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International Journal of Advanced Robotic Systems

Composite Fuzzy Logic Control Approachto a Flexible Joint ManipulatorRegular Paper

Mohd Ashraf Ahmad1,*, Mohd Zaidi Mohd Tumari1 and Ahmad Nor Kasruddin Nasir1

1 Control & Instrumentation (COINS) Research Group, Faculty of Electrical Engineering, University of Malaysia Pahang, Pekan, Malaysia* Corresponding author E-mail: [email protected]

Received 18 Jun 2012; Accepted 21 Aug 2012

DOI: 10.5772/52562

© 2013 Ahmad et al.; licensee InTech. This is an open access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract The raised complicatedness of the dynamics

of a robot manipulator considering joint elasticity

makes conventional model‐ based control strategies

complex and hard to synthesize. This paper presents

investigations into the development of hybrid

intelligent control schemes for the trajectory tracking

and vibration control of a flexible joint manipulator. To

study the effectiveness of the controllers, a collocated

proportional‐derivative (PD)‐type Fuzzy Logic

Controller (FLC) is first developed for the tip angular

position control of a flexible joint manipulator. This is

then extended to incorporate a non‐collocated Fuzzy

Logic Controller, a non‐collocated proportional‐

integral‐derivative (PID) and an input‐shaping scheme

for the vibration reduction of the flexible joint system.

The positive zero‐vibration‐derivative‐derivative

(ZVDD) shaper is designed based on the properties of

the system. The implementation results of the response

of the flexible joint manipulator with the controllers

are presented in time and frequency domains. The

performances of the hybrid control schemes are

examined in terms of input tracking capability, level of

vibration

reduction

and

time

response

specifications.

Finally, a comparative assessment of the control

techniques is presented and discussed.

Keywords Elastic Joint, Vibration Control, Fuzzy Logic,

Input‐Shaping, Collocated and Non‐Collocated Control

1. Introduction

Currently, elastic joint manipulators have received a great

deal of attention due to their light weight, high

manoeuvrability, flexibility, high power efficiency and

large number of applications. However, controlling such

systems still faces numerous challenges that need to be

addressed. The

control

issue

of

the

flexible

joint

is

to

design the controller so that the link of the robot can track

a prescribed trajectory precisely with minimum vibration

to the link. In order to achieve these objectives, various

methods using different techniques have been proposed.

Yim [1], Oh and Lee [2] proposed an adaptive output‐

feedback controller based on a backstepping design. This

technique is proposed in order to deal with parametric

uncertainty in a flexible joint. The relevant work also

being done by Ghorbel et al. [3]. Lin and Yuan [4] and

Spong et al. [5] introduced a nonlinear control approach

using the feedback linearization technique and the

integral manifold

technique

respectively.

A

robust

control

design was reported by Tomei [6] by using simple PD

1Mohd Ashraf Ahmad, Mohd Zaidi Mohd Tumari and Ahmad Nor Kasruddin Nasir:

Composite Fuzzy Logic Control Approach to a Flexible Joint Manipulator

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ARTICLE

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control and Yeon and Park [7] by applying robust H∞

control. An open‐loop optimal control approach for

generating the optimal trajectory of the elastic robotic

arms in point‐to‐point motion is proposed by Korayem et

al. [8]. This method is based on Pontryagin’s minimum

principle which considers the mobility of the elastic

manipulator.

In recent years, tools of computational intelligence ‐such

as artificial neural networks and fuzzy logic controllers ‐

have been credited in various applications as powerful

tools capable of providing robust controllers for

mathematically ill‐defined systems. This has led to recent

advances in the area of intelligent control [9, 10]. Various

neural network models have been applied in the control

of flexible joint manipulators which have led to

satisfactory performances [11]. H. Chaoui et al. [12] used

a sliding mode control approach that learns the system’s dynamics through a feed‐forward neural network. A

time‐delay neuro‐fuzzy network was suggested in [13],

where a linear observer was used to estimate the joint

velocity signals and eliminated the need to measure them

explicitly. Subudhi et al. [14] presented a hybrid

architecture composed of a neural network to control the

slow dynamic subsystem and an H∞ to control the fast

subsystem. A feedback linearization technique using a

Takagi‐Sugeno neuro‐fuzzy engine was adopted in [15].

