: End-point displacement in time domain

The power spectral density (PSD) of the end-point acceleration is evaluated to

investigate the dynamic behavior of the system. Resonance frequencies of the system

were obtained by transforming the time domain representation of the system responses

into frequency domain using power spectral analysis. The PSD of bang-bang torque

input and shaped input with different order derivative positive input shaping as shown in

Figure 4.8. It can be observed that, the magnitudes of the PSD at the natural frequencies

were reduced effectively as the number of impulse increased.

35

Figure 4.8: PSD of unshaped and shaped bang-bang torque input

Figure 4.9 shows the end point residual response of the system. It is noted that

vibratory response from the bang-bang torque input occurs due to resonance modes of

the system. The end-point residue response is improved using input shaping technique

but results in a slower response by using higher order derivative input shaping.

Figure 4.9: End-point residual in time domain

The system responses of the flexible manipulator to the shaped bang-bang torque

input with exact natural frequencies using the positive shapers are shown in Figure 4.10.

36

Figure 4.10(a) shows the response of the hub-angle of the flexible manipulator system.

The bang-bang response has vibratory trajectory, while the input shaping has smooth

angle increment response. Figure 4.10(b) shows the response at the hub-velocity of the

flexible manipulator system. It is notice that the hub-velocity increase smoothly during

the movement of the manipulator and decreases smooth when the manipulator is stopped

at the desired position. The bang-bang input torque results the manipulator to moves and

stops fast at the desired position, causing vibration in the flexible manipulator. However,

the considerable amount of vibration is reduced using positive input shaping technique

and further smoother using higher order derivative. Similar to Figure 4.10(c), the

vibration in the end-point acceleration response was significantly reduced.

(a) Hub-angle

37

(b) Hub-velocity

(c) End-point acceleration

Figure 4.10: The response of the flexible manipulator to the shaped with PZV, PZVD,

PZVDD

38

Tables 4.1 and 4.2 summarize the rise time, settling time and overshoot of the

hub-angle response by the unshaped bang-bang torque input, positive ZV, positive ZVD

and positive ZVDD shaped input respectively. Figure 4.11 show the rise and settling

time of the hub-angle response in a bar graph. It is noticed that the positive ZVDD

shaper is the slowest system response compare with another positive input shaping in the

table. Hence, it is evidence that the speed of the system response reduced with the

increase in the number of impulses.

Table 4.1: Unshaped bang-bang torque input

Input Rise time (s) Settling time (s) Overshoot (%)

Unshaped bang-

bang torque input

0.443 0.817 0.049

Table 4.2: Positive input shaping with different derivative order

Type of shaper Rise time (s) Settling time (s) Overshoot (%)

Positive ZV 0.418 0.827 0.403

Positive ZVD 0.431 0.854 0.060

Positive ZVDD 0.438 0.871 0.050

Figure 4.11: Rise and settling time of the hub angle response using positive inputs

shaping

39

4.4 PIC embedded with positive input shaper

Figure 4.12 shows the result of bang-bang torque input convolved with positive

input shaping algorithm in PIC and shaped input with different order derivative in

matlab simulation. The PIC is embedded with positive input shaping with different

derivative order. From the Figure 4.12, it observed that the result of the PIC is almost

same with the results from the Matlab simulation. The shaped bang-bang torque is

capable to built or design in PIC.

It has slightly different in amplitude in certain time interval. The error is due to

the limitation of PIC microcontroller in order to show the output value in more than two

decimal. The last digit after two decimal is automatically disappeared in this case.

Therefore the PIC microcontroller is less accurate compare to the matlab simulation due

to the decimal number constraint of PIC microcontroller in programming.

(a) PZV in PIC

40

(b) PZVD in PIC

(c) PZVDD in PIC

Figure 4.12: The comparison graph of result in embedded positive input shaping and

Matlab simulation

41

Moreover, the time consumption for calculation process in PIC is much longer

than time consumption for simulation in Matlab software. This can be considered a time

delay in the PIC during calculation compare with Matlab simulation by using PC. This is

because the rate of processing and random access memory in PIC microcontroller is

much smaller than Matlab software in PC. In evaluate that, the input shaping algorithm

embedded into PIC is not suitable to use for the long input duration and complex

algorithm.

4.5 Comparative assessment

Figure 4.13 shows the comparison of power spectral density (PSD) of the end-

point acceleration of the flexible manipulator system between PIC and the Matlab

simulation with different order of derivation. It is to compare the behavior of the system

between PIC and Matlab simulation. It is found that the maximum magnitude for the

power spectral density (PSD) of the end point acceleration in PIC embedded with

positive input shaper algorithm is same with the maximum magnitude for Matlab

simulation in different order of derivation. This noticed that the behavior of the system

in PIC and Matlab simulation is same. However, the magnitude of the end point

acceleration in PIC is slightly different as compared to Matlab simulation at certain

frequency. The different is more significant when the positive input shaping derivative

order is higher. This is due to the limitation of PIC. The embedded PIC is unable to

show the digit more than two decimal places. More decimal places are needed to

consider for the higher order of derivative to make sure the results is accurate.

42

(a) PZV

(b) PZVD

43

(c) PZVDD

Figure 4.13: PSD of embedded positive input shaping and the Matlab simulation with

different derivative order.

Figure 4.14 show the end-point acceleration of embedded PIC and Matlab

simulation with different derivative order. From this figure, the end-point acceleration

using the embedded PIC is conforming in very detail as compared to the end-point

acceleration in Matlab simulation. The positive input shaper algorithm in PIC is verified.

44

(a) PZV

(b) PZVD

45

(c) PZVDD

Figure 4.14: End-point acceleration of embedded positive input shaping and matlab

simulation in different order of derivation

The comparative assessment of hub angle response of the flexible manipulator to

the shaped bang-bang torque input with exact natural frequency between embedded PIC

microcontroller and Matlab simulation is shown in Figure 4.15. Figure 4.16 shows the

bar chart of rise and settling time of the hub-angle using embedded positive input

shaping and positive input shaping in Matlab simulation. It is noticed that the vibration

in the hub-angle of embedded PIC and Matlab simulation is reduced in same response.

Table 4.3 summarize the rise time, settling time and overshoot of the hub-angle response

using the embedded PIC microcontroller. Based on the rise time, settling time and

overshoot of the hub angle data, it is found that the speed of the system response reduces

with the increase in the number of impulses. It is noted that the embedded positive input

shaping in PIC microcontroller have same characteristic with the positive input shaping

process in Matlab simulation. The embedded positive input shaping algorithm into PIC

is verified.

46

(a) PZV

(b) PZVD

47

(c) PZVDD

Figure 4.15: Comparisons in embedded PIC and Matlab simulation with different

derivative order for hub-angle response.

Table 4.3: Rise time, settling time and overshoot for hub-angle response using

embedded positive input shaping

Input Rise time (s) Settling time (s) Overshoot (%)

PZV 0.420 0.828 0.242

PZVD 0.437 0.862 0.015

PZVDD 0.441 0.902 0.001

Figure 4.16: Rise and settling time of the hub-angle using Matlab simulation and

embedded positive input shaping.

48

4.5 Summary

From the results, it is found that the speed of the system response reduces with

the increase in the number of impulses. This also means that the higher order positive

input shaper will reduce the speed of the system response. Also found that the transient

response of shaped input control is smoother compare to bang-bang torque input control

and further improved using higher derivative order. The vibration of the system can be

reduced effectively by using positive input shaping technique with higher order

derivative.

Embedded positive input shaping using PIC microcontroller is capable to shape

the bang-bang torque input. The outcome of embedded input shaping in PIC is same

with positive input shaping in Matlab simulation in terms of time response specifications

and vibration reduction. However, the embedded PIC provides less accuracy and slower

processing speed compared to Matlab simulation in computer. This is because the

microcontroller chip has its limitations. The embedded PIC is unable to calculate the

digit more than two decimal places and processing rate of PIC is slow compare to the

common PC.

CHAPTER 5

CONCLUSION AND RECOMENDATION

5.1 Conclusion

Flexible robot manipulator exhibits many advantages compared to their rigid

counterparts. One of the major disadvantages of a flexible manipulator is the presence of

vibrations due its flexible nature. In this work, a single link flexible manipulator that

moves in horizontal plane is considered. Modeling is done using assumed mode method

where two modal displacements are considered in characterizing the dynamic behavior

of the manipulator incorporating structural damping.

The vibrations in a system can be reduced effectively using positive input

shaping techniques. For any vibration system, the vibration reduction can be

accomplished by convolving any desired system input with an impulse sequence. This

yields a shaped input that drives the system to a location without vibration. This method

is based on feed-forward control strategy that requires simple estimated values of the

natural frequencies and damping ratios. The higher number of impulse provides higher

50

level of vibration reduction. However, with more impulse, the system response will

become very slow.

