American J. of Engineering and Applied Sciences 2 (1): 241-251, 2009
ISSN 1941-7020
© 2009 Science Publications
Corresponding Author: Mohd Ashraf Ahmad, Faculty of Electrical and Electronics Engineering, University Malaysia Pahang,
Lebuhraya Tun Razak, 26300, Kuantan, Pahang, Malaysia
241

Hybrid Fuzzy Logic Control with Input Shaping for Input Tracking and
Sway Suppression of a Gantry Crane System

1M.A. Ahmad and 2Z. Mohamed
1Faculty of Electrical and Electronics Engineering,
University Malaysia Pahang, Lebuhraya Tun Razak, 26300, Kuantan, Pahang, Malaysia
2Faculty of Electrical Engineering, University Technology Malaysia,
81310, UTM Skudai, Johor Bahru, Malaysia

Abstract: Problem statement: Most of the common gantry crane results in a sway motion when
transporting the load as fast as possible. In addition, precise cart position control of gantry crane must
required a zero or near zero residual sway. Approach: In this study, the development of hybrid control
schemes for input tracking and anti-sway control of a gantry crane system was investigated. To study
the effectiveness of the controllers, a Proportional-Derivative (PD)-type fuzzy logic control was
developed for cart position control of a gantry crane. It was then extended to incorporate input shaper
control schemes for anti-sway control of the system. The positive and new modified Specified
Negative Amplitude (SNA) input shapers were designed based on the properties of the system for
control of system sway. The new SNA was proposed to improve the robustness capability while
increasing the speed of the system response. Results: Simulation results of the response of the gantry
crane with the controllers were presented in time and frequency domains. The performances of the of
the hybrid control schemes were examined in terms of input tracking capability, level of sway
reduction and robustness to parameters uncertainty. Conclusion: A significant reduction in the system
sways had been achieved with the hybrid controllers regardless of the polarities of the shapers.

Key words: Gantry crane, anti-sway control, input shaping, PD-type fuzzy logic controller

INTRODUCTION

The main purpose of controlling a gantry crane is
transporting the load as fast as possible without causing
any excessive sway at the final position. However, most
of the common gantry crane results in a sway motion
when payload is suddenly stopped after a fast motion.
The sway motion can be reduced but will be time
consuming. Moreover, the gantry crane needs a skilful
operator to control manually based on his or her
experiences to stop the sway immediately at the right
position. The failure of controlling crane also might
cause accident and may harm people and the
surrounding.
The requirement of precise cart position control of
gantry crane implies that residual sway of the system
should be zero or near zero. Over the years,
investigations have been carried out to devise efficient
approaches to reduce the sway of gantry crane. The
considered sway control schemes can be divided into
two main categories: Feed-forward control and
feedback control techniques. Feed-forward techniques
for sway suppression involve developing the control
input through consideration of the physical and swaying
properties of the system, so that system sways at
dominant response modes are reduced. This method
does not require additional sensors or actuators and
does not account for changes in the system once the
input is developed. On the other hand, feedback-control
techniques use measurement and estimations of the
system states to reduce sways. Feedback controllers can
be designed to be robust to parameter uncertainty. For
gantry crane, feed-forward and feedback control
techniques are used for sway suppression and cart
position control respectively. An acceptable system
performance without sway that accounts for system
changes can be achieved by developing a hybrid
controller consisting of both control techniques. Thus,
with a properly designed feed-forward controller, the
complexity of the required feedback controller can be
reduced.
Various attempts in controlling gantry cranes
system based on feed-forward control schemes were
proposed. For example, open loop time optimal