Lin and Chen [16] propose a combined rigid model‐ based

the computed torque and fuzzy control of flexible‐ joint

manipulators.

As to another aspect, an acceptable system performance

with reduced vibration that accounts for system changes

can be achieved by developing a hybrid control scheme

that caters for the 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 or feed‐forward with

feedback controllers. In each case, the former can be used

for vibration suppression and the latter for the input

tracking of a flexible manipulator. A hybrid collocated

and non‐collocated controller has been widely proposed

for the control of flexible structures [17, 18, 19]. The works

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

feedback control with a feed‐forward control for

regulating the position of a flexible structure has been

proposed previously [20, 21]. A control law partitioning

scheme which uses the end‐point sensing device has also

been reported [22]. The scheme uses an end‐point

position signal in an outer loop controller to control the

flexible modes, whereas the inner loop controls the rigid

body motion independently of the flexible dynamics of

the

manipulator.

However,

to

the

best

of

our

knowledge,

there is still no research which adopts intelligent schemes

‐ especially the fuzzy logic approach ‐ for both collocated

and non‐collocated feedback schemes. Moreover, there is

still no article focusing on a comparison study between

the non‐collocated control and feed‐forward control of an

elastic joint manipulator.

This paper presents an investigation into the development of hybrid intelligent control schemes for the

trajectory tracking of the tip angular position and the

vibration control of a flexible joint manipulator. Control

strategies are investigated based on a collocated PD‐type

FLC with non‐collocated control and a collocated PD‐type

FLC with a feed‐forward scheme. For non‐collocated

control, a deflection angle is fed back through a fuzzy

logic control configuration. In order to evaluate the

performance of the non‐collocated fuzzy logic scheme, it

will be compared with the non‐collocated PID scheme.

For the feed‐forward scheme, an input‐shaping strategy is

utilized

for

reducing

a

deflection

effect.

The

positive

zero‐

vibration‐derivative‐derivative (ZVDD) shaper is

designed based on the properties of the flexible joint

manipulator. In this study, we will provide a comparative assessment of the performances of the composite

strategies which are evaluated in terms of input tracking

capability, level of vibration reduction in the frequency

domain and time response specifications. The

implementation environment is developed within

Simulink and Matlab for the evaluation of the

performance of the control schemes. The rest of the paper

is structured as follows: Section 2 provides a brief

description of the single‐link flexible joint manipulator

system considered in this study. Section 3 describes the

modelling of the system derived using Euler‐Lagrange

formulation. The composite collocated PD‐type FLC with

a Fuzzy Logic Control, PID control and input‐shaping

scheme are described in Section 4. The simulation results

and a comparative assessment are presented in Section 5

and the paper is concluded in Section 6.

2. The Flexible Joint Manipulator System

In this study, the joint flexibility of the robot is

represented by a linear spring, as shown in Figure 1. The

rotary

flexible

joint

module

provided

by

the

Quanser

system [23] includes a servomotor in the high gear ratio

configurations and a free arm attached to two identical

springs. The springs are mounted to an aluminium

chassis which is driven by the servomotor. Rotating the

base of the arm causes the entire arm to oscillate due to

the joint flexibility introduced by the springs. An optical

encoder attached to the shaft of the DC motor is used to

measure the angular position of the shaft θ(t). The joint

deflection α(t) is measured by an encoder located at the

motor end of the arm.

In

Figure

2,

is

the

tip

angular

position

and

is

the

deflection angle of the flexible link. The base of the FJM

which determines the tip angular position of the FJM is

2 Int J Adv Robotic Sy, 2013, Vol. 10, 58:2013 www.intechopen.com



driven by a servomotor. The deflection of the link will be

determined by the flexibility of the spring as their

intrinsic physical characteristics.

Figure 1. Rotary flexible joint manipulator

Figure 2. Description of the flexible joint manipulator system

3. The Modelling of the Flexible Joint Manipulator

This section

provides

a brief

description

on

the

modelling

of the FJM system as a basis of a simulation environment

for the development and assessment of the proposed

control techniques. The Euler‐Lagrange formulation is

considered in characterizing the dynamic behaviour of

the system.