From the results, the higher levels of vibration reduction were obtained with

positive ZVDD shaper as compared to the shaped input with positive ZVD and ZV

shaper. The speed of the system response reduces with the increase in the number of

impulse. The vibration can be further reduced as the number of derivative is increased.

The implementation of embedded positive input shaping algorithm with different

order of derivative have been validated with simulation work in Matlab. The response of

the embedded input shaping show almost similar results as compared to Matlab

simulation. However, the processing time is much longer as compared to the processing

time in Matlab software by using PC and less accurate due to the limitation of PIC

controller.

5.2 Recommendation

For future development in this field, it is suggested to conduct research on the

performance of the developed input shaping technique, in terms robustness analysis with

parameter variation in the dynamic of the system. The performance of positive input

shaping should experimentally compare to other method in reducing the vibration.

Finally, to overcome the slow processing rate and a smaller random access

memory in PIC microcontroller, the advance Digital Signal Processing board should be

applied as the next platform of embedded system.

51

REFERENCES

[1]. J.M. Martins, Z. Mohamed. and M.O.Tokhi, J.A. 2003. Approaches for dynamic

modeling of flexible manipulator systems. Journal of the university of Sheffield,.

8(3): 411.

[2]. David Wang, and M. Vidyasagar, J.A. 1989. Transfer functions for a single flexible

link. Journal of Structural Engineering ASCE. 7(92): 1-6.

[3]. Smith, O.J.M. (1957). Posicast Control of Damped Oscillatory Systems.

Proceedings of the IRE. 45: 1249-1255

[4]. Junkins, John, L., Tuner and James, D. (1986). Optimal Spacecraft Rotational

Maneuvers. New York: Elsevier Science Publisher.

[5]. Gupta and Narendra, K. (1980). Frequency-shaped Cost Functions: Extension of

Linear-Quandratic-Gaussian Design Methods. Nov-Dec 1980. Journal of

Guidance and Control. 3(6): 529-535

[6]. Farrenkopf, R.L. (1979). Optimal open-Loop Maneuver Profiles for flexible

spacecraft. Journal of Guidance and Control, Nov-Dec. 1979. 2(6): 491-498

[7]. Swigert C.J. (1980). Shaped Torque Technique. Journal of Guidance and Control,

3(5): 460-467

[8]. Sadettin Kapucu, Gursel Alici and Sedat Baysec. 2001. Residual Swing/Vibration

Reduction using a hybrid Input Shaping Method. Journal of Mechanism and

Machine theory. 125(36): 311-326.

[9]. Fortgang, J. and Singhose, W.E. 2002. Concurrent Design of Input Shaping and

Vibration Absorber. Proceedings of the American Control conference. May 8-10.

Anchorage, AK: 1491-1496

[10]. Kai Zoo. and David Wang, J.A. 1992. Closed loop shaper-input control of a class

of manipulator with a single flexible link. Proceedings of international

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conference on Robotics and Automation. May 1992. Nice, France, IEEE: 782-

787

[11]. Magee, David.P. Cannon, David W. And Book Wayne, J.. 1997. Combined

command shaping and inertial damping for flexure control. Proceedings of the

American control conference June 1007. Albuquerque, New Mexico: 1330-1334.

[12]. Neil C. Singer and Warren P. Seering. January 1989. Preshaping Command Inputs

to reduce system vibration. Journal of Massachusetts Institute of Technology.

125(92): 152-162.

[13]. Singhose, W.E., Seering, W.P. and Singer, N.C. (1990). Shaping Inputs to

Reduced Vibration: A Vector Diagram Approach. IEEE conference on Robotics

and Automations. Cincinati, Ohio. 992-927

[14]. Singhose, W.E. and Lucy Y. Pao. 1997. A comparison of input shaping and time-

optimal flexible-body control. Control engineering pratice. 5(4): 459-467.

[15]. Hyde, J. M. And Seering, W.P 1991. Inhibiting Multiple mode vibration in

controlled flexible system. Proceedings of American Control Conference. Boston,

MA

[16]. Gurleyuk. SS., and Cinal, S., 2007. Three-Step input shaper for damping tubular

step motor vibrations. Journal of Vibration and Control, Zonguldak, Turkry: 1-3

[17]. Warren F.Philips,. 1991.Device and method for control of flexible link robot

manipulators . Journal of Utah state University Foundation. 114(4): 142-155.

[18]. M. A. Ahmad, Z. Mohamed, H. Ishak and A. N. K. Nasir. 2008. Vibration

suppression technique in feedback control of a very flexible robot manipulator.

Journal of faculty of electrical and electronic engineering, Universiti Malaysia

Pahang . 6(3): 1-6

53

APPENDIX A

Software development source code

#include <18LF14K50.h>

#include <stdlib.h>

#fuses INTRC,NOWDT,NOPROTECT,NOLVP

#use delay(clock=16000000)

#use rs232(baud=9600, xmit=PIN_B7, rcv=PIN_B5)

int q=0;

int j=0;

int i;

int a[10][7];

int z[10];

#int_rda

void serial_isr()

{

a[j][q++] = getc();

if(q==1)

{

z[j] = atoi(a[j]);

z[0]=z[0]+1;

z[1]=z[1]+2;

z[2]=z[2]+3;

if (z[0] ==2)

{

for (i=1;i<=200; ++i)

printf(" \r 0.00 ");

for (i=1; i<=9; ++i)

printf(" \r 0.07");

for (i=1; i<=24; ++i)

printf(" \r 0.15 ");

for (i=1; i<=9; ++i)

54

printf("\r 0.22");

for (i=1; i<=129; ++i)

printf("\r 0.30");

for (i=1; i<=129; ++i)

printf("\r 0.30 ");

for (i=1; i<=9 ; ++i)

printf("\r 0.14");

for (i=1; i<=24 ; ++i)

printf("\r -0.00");

for (i=1; i<=9 ; ++i)

printf("\r -0.15");

for (i=1; i<=129 ; ++i)

printf("\r -0.30");

for (i=1; i<=129; ++i)

printf("\r -0.30 ");

for (i=1; i<=9; ++i)

printf("\r -0.22");

for (i=1; i<=24; ++i)

printf("\r -0.14");

for (i=1; i<=9; ++i)

printf("\r -0.07");

for (i=1; i<=157; ++i)

printf("\r 0.00");

}

else if (z[0]==4)

{

for (i=1; i<=200; ++i)

printf("\r 0.00");

for (i=1; i<=9; ++i)

printf("\r 0.019");

for (i=1; i<=9; ++i)

printf("\r 0.05");

for (i=1; i<=15; ++i)

printf("\r 0.07");

for (i=1; i<=9; ++i)

printf("\r 0.11");

for (i=1; i<=9; ++i)

printf("\r 0.19");

for (i=1; i<=16; ++i)

printf("\r 0.22");

55

for (i=1; i<=9; ++i)

printf("\r 0.24");

for (i=1; i<=9; ++i)

printf("\r 0.28");

for (i=1; i<=215; ++i)

printf("\r 0.30");

for (i=1; i<=9; ++i)

printf("\r 0.26");

for (i=1; i<=9; ++i)

printf("\r 0.18");

for (i=1; i<=15; ++i)

printf("\r 0.14");

for (i=1; i<=9; ++i)

printf("\r 0.06");

for (i=1; i<=9; ++i)

printf("\r -0.08");

for (i=1; i<=16; ++i)

printf("\r -0.15");

for (i=1; i<=9; ++i)

printf("\r -0.19");

for (i=1; i<=9; ++i)

printf("\r -0.26");

for (i=1; i<=215; ++i)

printf("\r -0.30");

for (i=1; i<=9; ++i)

printf("\r -0.28");

for (i=1; i<=9; ++i)

printf("\r -0.24");

for (i=1; i<=15; ++i)

printf("\r -0.22");

for (i=1; i<=9; ++i)

printf("\r -0.18");

for (i=1; i<=9; ++i)

printf("\r -0.10");

for (i=1; i<=16; ++i)

printf("\r -0.07");

for (i=1; i<=9; ++i)

printf("\r -0.05");

for (i=1; i<=9; ++i)

printf("\r -0.01");

for (i=1; i<=114; ++i)

56

printf("\r 0.00");

}

else if (z[0]==6)