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

242

strategies were applied to the crane by many
researchers such as discussed in[1]. They came out with
poor results because feed-forward strategy is sensitive
to the system parameters (e.g., rope length) and could
not compensate for wind disturbances. Another feed-
forward control strategy is input shaping[2-4]. Input
shaping is implemented in real time by convolving the
command signal with an impulse sequence. The process
has the effect of placing zeros at the locations of the
flexible poles of the original system. An IIR filtering
technique related to input shaping has been proposed
for controlling suspended payloads[5]. Input shaping has
been shown to be effective for controlling oscillation of
gantry cranes when the load does not undergo
hoisting[6,7]. Experimental results also indicate that
shaped commands can be of benefit when the load is
hoisted during the motion[8].
Investigations have shown that with the input
shaping technique, a system response with delay is
obtained. To reduce the delay and thus increase the
speed of the response, negative amplitude input shapers
have been introduced and investigated in vibration
control. By allowing the shaper to contain negative
impulses, the shaper duration can be shortened, while
satisfying the same robustness constraint. A significant
number of negative shapers for vibration control have
also been proposed. These include negative Unity-
Magnitude (UM) shaper, Specified-Negative-Amplitude
(SNA) shaper, negative Zero-Vibration (ZV) shaper,
negative Zero-Vibration-Derivative (ZVD) shaper and
negative Zero-Vibration-Derivative-Derivative (ZVDD)
shaper[9-11]. Comparisons of positive and negative input
shapers for vibration control of a single-link flexible
manipulator have also been reported[11].
On the other hand, feedback control which is well
known to be less sensitive to disturbances and
parameter variations[12] is also adopted for controlling
the gantry crane system. Recent research on gantry
crane control system was presented by[13]. The author
had proposed proportional-derivative PD controllers for
both position and anti-sway controls. Furthermore, a
fuzzy-based intelligent gantry crane system has been
proposed[14]. The proposed fuzzy logic controllers
consist of position as well as anti-sway controllers.
However, most of the feedback control system
proposed needs sensors for measuring the cart position
as well as the load sway angle. In addition, designing
the sway angle measurement of the real gantry crane
system, in particular, is not an easy task since there is a
hoisting mechanism.
This study presents investigations into the
development of hybrid control schemes for input
tracking and anti-sway control of a gantry crane system.
A nonlinear overhead gantry crane system is considered
and the dynamic model of the system is derived using
the Euler-Lagrange formulation. Hybrid control
schemes based on feed-forward with collocated
feedback controllers are investigated. In this study,
feed-forward control based on input shaping with
positive Zero-Sway-Derivative-Derivative (ZSDD) input
shapers and new modified SNA Zero-Sway-Derivative-
Derivative (ZSDD) input shapers are considered. A new
modified shaper from the previous SNA input shapers[11]
is proposed where more negative impulses are added to
improve the robustness of the controller while increasing
the speed of the system response. To demonstrate the
effectiveness of the proposed control schemes, a PD-type
Fuzzy Logic controller is developed for control of cart
motion of the gantry crane. This is then extended to
incorporate the proposed input shapers for control of
sway of hoisting rope. Simulation exercises are
performed within the gantry crane simulation
environment. Performances of the developed controllers
are examined in terms of input tracking capability, level
of sway reduction and robustness to errors in sway
frequency. In this case, the robustness of the hybrid
control schemes is assessed with up to 30% error
tolerance in sway frequencies. Simulation results in time
and frequency domains of the response of the gantry
crane to the unshaped input and shaped inputs with
positive and modified SNA input shapers are presented.
Moreover, a comparative assessment of the effectiveness
of the hybrid controllers with positive and negative input
shapers in suppressing sway and maintaining the input
tracking capability of the gantry crane is discussed.

The gantry crane system: The two-dimensional gantry
crane system with its payload considered in this study is
shown in Fig. 1, where x is the horizontal position of
the cart, l is the length of the rope, θ is the sway angle
of the rope, M and m is the mass of the cart and payload
respectively. In this simulation, the cart and payload can
be considered as point masses and are assumed to move
in two-dimensional, x-y plane. The tension force that
may cause the hoisting rope elongate is also ignored. In
this study the length of the cart, l = 1.00 m, M = 2.49 kg,
m = 1.00 kg and g = 9.81 m s−2 is considered.

Modeling of the gantry crane: In this research, the
mathematical modeling of the gantry crane system is
considered as a basis of a simulation environment for
development and assessment of the input shaping
control techniques. The Euler-Lagrange formulation is
considered in characterizing the dynamic behavior of
the crane system incorporating payload.

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

243



Fig. 1: Description of the gantry crane system.

Considering the motion of the gantry crane system
on a two-dimensional plane, the kinetic energy of the
system can thus be formulated as:

2 21 1T Mx m(x i2 l2 2
2 2
2xlsin 2xl cos )
= + + + θ +
θ+ θ θ
& &
(1)

The potential energy of the beam can be
formulated as:

U mglcos= − θ

(2)

To obtain a closed-form dynamic model of the
gantry crane, the energy expressions in (1) and (2) are
used to formulate the Lagrangian L T U= − . Let the
generalized forces corresponding to the generalized
displacements q {x, }= θ be
xF {F ,0}= . Using
Lagrangian’s equation:

j
j j
d L L F j 1,2
dt q q
 ∂ ∂
− = =  ∂ ∂ &

(3)

the equation of motion is obtained as:

2
xF (M m)x ml( cos sin )
2ml cos ml sin
= + + θ θ − θ θ
θ θ + θ
&& &&&
& &&& (4)