The linear model of the uncontrolled system can be

represented in a state‐space form [23] as shown in

equation (1), that is:

,

x Ax Bu

y Cx

(1)

where the vector T

x and the matrices A ,

B and C are given by:

2

2

0 0 1 0

0 0 0 1

0 0

0 0

0 0 , 1 0 0 0 .

stiff m g t m g eq m

eq eq m

stiff eq arm m g t m g eq m

eq arm eq m

m g t g m g t g

eq m eq m

K η η K K K B R A

J J R

K (J J ) η η K K K B R

J J J R

η η K K η η K K B C

J R J R

(2)

In equation (1), the input u is the input voltage of the

servomotor mV which determines the FJM base

movement. In this study, the values of the parameters are

defined in Table

1.

Symbol Quantity Value

Rm Armature Resistance (Ω) 2.6

K m Motor Back‐EMF Constant (V.s/rad) 0.00767

K t Motor Torque Constant (N.m/A) 0.00767

J link Total Arm Inertia (kg.m2) 0.0035

J eq Equivalent Inertia (kg.m2) 0.0026

K g High gear ratio 14:5

K stiff Joint Stiffness (N.m/rad) 1.2485

Beq Equivalent Viscous Damping (N.m.s/rad) 0.004

η g Gearbox Efficiency 0.9

ηm Motor Efficiency 0.69

Table 1. System Parameter of FJM

4. Control Algorithm

In this section, control schemes for the rigid body motion

control and vibration suppression of a flexible joint

manipulator are proposed. Initially, a collocated PD‐type

FLC controller is designed. Then, a non‐collocated fuzzy

logic, non‐collocated PID and input‐shaping schemes are

incorporated in the closed‐loop system for the control of

vibration of the system.

4.1 PD‐type fuzzy logic controller (PD‐FLC)

A PD‐type FLC utilizing tip angular position error and a

derivative of tip angular position error is developed to

control the rigid body motion of the system. The hybrid

fuzzy control system proposed in this work is shown in

Figure 3, where ( )r t , ( )t and ( )t are the desired angle,

tip angular position and deflection angle of the FJM,

whereas k1 , k2 and k3 are scaling factors for two inputs and

one output of the FLC used with the normalized universe

of discourse for the fuzzy membership functions. For a

PD‐type FLC, triangular membership functions are

chosen for the tip angle error, tip angle error rate and

input voltage with 50% overlap. Normalized universes of

discourse are used for both the tip angle error and its

error rate and input voltage. Scaling factors k1 and k2 are



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chosen in such a way as to convert the two inputs within

the universe of discourse and activate the rule base

effectively, whereas k3 is selected such that it activates the

system to generate the desired output. Initially, all these

scaling factors are chosen based on trial and error. To

construct a rule

base,

the

tip

angle

error,

tip

angle

error

rate and input voltage are partitioned into five primary

fuzzy sets as:

Tip angle error E = {NM NS ZE PS PM},

Tip angle error rate V = {NM NS ZE PS PM},

Voltage U = {NM NS ZE PS PM},

where E , V and U are the universes of discourse for tip

angle error, tip angle error rate and input voltage,

respectively. The nth rule of the rule base for the FLC,

with the angle error and angle error rate as inputs, is

given by:

Rn: IF ( e is Ei) AND ( e is V j) THEN (u is U k),

where , Rn , n=1, 2,…N max , is the nth fuzzy rule, Ei , V j and

U k for i , j , k = 1,2,…,5, are the primary fuzzy sets.

A PD‐type FLC was designed with 11 rules as a closed

loop component of the control strategy for maintaining

the angular position of the FJM. The rule base was

extracted based on the underdamped system response

and is shown in Table 2. The three scaling factors, k1 , k2

and k3 were chosen heuristically to achieve a satisfactory

set of time domain parameters. These values were recorded as k1 = 0.552, k2 = 0.073 and k3 = ‐985.

Figure 3. PD‐type fuzzy logic control structure

No. Rules

1. If ( e is NM) and ( e is ZE) then (u is PM)

2. If ( e is NS) and ( e is ZE) then (u is PS)

3. If ( e is NS) and ( e is PS) then (u is ZE)

4. If ( e is ZE) and ( e is NM) then (u is PM)

5. If ( e is ZE) and ( e is NS) then (u is PS)

6. If ( e is ZE) and ( e is ZE) then (u is ZE)

7. If ( e is ZE) and ( e is PS) then (u is NS)

8. If ( e is ZE) and ( e is PM) then (u is NM)

9. If ( e is PS) and ( e is NS) then (u is ZE)

10. If ( e is PS) and ( e is ZE) then (u is NS)

11. If ( e is PM) and ( e is ZE) then (u is NM)

Table 2. Linguistic Rules of the PD‐type Fuzzy Logic Controller

4.2 PD‐type fuzzy logic with a non‐collocated fuzzy logic

controller (PD‐FLC‐FLC)