{

for (i=1; i<=200; ++i)

printf("\r 0.00");

for (i=1; i<=9; ++i)

printf("\r 0.00");

for (i=1; i<=9; ++i)

printf("\r 0.01");

for (i=1; i<=9; ++i)

printf("\r 0.03");

for (i=1; i<=6; ++i)

printf("\r 0.03");

for (i=1; i<=9; ++i)

printf("\r 0.05");

for (i=1; i<=9; ++i)

printf("\r 0.09");

for (i=1; i<=9; ++i)

printf("\r 0.13");

for (i=1; i<=7; ++i)

printf("\r 0.15");

for (i=1; i<=9; ++i)

printf("\r 0.16");

for (i=1; i<=9; ++i)

printf("\r 0.20");

for (i=1; i<=9; ++i)

printf("\r 0.25");

for (i=1; i<=6; ++i)

printf("\r 0.26");

for (i=1; i<=9; ++i)

printf("\r 0.26");

for (i=1; i<=9; ++i)

printf("\r 0.28");

for (i=1; i<=9; ++i)

printf("\r 0.29");

for (i=1; i<=173; ++i)

printf("\r 0.30");

for (i=1; i<=9; ++i)

printf("\r 0.28");

57

for (i=1; i<=9; ++i)

printf("\r 0.26");

for (i=1; i<=9; ++i)

printf("\r 0.23");

for (i=1; i<=6; ++i)

printf("\r 0.22");

for (i=1; i<=9; ++i)

printf("\r 0.19");

for (i=1; i<=9; ++i)

printf("\r 0.10");

for (i=1; i<=9; ++i)

printf("\r 0.02");

for (i=1; i<=7; ++i)

printf("\r -0.00");

for (i=1; i<=9; ++i)

printf("\r -0.03");

for (i=1; i<=9; ++i)

printf("\r -0.11");

for (i=1; i<=9; ++i)

printf("\r -0.20");

for (i=1; i<=6; ++i)

printf("\r -0.22");

for (i=1; i<=9; ++i)

printf("\r -0.23");

for (i=1; i<=9; ++i)

printf("\r -0.26");

for (i=1; i<=9; ++i)

printf("\r -0.29");

for (i=1; i<=173; ++i)

printf("\r -0.30");

for (i=1; i<=9; ++i)

printf("\r -0.29");

for (i=1; i<=9; ++i)

printf("\r -0.28");

for (i=1; i<=9; ++i)

printf("\r -0.26");

for (i=1; i<=6; ++i)

printf("\r -0.26");

for (i=1; i<=9; ++i)

printf("\r -0.24");

for (i=1; i<=9; ++i)

58

printf("\r -0.20");

for (i=1; i<=9; ++i)

printf("\r -0.16");

for (i=1; i<=7; ++i)

printf("\r -0.14");

for (i=1; i<=9; ++i)

printf("\r -0.13");

for (i=1; i<=9; ++i)

printf("\r -0.09");

for (i=1; i<=9; ++i)

printf("\r -0.04");

for (i=1; i<=6; ++i)

printf("\r -0.03");

for (i=1; i<=9; ++i)

printf("\r -0.03");

for (i=1; i<=9; ++i)

printf("\r -0.01");

for (i=1; i<=9; ++i)

printf("\r -0.00");

for (i=1; i<=72; ++i)

printf("\r 0.00");

}

else

{

printf(" invalid");

}

q=0;

j++;

}

}

void main()

{

setup_oscillator(OSC_16MHZ|OSC_INTRC);

enable_interrupts(int_rda);

enable_interrupts(global);

59

while (true);

}

60

APPENDIX B

PIC18LF14K50 Datasheet

61

62

63

APPENDIX C

PIC18LF14K50 Block diagram

64

APPENDIX D

PIC programmer tools PICkit2 user’s guide

65

66

67

APPENDIX E

Conference Proceedings

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-1

TECHNIQUES OF VIBRATION AND END-POINT TRAJECTORY

CONTROL OF FLEXIBLE MANIPULATOR

Mohd Ashraf Ahmad Zaharuddin Mohamed

Universiti Malaysia Pahang Universiti Teknologi Malaysia

Faculty of Electrical and Electronics Engineering,

UMP, Locked bag 12, 25000, Kuantan, Pahang,

Malaysia.

Department of Mechatronic and Robotic,

Faculty of Electrical Engineering, UTM, 81310,

Skudai, Johor, Malaysia mashraf@ump.edu.my zahar@fke.utm.my

ABSTRACT

This paper presents investigations into the development of

control schemes for end-point vibration suppression and input

trajectory of a flexible manipulator. A constrained planar single-

link flexible manipulator is considered and the dynamic model of

the system is derived using the assumed mode method. To study

the effectiveness of the controllers, initially a Linear Quadratic

Regulator (LQR) is developed for control of rigid body motion.

This is then extended to incorporate a non-collocated PID

controller and a feedforward controller based on input shaping

techniques for control of vibration (flexible motion) of the

system. For feedforward controller, the positive input shapers are

proposed and designed based on the properties of the system.

Simulation results of the response of the manipulator with the

controllers are presented in time and frequency domains. The

performances of the control schemes are assessed in terms of

level of vibration reduction, input tracking capability and time

response specifications. Finally, a comparative assessment of the

control techniques is presented and discussed.

1. INTRODUCTION

An important aspect of the flexible manipulator control that has

received little attention is the interaction between the rigid and

flexible dynamics of the links. An acceptable system performance

with reduced vibration that accounts for system changes can be

achieved by developing a hybrid control scheme that caters for

rigid body motion and vibration of the system independently.

This can be realized by utilizing control strategies consisting of

either non-collocated with collocated feedback controllers and

feedforward with feedback controllers. In both cases, the former

can be used for vibration suppression and the latter for input

tracking of a flexible manipulator. Practically, a combination of

the control techniques would position the end-point of the

flexible manipulator from one point to another with reduced

vibration. Both feedforward and feedback control structures have

been utilized in the control of flexible manipulator systems. A

hybrid collocated and non-collocated controller has previously

been proposed for control of a flexible manipulator [1]. The

controller design utilizes end-point acceleration feedback through

a proportional-integral-derivative (PID) control scheme and a

proportional-derivative (PD) configuration for control of rigid

body motion. Experimental investigations have shown that the

control structure gives a satisfactory system response with

significant vibration reduction as compared to a response with a

collocated controller. A PD feedback control with a feedforward

control to regulate the position of a flexible manipulator has been

proposed [2]. Simulation results have shown that although the

pole-zero cancellation property of the feedforward control speeds

up the system response, it increases overshoot and oscillation. A

control law partitioning scheme which uses end-point sensing

device has been reported [3]. The scheme uses end-point position

signal in an outer loop controller to control the flexible modes,

whereas the inner loop controls the rigid body motion

independent of the flexible dynamics of the manipulator.

Performance of the scheme has been demonstrated in both

simulation and experimental trials incorporating the first two

flexible modes. A combined feedforward and feedback method in

which the end-point position is sensed by an accelerometer and

fed back to the motor controller, operating as a velocity servo,

has been proposed in the control a flexible manipulator system

[4]. This method uses a single mass-spring-damper system to

represent the manipulator and thus the technique is not suitable

for high speed operation.

This paper presents investigations into the development of

techniques for end-point vibration suppression and input tracking

of a flexible manipulator. A constrained planar single-link flexible

manipulator is considered. Control strategies based on

feedforward with LQR controllers and with combined non-

collocated and LQR controllers are investigated. A simulation

environment is developed within Simulink and Matlab for

evaluation of performance of the control schemes. In this work,

the dynamic model of the flexible manipulator is derived using the

assumed mode method (AMM). Previous simulation and

experimental studies have shown that the AMM method gives an

acceptable dynamic characterization of the actual system [5].

Moreover, two mode of vibration is sufficient to describe the

dynamic behavior of the manipulator reasonably well. To

demonstrate the effectiveness of the proposed control schemes,

initially an LQR controller utilizing full-state feedback is

developed for control of rigid body motion. This is then extended

to incorporate non-collocated and feedforward controllers for

vibration suppression of the manipulator. For non-collocated

control, end-point displacement feedback through a PID control

configuration is developed whereas in the feedforward scheme,

the positive input shapers are utilized as these have been shown to

be effective in reducing system vibration. Simulation results of the

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-2

response of the manipulator with the controllers are presented in

time and frequency domains. The performances of the control

schemes are assessed in terms of level of vibration reduction,

input tracking capability and time response specifications. Finally,

a comparative assessment of the control techniques is presented

and discussed.