A combination of PD‐type fuzzy logic and a non‐collocated

fuzzy logic control scheme for the control of the tip angular

position

and

the

vibration

suppression

of

the

system ‐

respectively ‐ is presented in this section. The use of a non‐

collocated control system, where the deflection angle of the

flexible joint manipulator is controlled by measuring its

angle, can be applied to improve the overall performance as

more reliable output measurement is obtained. The control

structure comprises two feedback loops: (1) The hub angle as

an input to the PD‐type FLC for tip angular position control.

(2) The deflection angle as an 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 composite fuzzy logic

control scheme is shown in Figure 4.

For tip angular position control, the PD‐type FLC strategy

developed in the previous section is adopted whereas for

the vibration control loop, the deflection angle feedback

through a non‐collocated fuzzy logic control scheme is

utilized. In designing the non‐collocated fuzzy logic

control, basic triangular and trapezoidal forms are chosen

for the input and output membership functions. Figure 5

shows the membership functions of the fuzzy logic

controller for vibration control. It consists of Negative Big

(NB), Negative Small (NS), Zero (Z), Positive Small (PS)

and Positive Big (PB), as shown in the diagram. The

universes of

discourses

of

the

deflection

angle,

deflection

angle rate and input voltage are from 1.2 to ‐1.2 rad, ‐

0.015 to 0.015 rad/s and ‐447 to 447 V respectively.

Table 3 lists the generated linguistic rules for vibration

control. The rules are designed based on the condition of the

deflection angle and the deflection angle rate, as illustrated

in Figure 6. Consider that the joint of the manipulator rotates

in an anti‐clockwise direction and that the link deflects in a

clockwise direction. As illustrated in Figure 6(a), under this

condition – and intuitively ‐ the torque should be applied in

a clockwise direction in order to compensate the deflection.

In

this

case,

the

relation

between

the

input

voltage

and

the

torque per inertia is shown in equation (3):

m m g t g

m

V η η K K

R (3)

Figure 4. PD‐type FLC with a non‐collocated fuzzy logic control

structure




Figure 5. Membership functions of the input and output signals Deflection angle

rate

Deflection angle

PB PS Z NS NB

PB PB PB PB NB NB

PS PB PS PS NS NB

Z PB PS Z NS NB

NS PB PS NS NS NB

NB PB PB NB NB NB

Table 3. Linguistic rules for non‐collocated fuzzy logic control

Figure 6. Rules generation based on the motion condition Meanwhile, if the joint rotates in a clockwise direction, as

shown in Figure 6(b), and the link deflects in an anti‐

clockwise direction,

the

torque

should

be

imposed

in

an

anti‐clockwise direction to suppress the deflection

motion. In the case where there is no deflection, no torque

should be applied. Furthermore, the proposed fuzzy logic

control adopts the well‐known Mamdani min‐max

inference and centre of area (COA) methods.

4.3 PD‐type fuzzy logic with a non‐collocated PID Controller

(PD‐FLC

‐PID)

A combination of a PD‐type FLC and non‐collocated PID

control scheme for the control of the rigid body motion

and vibration suppression of the system is presented in

this section. The control structure of the PD‐FLC‐PID is

not very different from the PD‐FLC‐FLC and a block

diagram of the control scheme is shown in Figure 7.

For the rigid body motion control, the PD‐type FLC

control strategy developed in the previous section is

adopted whereas, for the vibration control loop, the

deflection angle feedback through a PID control scheme

is utilized. The PID controller parameters were tuned

using the Signal Constraint blockset of MATLAB via a

closed‐loop technique. At this moment, the PID controller

is optimized by considering the following desired

specifications:

Overshoot ≤10%

Settling time ≤0.75 sec

Rise time ≤0.55 sec

The initial parameters for PID controllers must be

specified before the Signal Constraint blockset executes the

tuning and optimizing process. The initial controller

parameters can be obtained either by trial and error or

else given as a default by the Signal Constraint blockset.