2. THE FLEXIBLE MANIPULATOR SYSTEM

Figure 1 shows the single-link flexible manipulator system

considered in this work, where XoOYo and XOY represent the

stationary and moving coordinates frames respectively, τ

represents the applied torque at the hub. E, I, ρ, L, A and Ih

represent the Young modulus, area moment of inertia, mass

density per unit volume, length, cross-sectional area and hub

inertia of the manipulator respectively. In this work, the motion of

the manipulator is confined to XoOYo plane. Transverse shear and

rotary inertia effects are neglected, since the manipulator is long

and slender. Thus, the Bernoulli-Euler beam theory is allowed to

be used to model the elastic behavior of the manipulator. The

manipulator is assumed to be stiff in vertical bending and torsion,

allowing it to vibrate dominantly in the horizontal direction and

thus, the gravity effects are neglected. Moreover, the manipulator

is considered to have a constant cross-section and uniform

material properties throughout. In this study, an aluminium type

flexible manipulator of dimensions 900 × 19.008 × 3.2004 mm³, E

= 71 × 109 N/m², I = 5.1924 × 1011 m4 , ρ = 2710 kg/m3 and Ih =

5.8598 × 10-4 kgm2 is considered. These parameters constitute a

single-link flexible manipulator experimental-rig developed for

test and verification of control algorithms [6].

X 0

Y 0

X

t

Flexible Link ( EI, L )

Y

Rigid Hub ( I H, r)

vx,t

Figure 1. Description of the flexible manipulator system.

3. MODELLING OF THE FLEXIBLE MANIPULATOR

This section provides a brief description on the modelling of

the flexible manipulator system, as a basis of a simulation

environment for development and assessment of the hybrid

control techniques. The assume mode method with two modal

displacement is considered in characterizing the dynamic

behaviour of the manipulator incorporating structural damping.

The dynamic model has been validated with experimental

exercises where a close agreement between both theoretical and

experimental results has been achieved [5].

Considering revolute joints and motion of the manipulator on

a two-dimensional plane, the kinetic energy of the system can thus

be formulated as

L

bH dxxvvIIT

0

22 )2(2

1)(

2

1 (1)

where bI is the beam rotation inertia about the origin O0 as if it

were rigid. The potential energy of the beam can be formulated as

dxx

vEIU

L 2

0

2

2

2

1

(2)

This expression states the internal energy due to the elastic

deformation of the link as it bends. The potential energy due to

gravity is not accounted for since only motion in the plane

perpendicular to the gravitational field is considered.

To obtain a closed-form dynamic model of the manipulator,

the energy expressions in (1) and (2) are used to formulate the

Lagrangian UTL . Assembling the mass and stiffness

matrices and utilizing the Euler-Lagrange equation of motion, the

dynamic equation of motion of the flexible manipulator system

can be obtained as

)()()()(...

tFtKQtQDtQM (3)

where M, D and K are global mass, damping and stiffness matrices

of the manipulator respectively. The damping matrix is obtained

by assuming the manipulator exhibit the characteristic of Rayleigh

damping. F(t) is a vector of external forces and Q(t) is a modal

displacement vector given as

TTTn qqqqtQ ...)( 21 (4)

TtF 0...00)( (5)

Here, nq is the modal amplitude of the i th clamped-free mode

considered in the assumed modes method procedure and n

represents the total number of assumed modes. The model of the

uncontrolled system can be represented in a state-space form as

xy

uxx

C

BA

(6)

with the vector Tqqqqx 2121 and the matrices A and B

are given by

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-3

0, 0

0,

0

3131

113

113333

DC

BA

I

MDMKM

I

(7)

4. CONTROL SCHEMES

In this section, control schemes for rigid body motion control and

vibration suppression of a flexible manipulator are proposed.

Initially, an LQR controller is designed. Then a non-collocated

PID control and feedforward control based on input shaping are

incorporated in the closed-loop system for control of vibration of

the system.

4.1. LQR controller

A more common approach in the control of manipulator systems

involves the utilization linear quadratic regulator (LQR) design

[7]. Such an approach is adopted at this stage of the investigation

here. In order to design the LQR controller a linear state-space

model of the flexible manipulator was obtained by linearising the

equations of motion of the system. For a LTI system

BuAxx , (8)

the technique involves choosing a control law )(xu which

stabilizes the origin (i.e., regulates x to zero) while minimizing

the quadratic cost function

0

)()()()( dttRututQxtxJ TT (9)

where 0 TQQ and 0 TRR . The term “linear-quadratic”

refers to the linear system dynamics and the quadratic cost

function.

The matrices Q and R are called the state and control penalty

matrices, respectively. If the components of Q are chosen large

relative to those of R , then deviations of x from zero will be

penalized heavily relative to deviations of u from zero. On the

other hand, if the components of R are large relative to those

of Q , then control effort will be more costly and the state will not

converge to zero as quickly.

A famous and somewhat surprising result due to Kalman is

that the control law which minimizes J always takes the form

Kxxu )( . The optimal regulator for a LTI system with

respect to the quadratic cost function above is always a linear

control law. With this observation in mind, the closed-loop system

takes the form

xBKAx )( (10)

and the cost function J takes the form

0

))(())(()()( dttKxRtKxtQxtxJ TT (11)

0

)()()( dttxRKKQtxJ TT (12)

Assuming that the closed-loop system is internally stable,

which is a fundamental requirement for any feedback controller,

the following theorem allows the computation value of the cost

function for a given control gain matrix K.

In this investigation, the tracking performance of the LQR

applied to the flexible manipulator was investigated by setting the

value of vector K and N which determines the feedback

control law and for elimination of steady state error capability

respectively. For the single-link flexible manipulator described by

the state-space model given by Equation (6) and with M, K, and D

matrices calculated earlier, the LQR gain matrix for

3333

3333

00

0IQ and 1R

was calculated using Matlab and was found to be

4663.33416.02705.08810.90848.1000.1K

000.1N

4.2. LQR with non-collocated PID controller

A combination of full-state feedback and non-collocated control

scheme for control of rigid body motion and vibration

suppression of the system is presented in this section. The use of

a non-collocated control system, where the end-point of the

manipulator is controlled by measuring its position, can be

applied to improve the overall performance, as more reliable

output measurement is obtained. The control structure comprises

two feedback loops: (1) The full-state feedback as input to

optimize the control gain matrix for rigid body motion control.

(2) The end-point residual (elastic deformation) as input to a

separate non-collocated control law for vibration control. These

two loops are then summed together to give a torque input to the

system. A block diagram of the control scheme is shown in

Figure 2 where represents the end-point residual. r

represents end-point residual reference input, which is set to zero

as the control objective is to have zero vibration during

movement of the manipulator.

For rigid body motion control, the LQR control strategy

developed in the previous section is adopted whereas for the

vibration control loop, the end-point residual feedback through a

PID control scheme is utilized. The PID controller parameters

were tuned using the Ziegler-Nichols method using a closed-loop

technique, where the proportional gain Kp was initially tuned and

the integral gain Ki and derivative gain Kd were then calculated

[8]. Accordingly, the PID parameters Kp, Ki and Kd were deduced

as 0.7, 5 and 0.03 respectively. To decouple the end-point

measurement from the rigid body motion of the manipulator, a

third-order infinite impulse response (IIR) Butterworth High-pass

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-4

filter was utilised. In this investigation, a High-pass filter with

cut-off frequency of 5 Hz was designed.

Figure 2. The LQR and non-collocated PID control

structure.

4.3. LQR with input shaping control

A control structure for control of rigid body motion and vibration

suppression of the flexible manipulator based on LQR and input

shaping control is proposed in this section. The positive input

shapers are proposed and designed based on the properties of the

system. In this study, the input shaping control scheme is

developed using a Zero-Vibration-Derivative-Derivative (ZVDD)

input shaping technique [9]. Previous experimental study with a

flexible manipulator has shown that significant vibration

reduction and robustness is achieved using a ZVDD technique

[10]. A block diagram of the LQR with input shaping control

technique is shown in Figure 3.

The input shaping method involves convolving a desired

command with a sequence of impulses known as input shaper.

The design objectives are to determine the amplitude and time

location of the impulses based on the natural frequencies and

damping ratios of the system. The positive input shapers have

been used in most input shaping schemes. The requirement of

positive amplitude for the impulses is to avoid the problem of

large amplitude impulses. In this case, each individual impulse

must be less than one to satisfy the unity magnitude constraint. In

addition, the robustness of the input shaper to errors in natural

frequencies of the system can be increased by solving the

derivatives of the system vibration equation. This yields a positive

ZVDD shaper with parameter as

t1 = 0, t2 = d

, t3 =

d

2, t4 =

d

3

321

331

1

KKKA

,

322331

3

KKK

KA

32

2

3331

3

KKK

KA

,

32

3

4331 KKK

KA

(13)

where

21

eK , 21 nd

n and representing the natural frequency and damping ratio

respectively. For the impulses, tj and Aj are the time location and

amplitude of impulse j respectively.