From the results of a Signal Constraint tuning process, the

values were recorded as k p = 602.5128, ki = ‐43.8895 and kd

= ‐19.7696.

Figure 7. PD‐type FLC with a non‐collocated PID control

structure

4.4 PD‐type fuzzy logic with input‐shaping (PD‐FLC‐IS)

A control structure for the control of the rigid body

motion and deflection angle reduction of the flexible joint

manipulator based on a PD‐type FLC and input‐shaping

scheme 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‐

-400 -300 -200 -100 0 100 200 300 400

0

0.5

1

Input voltage (V)

NB NS Z PS PB

D e g r e e o f m e m b e r s h i p

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

0

0.5

1

Deflection angle rate (rad/s)


NB NS Z PS PB

1 0.8 0.6 0.4 0.2 0 -0.2 - 0.4 - 0.6 - 0.8 -1

0

0.5

1

Deflection angle (rad)

NB NS Z PS PB




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Derivative‐Derivative (ZVDD) input‐shaping technique

[21]. Previous experimental studies with a flexible

manipulator have shown that significant vibration

reduction and robustness is achieved using a ZVDD

technique [24]. A block diagram of the PD‐type FLC with

an input

‐shaping

control

technique

is

shown

in

Figure

8.

The input‐shaping method involves convolving a desired

command with a sequence of impulses known as input‐

shapers. 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 seeks to avoid the problem of large

amplitude impulses. In this case, each individual impulse

must be less than one in order to satisfy the unity

magnitude

constraint.

In

addition, the

robustness

of

the

input‐shaper to errors in the natural frequencies of the

system can be increased by solving the derivatives of the

system vibration equation. This yields a positive ZVDD

shaper with a parameter as:

t1 = 0, t2 =

d

, t3 =

2

d

, t4 =

3

d

1 2 3

1

1 3 3 A

H H H

, 2 2 3

3

1 3 3

H A

H H H

2

3 2 331 3 3

H AH H H

,

3

4 2 31 3 3H A

H H H

(4)

where:

21H e

,

n and represent the natural frequency and damping

ratio respectively. For the impulses, t j and A j are the time

location and amplitude of impulse j respectively.

Figure 8. PD‐type FLC with an 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 joint manipulator and the

corresponding results are presented. The manipulator is

required to

follow

a trajectory

of

50º.

System

responses

‐namely the tip angular position and the deflection angle ‐

are observed. To investigate the vibration of the system in

the frequency domain, the power spectral density (PSD)

of the deflection angle response is obtained. The

performances of the control schemes are assessed in

terms of vibration suppression, trajectory tracking and

time response specifications. Finally, a comparative

assessment of

the

performance

of

the

control

schemes

is

presented and discussed.

(a) Tip angular position

(b) Deflection angle

(c)

Power

spectral

density

Figure 9. Response of the flexible joint manipulator using PD‐

FLC

21 nd

0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

Time (s)

T i p a n g u l a r p o s i t i o n ( d e g )

0 0.5 1.0 1.5 2.0 2.5 3.0-20

-15

-10

-5

0

5

10

15

20

Time (s)

D e f l e c t i o n a n g

l e ( d e g )

0 2 4 6 8 10 12 14 16 18-100

-80

-60

-40

-20

0

20

40

Frequency (Hz)

P o w e r S p e c t r a l D e n s i t y ( d B )

8.83 Hz

2.94 Hz

14.52 Hz




Figure 9 shows the responses of the flexible joint

manipulator to the reference input trajectory using the

PD‐FLC in a time‐domain and a 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

fuzzy

logic control and input‐shaping scheme. The steady‐state

tip angular trajectory of 50º for the flexible joint

manipulator was achieved within the rise and settling

times and an overshoot of 0.222 s, 0.565 s and 1.78 %

respectively. It is noted that the manipulator reaches the

required position within 1 s, with little overshoot.

However, a noticeable amount of vibration occurs during

the movement of the manipulator. It is noted from the

deflection angle response that the vibration of the system

settles within 3 s with a maximum residual of 15º.

Moreover, and from the PSD of the deflection angle

response, the

vibrations

at

the

flexible

joint

are

dominated

by the first three vibration modes, which are obtained as

2.94 Hz, 8.83 Hz and 14.52 Hz with a magnitude of 32.38

dB, ‐12.08 dB and ‐26.52 dB respectively.