Figure 3. The LQR and input shaping control structure.

5. IMPLEMENTATION AND RESULTS

In this section, the proposed control schemes are implemented and

tested within the simulation environment of the flexible

manipulator and the corresponding results are presented. The

manipulator is required to follow a trajectory within the range of

8.0 radian. System responses namely the end-point trajectory,

displacement and end-point acceleration are observed. To

investigate the vibration of the system in the frequency domain,

power spectral density (PSD) of the end-point acceleration

response is obtained. The performances of the control schemes are

assessed in terms of vibration suppression, input tracking and time

response specifications. Finally, a comparative assessment of the

performance of the control schemes is presented and discussed.

Figures 4-6 show the responses of the flexible manipulator to

the reference input trajectory using LQR controller in time-

domain and frequency domain (PSD). These results were

considered as the system response under rigid body motion

control and will be used to evaluate the performance of the non-

collocated PID and input shaping control. The steady-state end-

point trajectory of +0.8 radian for the flexible manipulator was

achieved within the rise and settling times and overshoot of 0.421

s, 1.233 s and 6.06% respectively. It is noted that the manipulator

reaches the required position from +0.8 rad to -0.8 rad within 2 s,

with little overshoot. However, a noticeable amount of vibration

occurs during movement of the manipulator. It is noted from end-

point acceleration response, the vibration of the system settles

within 0.5 s with a maximum acceleration of ±600 m/s2.

Moreover, from the PSD of the end-point acceleration response

the vibrations at the end-point are dominated by the first two

vibration modes, which are obtained as 16 and 56 Hz with

magnitude of 1.367×105 m/s2/Hz and 138.4 m/s2/Hz respectively.

The end-point trajectory, end-point acceleration and power

spectral density responses of the flexible manipulator using LQR

with non-collocated PID (LQR-PID) and input shaping (LQR-IS)

control are shown in Figures 4-6 respectively. It is noted that the

proposed control schemes are capable of reducing the system

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-5

vibration while maintaining the input tracking performance of the

manipulator. Similar end-point trajectory, end-point acceleration

and power spectral density of end-point acceleration responses

were observed as compared to the LQR controller.

Table 1 summarizes the levels of vibration reduction of the

system responses at the first two modes in comparison to the LQR

control. In overall, higher levels of vibration reduction for the first

two modes were obtained using LQR-IS as compared to LQR-

PID. However, the system response using LQR-PID is faster than

the case of LQR-IS. It is noted with the input shaping controller,

the impulses sequence in input shaper increase the delay in the

system response. The corresponding rise time, setting time and

overshoot of the end-point trajectory response using LQR-IS and

LQR-PID is depicted in Table 1. Moreover, as demonstrated in

the end-point trajectory response with LQR-PID control, the

minimum phase behavior of the manipulator is unaffected. A

significant amount of vibration reduction was demonstrated at the

end-point of the manipulator with both control schemes. With the

LQR-PID control, the maximum acceleration at the end-point is

±500 m/s2 while with the LQR-IS control is ±100 m/s2. Hence, it

is noted that the magnitude of oscillation was significantly

reduced by using LQR with input shaping control as compared to

the case of LQR with non-collocated PID control. In overall, the

performance of the control schemes at input tracking capability is

maintained as the LQR control.

The simulation results show that performance of LQR-IS

control scheme is better than LQR-PID schemes in vibration

suppression of the flexible manipulator. This is further evidenced

in Figure 7 that demonstrates the level of vibration reduction at

the resonance modes of the LQR with non-collocated and input

shaping control respectively as compared to the LQR controller. It

is noted that higher vibration reduction is achieved with LQR-IS

at the first two modes of vibration. Almost twofold and more than

fourfold improvement in the vibration reduction at the first and

second resonance mode respectively were observed with LQR-IS

as compared to LQR-PID. Moreover, implementation of LQR

with input shaping control is easier than LQR with non-collocated

PID control as a large amount of design effort is required to

determine the best PID parameters. Note that a properly tuned

PID could produce better results. However, as demonstrated in the

end-point trajectory response, slightly slower response is obtained

using LQR with input shaping control as compared to the LQR

with non-collocated control. Further comparisons of the

specifications of the end-point trajectory responses are

summarized in Figure 8 for the rise and settling times. The work

thus developed and reported in this paper forms the basis of

design and development of hybrid control schemes for input

tracking and vibration suppression of multi-link flexible

manipulator systems and can be extended to and adopted in

practical applications.

0 1 2 3 4 5 6 7 8-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

End-p

oin

t tr

aje

cto

ry (

rad)

LQR

LQR-PID

LQR-IS

0.35 0.40 0.450.5

0.52

0.54

3.42 3.46 3.50-0.48

-0.47

Figure 4. End-point trajectory response with LQR and

LQR-PID and LQR-IS.

0 1 2 3 4 5 6 7 8-1000

-800

-600

-400

-200

0

200

400

600

800

1000

Time (s)

End-p

oin

t accele

ratio

n (

m/s

ec/s

ec)

LQR

LQR-PID

LQR-IS

3.0 3.1 3.2 3.3 3.4 3.5-400

-200

0

200

400

Figure 5. End-point acceleration response with LQR and

LQR-PID and LQR-IS.

0 10 20 30 40 50 60 70 80

10-2

100

102

104

106

Frequency (Hz)

Magnitu

de (

(m/s

ec/s

ec)*

(m/s

ec/s

ec)/

Hz)

LQR

LQR-PID

LQR-IS

Figure 6. Power spectral density response with LQR and

LQR-PID and LQR-IS.

Proceeding of the 6th International Symposium on Mechatronics and its Applications (ISMA09), Sharjah, UAE, March 24-26, 2009

ISMA09-6

0

20

40

60

80

100

120

140

160

Mode 1 Mode 2

Mode of vibration

Le

ve

l o

f vib

ratio

n r

ed

uctio

n (

dB

)

LQR-PID

LQR-IS

Figure 7. Level of vibration reduction with LQR-IS and LQR-

PID. at the end-point of the manipulator.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Rise time (s) Settling time (s)

Tim

e (

s)

LQR-PID

LQR-IS

Figure 8. Rise and settling times of the end-point trajectory with

LQR-IS and LQR-PID.

6. CONCLUSIONS

The development of techniques for end-point vibration

suppression and input tracking of a flexible manipulator has been

presented. The control schemes have been developed based on

LQR with non-collocated PID control and LQR with input shaper

technique. The proposed control schemes have been implemented

and tested within simulation environment of a single-link flexible

manipulator. The performances of the control schemes have been

evaluated in terms of end-point vibration suppression and input

tracking capability at the resonance modes of the manipulator.

Acceptable performance in end-point vibration suppression and

input tracking control has been achieved with proposed control

strategies. A comparative assessment of the control schemes has

shown that the LQR control with input shaping performs better

than the LQR with non-collocated PID control in respect of

vibration reduction at the end-point of the manipulator. However,

the speed of the response is slightly improved at the expenses of

decrease in the level of vibration reduction by using the LQR

with non-collocated PID control. It is concluded that the

proposed controllers are capable of reducing the system vibration

while maintaining the input tracking performance of the

manipulator.

7. REFERENCES

[1] Tokhi, M.O. and Azad, A.K.M. “Control of flexible

manipulator systems”, Proceedings IMechE-I: Journal of

Systems and Control Engineering, 210, 113-130, 1996.

[2] Shchuka, A. and Goldenberg, A.A. “Tip control of a single-

link flexible arm using feedforward technique”, Mechanical

Machine Theory, 24, 439-455, 1989.

[3] Rattan, K.S., Feliu, V. and Brown, H.B. “Tip position

control of flexible arms”, Proceedings of the IEEE

Conference on Decision and Control, Honolulu, 1803-1808,

1990.

[4] Wells, R.L. and Schueller, J.K. “Feedforward and feedback

control of a flexible manipulator”, IEEE Control System

Magazine, 10, 9-15, 1990.

[5] Martins, J.M., Mohamed, Z., Tokhi, M.O., Sá da Costa, J.

and Botto, M.A. “Approaches for dynamic modelling of

flexible manipulator systems”, IEE Proceedings-Control

Theory and Application. 150(4), 401-411, 2003.

[6] Tokhi, M.O., Mohamed, Z. and Shaheed, M.H. “Dynamic

characterisation of a flexible manipulator system”, Robotica,

19(5), 571-580, 2001.

[7] Ogata, K. Modern Control Engineering, Prentice-Hall

International, Upper Saddle River, NJ, 1997.

[8] Warwick, K. Control systems: an introduction, Prentice Hall,

London, 1989.

[9] Z. Mohamed and M.A. Ahmad, “Hybrid Input Shaping and

Feedback Control Schemes of a Flexible Robot

Manipulator”, Proceedings of the 17th World Congress The

International Federation of Automatic Control, Seoul,

Korea, July 6-11, 2008, pp. 11714-11719.

[10] Mohamed, Z. and Tokhi, M.O. “Vibration control of a

single-link flexible manipulator using command shaping

techniques”, Proceedings IMechE-I: Journal of Systems and

Control Engineering, 216, 191-210, 2002.

Table 1. Level of vibration reduction of the end-point acceleration and specifications of end-point trajectory response for hybrid

control schemes.

Controller

Attenuation (dB) of vibration end-

point acceleration Specifications of end-point trajectory response

Mode 1 Mode 2 Rise time (s) Settling time (s) Overshoot (%)

LQR - PID 37.14 8.04 0.418 1.232 6.06

LQR - IS 62.59 146.73 0.423 1.291 6.00

Abstract—This paper presents theoretical investigations into

the dynamic characterisation of a flexible manipulator system.

A constrained planar single-link flexible manipulator is

considered. A dynamic model of the system, incorporating

structural damping and hub inertia, is developed using finite

element method. Simulation exercises are performed with

bang-bang input torque applied to the actuator. The simulation

algorithm thus developed is implemented in Matlab. To study

the effects of length on the response of the flexible manipulator,

the results are evaluated with varying beam’s length in the

algorithm. Simulation results are presented in time and

frequency domains. Performance of the algorithm in describing

the dynamic behaviour of the system is examined in terms of

level of vibration frequencies and time response specifications.

Finally, a comparative assessment of different beam’s length to

the system performance is assessed and discussed.

I. INTRODUCTION

Various approaches have previously been developed

for modelling of flexible manipulators [1]. These can be

divided into two categories. The first approach looks at

obtaining approximate modes by solving the partial

differential equation (PDE) characterising the dynamic

behaviour of a flexible manipulator system. Previous

investigations utilising this approach for a single-link

flexible manipulator have shown that the model eigenvalues

agree well with experimentally determined frequencies of the

vibratory model [2,3,4]. However, with this approach, the

model does not always represent the fine details of the system

[5].

The second approach uses numerical analysis techniques

based on finite difference (FD) and finite element (FE)

methods to solve the PDE. Previous simulation studies using

FD methods have shown that the method is simple in

mathematical terms and is more appropriate in applications

involving uniform structures, such as flexible manipulator

M.A. Ahmad is with the Universiti Malaysia Pahang, Lebuhraya Tun

Razak, 26300, Kuantan, Pahang, Malaysia (phone: 609-5492366; fax:

609-5492377; e-mail: mashraf@ump.edu.my).

M.A. Zawawi is with the Universiti Malaysia Pahang, Lebuhraya Tun

Razak, 26300, Kuantan, Pahang, Malaysia (phone: 609-5492366; fax:

609-5492377; email: mohdanwar@ump.edu.my)

Z. Mohamed is with the Universiti Teknologi Malaysia, UTM Skudai,

81310, Johor, Malaysia (e-mail: zahar@fke.utm.my).

systems. Further studies have shown the relative simplicity of

the method [6]. This approach has previously been utilised in

the dynamic characterisation of single-link flexible

manipulator systems incorporating damping, hub inertia and

payload [7,8]. Experiments have also been conducted, where

acceptable agreement between simulation and experimental

results has been achieved.

The FE method has been successfully used in solving

many material and structural problems. The method involves

discretising the actual system into a number of elements with

associated elastic and inertia properties of the system. This

gives approximate static and dynamic characterisation of the

actual system [9]. The performance of this technique in

modelling of flexible manipulators has also been investigated

[10,11,12,13]. These investigations have shown that the

method can be used to obtain a good representation of the

system. It has been reported that in using FE methods, a

single element is sufficient to describe the dynamic

behaviour of a flexible manipulator reasonably well. Using a

single element, the first two modes of vibration are well

described [10]. Moreover, the FE method exhibits several

advantages over the FD method [12]. However, in modelling

of the manipulator using FE methods, the effects of beam’s

length have not been adequately addressed. The effect of

length on the manipulator is important for modelling and

control purposes, as successful implementation of a flexible

manipulator control is contingent upon achieving acceptable

uniform performance in the presence of length variations.

II. THE FLEXIBLE MANIPULATOR SYSTEM

The single-link flexible manipulator system considered in

this work is shown in Fig. 1, where XoOYo and XOY

represent the stationary and moving coordinates frames

respectively, τ represents the applied torque at the hub. E, I,

ρ, A, Ih and mp represent the Young modulus, area moment of

inertia, mass density per unit volume, cross-sectional area,

hub inertia and payload mass of the manipulator respectively.

In this work, the motion of the manipulator is confined to

XoOYo plane. Transverse shear and rotary inertia effects are

neglected, since the manipulator is long and slender. Thus,

the Bernoulli-Euler beam theory is allowed to be used to

model the elastic behaviour of the manipulator. The

manipulator is assumed to be stiff in vertical bending and

M.A. Ahmad1, M.A. Zawawi

1 and Z. Mohamed

2

1Control and Instrumentation Research Group, Faculty of Electrical and Electronics Engineering,

Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Kuantan, Pahang, Malaysia.

2Department of Mechatronic and Robotic, Faculty of Electrical Engineering, Universiti Teknologi

Malaysia, UTM Skudai, 81310, Johor, Malaysia

Effect of Beam’s Length on the Dynamic Modelling of Flexible

Manipulator System

torsion, allowing it to vibrate dominantly in the horizontal

direction and thus, the gravity effects are neglected.

Moreover, the manipulator is considered to have a constant

cross-section and uniform material properties throughout. In

this study, an aluminium type flexible manipulator of

dimensions L × 19.008 × 3.2004 mm³, E = 71 × 109 N/m², I =

5.1924 × 1011

m4, ρ = 2710 kg/m

3 and Ih = 5.8598 × 10

-4 kgm

2

is considered. L is the length of the beam varied from 0.5 m to

1.0 m.

X0

Y0

X

t

Flexible Link ( EI, L )

Y

Rigid Hub ( Ih )

wx,t

mp

O

x

Fig. 1 Description of the flexible manipulator system.

III. ALGORITHM DEVELOPMENT

This section focuses on the development of the FE

simulation algorithm characterising the dynamic behaviour

of the flexible manipulator system. Firstly, the FE method is

briefly discussed. Then formulations to obtain the mass,

stiffness and damping matrices and the dynamic equations of

motion of the manipulator utilising the Lagrange equation are

presented. The procedure is further extended to incorporate

hub inertia, structural damping and payload into the dynamic

model. The equations of motion are then expressed in a

state-space form, so as to be solved using control system

approaches.

A. The Finite Element Method

Since its introduction in the 1950s, the FE method has

been continually developed and improved [9]. The method

involves decomposing a structure into several simple pieces

or elements. The elements are assumed to be interconnected

at certain points, known as nodes. For each element, an

equation describing the behaviour of the element is obtained

through an approximation technique. The elemental

equations are then assembled to form the system equation. It

is found that by reducing the element size of the structure,

that is, increasing the number of elements, the overall

solution of the system equation can be made to converge to

the exact solution.

The main steps in an FE analysis include (1)

discretisation of the structure into elements; (2) selection of

an approximating function to interpolate the result; (3)

derivation of the basic element equation; (4) calculation of

the system equation; (5) incorporation of the boundary

conditions and (6) solving the system equation with the

inclusion of the boundary conditions. In this manner, the

flexible manipulator is treated as an assemblage of n

elements and the development of the algorithm can be

divided into three main parts: the FE analysis, state-space

representation and obtaining and analysing the system

response.

B. Simulation Algorithm

For an angular displacement )(t and an elastic

deflection ),( txw , the total displacement ),( txy of a point

along the manipulator at a distance x from the hub can be

described as a function of both the rigid body motion

)(t and elastic deflection ),( txw measured from the line

OX as

),()(),( txwtxtxy (1)

Using the standard FE method to solve dynamic problems,

leads to the well-known equation

tQxNtxw aa, (2)

where xNa and tQa represent the shape function and

nodal displacement respectively. For the flexible

manipulator under consideration, txw , in equation (2)

represents the residual motion of the system. The

manipulator is approximated by partitioning it into n

elements. As a consequence of using the Bernoulli-Euler

beam theory, the FE method requires each node to possess

two degrees of freedom, a transverse deflection and rotation.