The tip angular position, deflection angle and power

spectral density responses of the flexible joint

manipulator using PD‐FLC‐FLC, PD‐FLC‐PID and PD‐

FLC‐IS are shown in Figure 10. It is noted that the

proposed control schemes are capable of reducing the

system vibration while maintaining the trajectory

tracking performance of the manipulator. A similar tip

angular

position,

deflection

angle

and

power

spectral

density of the deflection angle responses were observed

as compared to the PD‐FLC. The steady‐state tip angular

trajectory of non‐collocated fuzzy logic was achieved

within the rise and settling times and overshoot of 0.215 s,

0.613 s and 9.68 %, respectively and 0.222 s, 0.501 s, and

9.40 %, respectively for PID control.. Meanwhile, with

PD‐FLC‐IS, the manipulator reached the rise, settling

times and overshoot of 0.469 s, 0.857 s and 0.16 %

respectively. It is notable that the settling time of PD‐FLC‐

FLC is much faster as compared to the case of PD‐FLC‐

PID and PD‐FLC‐IS. However, the percentage overshoot

of

PD‐

FLC‐

IS

is

much

lower

than

both

cases

of

PD‐

FLC

with non‐collocated control. Besides this, the results also

demonstrate a significant amount of deflection angle

reduction at the tip angle of the manipulator with the

proposed composite controllers. The vibration of the

system using PD‐FLC‐FLC and PD‐FLC‐PID settle within

1 s, which is much faster as compared to PD‐FLC‐IS.

However, in terms of the maximum residual of the

deflection angle, the PD‐FLC‐IS produces almost a four‐

fold improvement as compared to the PD‐FLC scheme.

This result is slightly higher than with both cases of PD‐

FLC‐PID and PD‐FLC‐FLC, with only a twofold

improvement

over

the

PD‐

FLC

scheme.

In

terms

of

the

power spectral density of the deflection angle response,

the magnitudes of vibrations using PD‐FLC‐FLC, PD‐

FLC‐PID and PD‐FLC‐IS were reduced to [1.87, ‐41.95, ‐

48.25] dB, [‐2.55, ‐33.53, ‐45.55] dB and [17.59, ‐25.28, ‐

36.69] dB respectively for the first three modes of

vibration. It is noted that both the PD‐FLC‐PID and PD‐

FLC‐FLC schemes produce a higher level of vibration

reduction as

compared

to

PD

‐FLC

‐IS.

(a) Tip angular position

(b) Deflection angle

(c) Power spectral density

Figure 10. Response of the flexible joint manipulator using

composite PD‐FLC‐FLC, PD‐FLC‐PID and PD‐FLC‐IS

0 0.5 1.0 1.5 2.0 2.5 3.00

10

20

30

40

50

60

Time (s)

T i p a n g u l a r p o s i t i o n ( d e g )

PD-FLC-FLC

PD-FLC-PID

PD-FLC-IS

0 0.5 1.0 1.5 2.0 2.5 3.0-15

-10

-5

0

5

10

Time (s)

D e f l e c t i o n a

n g l e ( d e g )

PD-FLC-FLC

PD-FLC-PID

PD-FLC-IS

0 2 4 6 8 10 12 14 16 18-100

-80

-60

-40

-20

0

20

40

Frequency (Hz)

P o w e r S p e c t r a l D e n s i t y ( d B )

PD-FLC-FLC

PD-FLC-PID

PD-FLC-IS

2.94 Hz

8.83 Hz

14.52 Hz



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Table 4 and Figure 11 summarize the magnitude of the

vibration and the level of the vibration reduction of

deflection, respectively, for the proposed composite control

schemes. It is seen that a high performance in the reduction

of the vibration of the system is achieved using both non‐

collocated fuzzy

logic

and

PID

control

as

compared

to

feed

‐

forward control based on an input‐shaping technique. This

is observed and compared to the PD‐FLC for the first three

modes of vibration. In addition, as demonstrated in the tip

angular trajectory response, a slightly faster response with a

higher overshoot is obtained using both non‐collocated

fuzzy logic and PID control scheme as compared to the

input‐shaping technique. Comparisons of the specifications

of the tip angular trajectory responses are summarized in

Table 5. In addition, and as demonstrated in the tip angular

trajectory response with PD‐FLC‐FLC and PD‐FLC‐PID, the

minimum phase behaviour of the manipulator is unaffected.