These necessitate the use of Hermite cubic basis functions as

the element shape function [14]. Hence, for the elemental

length l , the shape function can be obtained as

)()()()()( 4321 xxxxxNa

where

3

3

2

2

123

1)(l

x

l

xx ;

2

32

22

)(l

x

l

xxx ;

3

3

2

2

323

)(l

x

l

xx ;

2

32

4 )(l

x

l

xx .

For element n the nodal displacement vector is given as

)()()()()( 11 ttwttwtQ nnnna

where )(1 twn and )(twn are the elastic deflections of the

element and )(1 tn and )(tn are the corresponding

rotations. Substituting for txw , from equation (2) into

equation (1) and simplifying yields

)()(, tQxNtxy (3)

where

)()( xNxxN a and T

tQttQ a )()()(

The new shape function )(xN and nodal displacement

vector )(tQ in equation (3) incorporate local and global

variables. Among these, the angle )(t and the distance x

are global variables while )(xNa and )(tQa are local

variables. Defining

1

1

n

i

ilxs as a local variable of the

thn element, where il is the length of the ith element, the

kinetic energy of an element n can be expressed as

QdsNNAQds

t

tsyAT T

lTl

n )(2

1),(

00

2

(4)

and the potential energy of the element can be obtained as

QdsBBEIQ

dsQBQBEI

dss

tsyEIP

Tl

T

Tl

l

n

)(2

1

)()(2

1

),(

2

1

0

0

2

2

2

0

(5)

where 2

2

ds

NdB .

Defining nM and nK as

dsNNAM Tl

n )(

0

= element mass matrix (6)

dsBBEIK Tl

n )(

0

= element stiffness matrix (7)

and solving equations (6) and (7) for the n elements, the

element mass and stiffness matrices can be obtained as

2251

41

2231

21

1514131211

422313

221561354

313422

135422156

420

llllm

llm

lllllm

llm

mmmmm

AlM n

22

22

3

46260

6126120

26460

6126120

00000

llll

ll

llll

ll

l

EIKn

where

)25(7

)310(21

)35(7

)710(21

)133(140

25115

4114

23113

2112

2211

nlmm

nlmm

nlmm

nlmm

nnlm

Assembling the element mass and stiffness matrices, the

total kinetic and potential energies from equations (4) and (5)

can be written as

QMQT

T

2

1

QKQP T

2

1

where TnnwwtQ ...)( 00 ,

M and K are global mass and stiffness matrices of the

manipulator respectively. The dynamic equations of motion

of the flexible manipulator can be derived utilising the

Lagrange equation;

F

Q

L

Q

L

dt

d

where PTL is the Lagrangian and F is a vector of

external forces and moments. Considering the damping, the

desired dynamic equations of motion of the system can

accordingly be obtained as

)()()()( tFtKQtQDtQM

(8)

where D is a global damping matrix, normally determined

through experimentation.

For the flexible manipulator under consideration, the

global mass matrix can be represented as

www

w

MM

MMM

where wwM is associated with the elastic degrees of

freedom (residual motion), wM represents the coupling

between these elastic degrees of freedom and the hub angle

and M is associated with the inertia of the system

about the motor axis. Similarly, the global stiffness matrix

can be written as

wwKK

0

00

where wwK is associated with the elastic degrees of freedom

(residual motion). It can be shown that the elastic degrees of

freedom do not couple with the hub angle through the

stiffness matrix.

The global damping matrix D in equation (8) can be

represented as

wwDD

0

00

where wwD denotes the sub-matrix associated with the

structural damping. The matrix is obtained by assuming that

the manipulator exhibits the characteristics of Rayleigh

damping. This proportional damping model has been

assumed because it allows experimentally determined

damping ratios of individual modes to be used directly in

forming the global matrix. It also allows assignment of

individual damping ratios to individual modes, such that the

total manipulator damping is constituted with the sum of the

dampings associated with the modes [15]. Using this

assumption, the damping can be obtained as

wwwwww KMD (9)

where

21

22

122121 )(2

ff

ffff

;

21

22

1122 )(2

ff

ff

with 1 , 2 , 1f and 2f representing the damping ratios

and natural frequencies of modes 1 and 2 respectively.

C. State-space Representation

The M , D and K matrices in equation (8) are of size

mm and )(tF is of size 1m , where 12 nm . For the

manipulator, considered as a pinned-free arm with the

applied torque at the hub, the flexural and rotational

displacement, velocity and acceleration are all zero at the hub

at 0t and the external force is TtF 00 .

Moreover, in this work, it is assumed that 0)0( Q .

The matrix differential equation in equation (8) can be

represented in a state-space form as

Cvy

BuAvv

where

12

11

11

0, 0

0,

0

mmm

mmm

I

MDMKM

I

DC

BA

,

m0 is an mm null matrix, mI is an mm identity

matrix, 10 m is an 1m null vector, Tu 00 ,

T

nnnn wwwwv

1111

Solving the state-space matrices gives the vector of states v ,

that is, the angular, nodal flexural and rotational

displacements and velocities.

IV. RESULTS

In this section, simulation results of the dynamic

behaviour of the flexible manipulator system are presented in

the time and frequency domains. The system is considered

with variation of beams’s length. A bang-bang signal of

amplitude 0.3 Nm is used as an input torque, applied at the

hub of the manipulator. A bang-bang torque has a positive

(acceleration) and negative (deceleration) period allowing

the manipulator to, initially, accelerate and then decelerate

and eventually stop at a target location. System responses are

monitored for duration of 3 sec, and the results are recorded

with a sampling time of 1 msec. The hub angle, hub velocity,

end-point acceleration response with the PSDs are obtained

and evaluated.

To demonstrate the effects of length on the dynamic

behaviour of the system, various beams’ lengths from 0.5 to

1.0 m were simulated. Figs. 2, 3 and 4 show the hub angle,

hub velocity and end-point acceleration responses with

various lengths. Moreover, the corresponding PSDs of

end-point acceleration response are shown in Fig. 5. It is

noted that the hub angle decreases with increasing lengths.

With increasing length, it is also noted that the magnitudes of

end-point acceleration and hub velocity of the manipulator

decrease. It is also evidenced from the PSD of the system

response that the resonance modes of vibration of the system

shift to lower frequencies with increasing lengths. This

implies that the manipulator oscillates at lower frequency

rates with high value of length. Table I summarises the

relation between length and the resonance frequencies of the

system.

The time response specifications of hub angle have

shown significant changes with the variations of length.

Table II summarises the time response specifications of hub

angle of the flexible manipulator system. By comparing the

results presented in Table II, it is noted that the settling time

of the manipulator response was affected by variations in the

length. It is also evidenced that the settling time response

increases with increasing lengths. It shows that, by

incorporating more beam’s length resulted in a slower

response. In addition, the percentage overshoot results

produce a similar pattern with variation of lengths. With

increasing length, the overshoots of the hub angle response is

gradually increase.

0 0.5 1 1.5 2 2.5 30

50

100

150

200

Time (sec)

Hu

b a

ng

le (

de

g.)

0.5 m

0.7 m

0.9 m

Fig. 2 Hub angle response.

0 0.5 1 1.5 2 2.5 3

-100

0

100

200

300

400

500

600

700

Time (sec)

Hu

b v

elo

city (

de

g./se

c)

0.5 m

0.7 m

0.9 m

Fig. 3 Hub velocity response.

0 0.5 1 1.5 2 2.5 3

-300

-200

-100

0

100

200

300

Time (sec)

En

d-p

oin

t a

cce

lera

tio

n (

m/s

ec/s

ec)

0.5 m

0.7 m

0.9 m

Fig. 4 End-point acceleration response.

0 20 40 60 80 100

100

105

1010

Frequency (Hz)

Ma

gn

itu

de

((m

/se

c/s

ec)*

(m/s

ec/s

ec)/

Hz)

0.5 m

0.7 m

0.9 m

Fig. 5 PSD response.

TABLE I

RELATION BETWEEN LENGTH AND RESONANCE FREQUENCIES OF THE FLEXIBLE

MANIPULATOR

Length

(mm)

Resonance frequencies

Mode 1

(Hz)

Mode 2

(Hz)

Mode 3

(Hz)

0.5 25 60 147

0.6 20 45 105

0.7 17 37 77

0.8 12 32 62

0.9 12 27 50

1.0 9 25 42

TABLE II

RELATION BETWEEN LENGTH AND SPECIFICATIONS OF HUB ANGLE RESPONSES

OF THE FLEXIBLE MANIPULATOR

Length (m)

Time responses specifications of hub

angle

Rise time

(s)

Settling

time (s)

Overshoot

(%)

0.5 0.335 0.543 0.34

0.6 0.341 0.554 0.56

0.7 0.352 0.545 0.50

0.8 0.344 0.585 0.54

0.9 0.386 0.586 0.95

1.0 0.413 0.627 4.02

VI. CONCLUSIONS

Theoretical investigations into the dynamic modelling

and characterisation of a single-link flexible manipulator

system have been presented. A dynamic model of the

manipulator incorporating damping and hub inertia has been

developed using FE methods. The derived dynamic model

has been simulated with bang-bang torque inputs and the

performance algorithm of the system have been analysed in

time and frequency domains. The effects of beam’s length on

the system behaviour have been addressed. The resonance

modes of vibration of the system shift to lower frequencies

and produce a slower response with increasing lengths.

These results are very helpful and important in the

development of effective control algorithms for a flexible

manipulator with varying length.

ACKNOWLEDGMENT

This work was supported by Faculty of Electrical &

Electronics Engineering, Universiti Malaysia Pahang,

especially Control & Instrumentation (COINS) Research

Group. The authors also gratefully acknowledge Research

Management Centre (UMP) for the research funding under

RDU 080314.

REFERENCES

[1] Azad, A. K. M. (1995). Analysis and design of control

mechanisms for flexible manipulator systems, PhD. Thesis,

Department of Automatic Control and Systems Engineering,

The University of Sheffield, UK.

[2] Book, W. J. (1984). “Recursive lagrangian dynamics of

flexible manipulator arms”, International Journal of Robotics

Research, Vol. 3, pp. 87-101.

[3] Cannon, R. H. and Schmitz, E. (1984). “Initial experiment on

the end-point control of a flexible one-link robot”,

International Journal of Robotics Research, Vol. 3, pp. 62-75.

[4] Hasting, G. G. and Book, W. J. (1987). “A linear dynamic

model for flexible robot manipulators”, IEEE Control Systems

Magazine, Vol. 7, pp. 61-64.

[5] Hughes, P. C. (1987). “Space structure vibration modes: How

many exist? Which are important”, IEEE Control Systems

Magazine, Vol. 7, pp. 22-28.

[6] Kourmoulis, P. K. (1990). Parallel processing in the

simulation and control of flexible beam structures, PhD.

Thesis, Department of Automatic Control and Systems

Engineering, The University of Sheffield, UK.

[7] Tokhi, M. O. and Azad, A. K. M. (1995). “Real time finite

difference simulation of a single-link flexible manipulator

incorporating hub inertia and payload”, Proceedings of

IMechE-I: Journal of Systems and Control Engineering, Vol.

209, pp. 21-33.

[8] Tokhi, M. O. Poerwanto, H. and Azad, A. K. M. (1995).

“Dynamic simulation of flexible manipulators incorporating

hub inertia, payload and damping”, Machine Vibration, Vol.

4, pp. 106-124.

[9] Rao, S. S. (1989). The finite element method in engineering,

Pergamon Press, Oxford.

[10] Aoustin, Y. Chevallereau, C. Glumineau, A. and Moog, C. H.

(1994). “Experimental results for the end-effector control of a

single flexible robotic arm”, IEEE Transactions on Control

Systems Technology, Vol. 2, pp. 371-381.

[11] Tokhi, M. O. and Mohamed, Z. (1999). “Finite element

approach to dynamic modelling of a flexible robot

manipulator: Performance evaluation and computational

requirements”, Communications in Numerical Methods in

Engineering, Vol. 15, pp. 669-676.

[12] Tokhi, M. O. Mohamed, Z. and Azad, A. K. M. (1997).

“Finite difference and finite element approaches to dynamic

modelling of a flexible manipulator”, Proceedings of

IMechE-I: Journal of Systems and Control Engineering, Vol.

211, pp. 145-156.

[13] Usoro, P. B. Nadira, R. and Mahil, S. S. (1986). “A finite

element/lagrange approach to modelling lightweight flexible

manipulators”, Transactions of ASME: Journal of Dynamic

Systems, Measurement and Control, Vol. 108, pp. 198-205.

[14] Ross, C. T. F. (1996). Finite element techniques in structural

mechanics, Albion Publishing Limited, West Sussex.

[15] Chapnik, B. V. Heppler, G. R. and Aplevich, J. D. (1991).

“Modeling impact on a one-link flexible robotic arm”, IEEE

Transactions on Robotics and Automation, Vol. 7, pp.

479-488.

80

APPENDIX F

Equipment Submission Form and Preliminary IP Screening Form

- 1 -

1. PROJECT TITLE IDENTIFICATION :

THE DEVELOPMENT OF EMBEDDED INPUT SHAPING TECHNIQUES FOR

VIBRATION CONTROL OF FLEXIBLE MANIPULATOR SYSTEM

Vote No: RDU080314

2. PROJEK LEADER :

Name : MOHD ASHRAF BIN AHMAD

Address :

FAKULTI KEJURUTERAAN ELEKTRIK DAN ELEKTRONIK, UNVERSITI

MALAYSIA PAHANG, PEKAN, 26600, PAHANG

Tel : 094242070 Fax : 094242032 E-mail: mashraf@ump.edu.my

RESEARCH MANAGEMENT CENTRE

PRELIMINARY IP SCREENING & TECHNOLOGY ASSESSMENT FORM (To be completed by Project Leader submission of Final Report to RMC or whenever IP protection arrangement is required)

UMP/RMC/LA-2/07

- 2 -

3. DIRECT OUTPUT OF PROJECT (Please tick where applicable)

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Process Development

Algorithm

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√ √

√

√

- 3 -

5. LIST OF EQUIPMENT BOUGHT USING THIS VOT

No Item Serial No Location

1 Data Acquisition Card PCI

1710 HG

FTK1000-PB08-01706-

00001 Makmal PSM, FKEE

2 FPGA Virtex-4 Family

24192

FTK1000-PB101-0907-

0001-00001 Makmal Robotik, FKEE

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T!TlTBALAN DEKAN

FAKLJLTI KE.'URUTERMN ELEKTRIK & ELEKTRONIKU NIVERSITI IMALAYSIA PAHANG25600 PEfr\NPAHAI'IG DARULMAKMURTEl i 09-4242142 FAKS : 09-4242032

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PUSAT PENGURUSAN PENYELIDIKANBORANG PENYERAHAN PERALATAN YANG MENGGUNAKAN PERUNTUKAN VOT PROJEK

PENYETIDIKAN

A. BUTIRAN PENYETIDIK

Nomo PenyelidikTojuk Projek

No Vot ProjekFokuli iNo. Tel/hp

:MOHD ASHRAF B IN AHMAD:THE DEVELOPMENT OF EMBEDDED INPUT SHAPING TECHNIQUESFOR VIBRATION CONTROL OF FLEXIBLE MANIPULATOR SYSTEM: RDU 08031 4: FAKULTI KEJURUTERAAN ELEKTRIK DAN ELEKTRONIK:0139264212

B. BUTIRAN SERAHAN PERAIATAN

C. PENGAKUAN PENYEI.IDIK

Soyo dengon ini menyerohkon peroloion yong teloh dibeli dengon menggunokonperuntukon vot projek penyelidikon_RDUO8O3.|4_ kepodo Fokulti _KEJURUTERAANELEKTRIK DAN ELEKTRONIK- podo -l JUN 2010_ berikuton projek penyelidikon ini telohselesoi dijolonkon.

Tondotongon & Cop Ketuo Penyelidik.$UTU ASHrlAi gN AHfuI,ALPENSYAFJ HFAKULTI KEJURUTERAAN ELEKTRIK & ELEKTRONIKUNiVERSITi ili[ALAYSIA PAHANG2tJ6OO PEKANPAHANG DARULVIAKMUREL i O94242o70fAKS ; 094242932utsonKon utenPengerusi J/Kuoso Penyelidikon Fokulti

r,/^l,{" [t^o*(:ljNvEr-li',rl'J\l'l & r.'t:NG/rJlAN SISWAZAH)F/iKi.i1.r i Ml r-rRlii"ERnnru ELEKTRTK & ElExrnOl,lKt,,I.IiVE!.iSiIi MAi.AYSIA PAHANG2040C F'FlKr'il"lFAHANG TJARLI L I,/AKMU RTEL | 09-4212142 FAKS i 09-4242032

Bil Perololon No. Tos HorqoDoto Acquis i t ion Cord PCI lZl0 HG FTK.l 000-P808-

0t 206-000012,7?7.50

2. FPGA Virtex-4 Fomily 24192 FTK I 000-PB I 0r -0907-0001 -0000,l

3,600.00

* Jiko ruong lidok mencukupi, silo guno lompiron mengikut formqt di qtos