In terms

of

the

design

complexity,

the

implementation

of

the

input‐shaper technique is much easier as compared to both

non‐collocated controls as a large amount of design effort is

required in order to determine the controller parameters,

such as the range of the membership function in the fuzzy

logic design and k p , ki and kd gains in the PID design.

However, the input‐shaper strategy is very sensitive to the

system parameter variation and could not compensate for

any effect of disturbance as compared to the non‐collocated

control.

Controller Mode 1 Mode 2 Mode 3

Magnitude of

vibration (dB) PD

‐

FLC‐

FLC 1.87 ‐

41.95 ‐

48.25

PD‐FLC‐PID ‐2.55 ‐33.53 ‐45.55

PD‐FLC‐IS 17.59 ‐25.28 ‐36.69

Table 4. Magnitude of the vibration and level of vibration

reduction of the deflection angle

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

PD‐FLC‐FLC 0.613 0.215 9.68

PD‐FLC‐PID 0.501 0.222 9.40

PD‐FLC‐IS 0.857 0.469 0.16

Table 5. Time response specifications of tip angular position

Figure 11. Level of the vibration reduction of the deflection angle

6. Conclusions

The development of composite fuzzy logic schemes for

the trajectory tracking and vibration suppression of a

flexible joint manipulator has been presented. The control

schemes

have

been

developed

based

on

a

PD‐

type

FLC

with non‐collocated fuzzy logic control, a PD‐type FLC

with non‐collocated PID control and a PD‐type FLC with

an input‐shaping scheme. The proposed composite

control schemes have been implemented and tested on a

flexible joint manipulator. The performances of the

control schemes have been evaluated in terms of input

tracking capability and vibration suppression for the

resonance modes of the manipulator. An acceptable

performance in input tracking and vibration control has

been achieved with the proposed control strategies. A

comparative assessment of the control schemes has

shown that the PD‐FLC with non‐collocated strategies

performs better

than

the

PD

‐FLC

with

a

feed‐forward

technique in respect of the deflection angle reduction of

the elastic joint. Moreover, in terms of the speed of

responses, PD‐FLC with non‐collocated PID and FLC

results in a faster settling time response with high

overshoot as compared to PD‐FLC with a feed‐forward

scheme. The work thus developed and reported in this

paper forms the basis of the design and development of

composite control schemes for the input tracking and

vibration suppression of multi‐degree of freedom robotic

arms with flexible links and joints.

7. Acknowledgments

This work was supported by the Faculty of Electrical &

Electronics Engineering, University of Malaysia Pahang,

and especially the Control & Instrumentation (COINS)

Research Group.

8. References

[1] Yim, W. (2001) Adaptive Control of a Flexible Joint

Manipulator. Proc. 2001 IEEE, International Robotics

& Automation, Seoul, Korea, pp. 3441–3446.

[2] Oh, J. H. and Lee, J. S. (1997) Control of Flexible Joint

Robot System by Backstepping Design Approach.

Proc. of

IEEE

International

Conference

on

Robotics

&

Automation, pp. 3435–3440.

[3] Ghorbel, F., Hung, J.Y. and Spong, M.W. (1989)

Adaptive Control of Flexible Joint Manipulators.

Control Systems Magazine. 9: 9‐13.

[4] Lin, L.C. and Yuan, K. (2007) Control of Flexible Joint

Robots via External Linearization Approach. Journal

of Robotic Systems. 1(1): 1‐22.

[5] Spong, M. W., Khorasani, K. and Kokotovic, P. V.

(1987) An Integral Manifold Approach to the

Feedback Control of Flexible Joint Robots. IEEE

Journal of Robotics and Automation. 3(4): 291‐300.

[6]

Tomei,

P.

(1991)

A

Simple

PD

Controller

for

Robots

with Elastic Joints. IEEE Trans. on Automatic

Control. 36(10): 1208‐1213.

0 5 10 15 20 25 30 35

1

2

3

Level of vibration reduction (dB)

M o d e o f f r e q u e n c i e s

PD-FLC-FLC

PD-FLC-PID

PD-FLC-IS




[7] Yeon, J. S. and Park, J. H. (2008) Practical Robust

Control for Flexible Joint Robot Manipulators. Proc.

2008 IEEE International Conference on Robotic and

Automation, Pasadena, CA, USA, pp. 3377–3382.

[8] Korayem, M.H., Nohooji, H.R. and Nikoobin, A.

(2011) Path

planning

of

mobile

elastic

robotic

arms

by indirect approach of optimal control. International

Journal of Advance Robotic Systems. 8(1): 10‐20.

[9] Ahmad, M.A., Raja Ismail, R.M.T., Ramli, M.S.,

Zawawi, M.A., Hambali, N. and Abd Ghani, N.M.

(2009) Vibration Control of Flexible Joint

Manipulator using Input Shaping with PD‐type

Fuzzy Logic Control. Proceedings of IEEE

International Symposium on Industrial Electronics,

Seoul, pp. 1184‐1189.

[10] Ahmad, M.A., Nasir, A.N.K., Hambali, N. and Ishak,

H. (2008) Vibration and Input Tracking Control of

Flexible Manipulator

using

Hybrid

Fuzzy

Logic

Controller. Proceedings of the IEEE International

Conference of Mechatronics and Automation,

Kagawa, pp. 593‐598.

[11] Chaoui, H., Gueaieb, W., Yagoub, M. and Sicard, P.

(2006) Hybrid neural fuzzy sliding mode control of

flexible‐ joint manipulators with unknown dynamics.

Proceedings of the 32nd Annual Conference of the

IEEE Industrial Electronics Society (IECON‐2006),

pp. 4082–4087.

[12] Chaoui, H., Sicard, P. and Lakhsasi, A. (2004)

Reference model supervisory loop for neural

network

based

adaptive

control

of

a

flexible

joint

with hard nonlinearities. IEEE Canadian Conference

on Electrical and Computer Engineering. 4: 2029–

2034.

[13] Hui, D., Fuchun, S. and Zengqi, S. (2002) Observer‐

based adaptive controller design of flexible

manipulators using time‐delay neuro‐fuzzy

networks. J. Intell. Robot. Syst.: Theory and

Applications. 34(4): 453–466.

[14] Subudhi, B. and Morris, A. (2006) Singular

perturbation based neuro‐h innity control scheme

for a manipulator with exible links and joints.

Robotica. 24(2): 151–161.

[15] Park, C.W. (2004) Robust stable fuzzy control via

fuzzy modeling and feedback linearization with its

applications to controlling uncertain single‐link

flexible joint manipulators. J. Intell. Robot. Syst.:

Theory and Applications. 39(2): 131–147.

[16] Lin, L. C. and Chen,

C.

C.

(1995)

Rigid

model

‐ based

fuzzy control of flexible‐ joint manipulators. J. of

Intelligent and Robotic Systems. 13: 107–126.

[17] Tokhi, M.O. and Azad, A.K.M. (1996) Control of

flexible manipulator systems. Proceedings IMechE‐I:

Journal of Systems and Control Engineering. 210:

113‐130.

[18] Ahmad, M.A., Suid, M.H., Ramli, M.S., Zawawi,

M.A., Ismail, R.M.T.R. (2010) PD Fuzzy Logic with

non‐collocated PID approach for vibration control of

flexible joint manipulator. Proceedings of 6th

International Colloquium on Signal Processing and

Its Applications,

Mallaca,

Malaysia,

pp.

1‐5.

[19] Ahmad, M.A. (2008) Vibration and Input Tracking

Control of Flexible Manipulator Using LQR with

Non‐Collocated PID Controller. Proceedings of the

2nd UKSIM European Symposium on Computer

Modeling and Simulation, Liverpool, United

Kingdom, pp. 40‐45.

[20] Shchuka, A. and Goldenberg, A.A. (1989) Tip control

of a single‐link flexible arm using feedforward

technique. Mechanical Machine Theory. 24: 439‐455.

[21] Mohamed, Z. and Ahmad, M.A. (2008) 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, pp. 11714‐11719.

[22] Rattan, K.S., Feliu, V. and Brown, H.B. (1990) Tip

position control of flexible arms. Proceedings of the

IEEE Conference on Decision and Control, Honolulu,

pp. 1803‐1808.

[23] Quanser Student Handout, Rotary Flexible Joint

Module. http://www.quanser.com.

[24]Mohamed, Z. and Tokhi, M.O. (2002) Vibration control

of a single‐link flexible manipulator using command

shaping techniques. Proceedings IMechE‐I: Journal of

Systems and Control Engineering. 216: 191‐210.



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