2
x
F (M m)x ml( cos sin ) 2ml cos
ml sin l 2l x cos gsin 0
= + + θ θ − θ θ + θ θ
+ θ θ + θ + θ + θ =
&&& & &&&
&& &&& & &&
(5)
In order to eliminate the nonlinearity equation in
the system, a linear model of gantry crane system is
obtained. The linear model of the uncontrolled system
can be represented in a state-space form as shown in
Eq. 6 by assuming the change of rope and sway angle
are very small:

x Ax Bu
y Cx
= +
=
&

(6)

with the vector
T
x x x = θ θ && and the matrices A and
B are given by:

[ ] [ ]
0 0 1 0 0
0 0 0 1 0
mg 1A , B ,0 0 0
M M
(M m)g 10 0 0
Ml Ml
C 1 0 0 0 , D 0
            
= =      
+   
− −      
= =
(7)

MATERIALS AND METHODS

PD-type fuzzy logic control scheme: Fuzzy control
can be viewed as a way of converting expert knowledge
into an automatic control strategy without a detailed
knowledge of the plant. The input is first fuzzified and
then processed by the fuzzy inference engine using
heuristic decision rules. FLC uses rules in the form of
‘‘IF [condition] THEN [action]’’ to linguistically
describe the input/output relationship. The membership
functions convert linguistic terms into precise numeric
values. The output of the fuzzy controller is obtained by
a defuzzification process that converts the fuzzy
quantities representing the control signal into a signal
that can be used as the control input to the plant.
A PD-type fuzzy logic controller utilizing hub
angle and hub velocity feedback is developed to control
the rigid body motion of the system[15]. The hybrid
fuzzy control system proposed in this study is shown in
Fig. 2, where Rf is the reference horizontal position, x
and x& represent horizontal position and velocity of the
cart, respectively, θ

and θ& represent swing angle and
swing velocity, respectively, whereas k1, k2 and k3 are
scaling factors for two inputs and one output of the
fuzzy logic controller used with the normalized
universe of discourse for the fuzzy membership
functions.

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

244



Fig. 2: PD-type Fuzzy Logic control structure

In this study, the triangular membership functions
are chosen for inputs and output. Normalized universes
of discourse are used for both hub angle and velocity
and output torque. Scaling factors k1 and k2 are 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 cart position error, cart
position error derivative and force input are partitioned
into five primary fuzzy sets as[15]:

Cart position error E = {NM NS ZE PS PM}

Cart position error derivative V = {NM NS ZE PS PM}

Force U = {NM NS ZE PS PM}

where E, V and U are the universes of discourse cart
position, cart velocity and force input, respectively. The
nth rule of the rule base for the FLC, with cart position
error and derivative of cart position error as inputs, is
given by:

Rn: IF(e is Ei) AND ( e& is Vj) THEN (u is Uk)

where, Rn, n = 1, 2,…Nmax is the nth fuzzy rule, Ei, Vj
and Uk, for i, j, k = 1,2,…,5 are the primary fuzzy sets.
A PD-type fuzzy logic controller was designed
with 11 rules as a closed loop component of the control
strategy for maintaining the cart position of gantry
crane system while suppressing the swaying effect. The
rule base was extracted based on underdamped system
response and is shown in Table 1. 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 = 0.05, k2 = 0.001
and k3 = -350.

INPUT shaping control schemes: Input shaping
technique is a feed-forward control technique that
involves convolving a desired command with a
sequence of impulses known as input shaper.
Table 1: Linguistic rules of Fuzzy Logic Controller
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)



Fig. 3: Illustration of input shaping technique

The shaped command that results from the convolution
is then used to drive the system. Design objectives are
to determine the amplitude and time locations of the
impulses, so that the shaped command reduces the
detrimental effects of system flexibility. These
parameters are obtained from the natural frequencies
and damping ratios of the system. Thus, sway reduction
of a gantry crane system can be achieved with the input
shaping technique. Figure 3 shows the input shaping
process. Several techniques have been investigated to
obtain an efficient input shaper for a particular system.
A brief description and derivation of the control
technique is presented in this study.
Generally, a vibratory system of any order can be
modeled as a superposition of second order systems
each with a transfer function:

2
2 2G(s) s 2 s
ω
=
+ ζω + ω (8)

Where:
ω = The natural frequency of the vibratory system
ζ = The damping ratio of the system

Thus, the response of the system in time domain
can be obtained as:

( )0( t t ) 2 02Ay(t) exp sin 1 (t t )1 −ζω −ω= ω − ζ −− ζ (9)

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

245

where, A and t0 are the amplitude and the time location
of the impulse respectively. The response to a sequence
of impulses can be obtained by superposition of the
impulse responses. Thus, for N impulses, with
( )2d 1ω = ω − ζ , the impulse response can be expressed
as:

( )dy(t) M sin t= ω + β

(10)

Where:
M =
2 2N N
i i i i
i 1 i 1
B cos B sin
= =
   φ + φ      ∑ ∑
Bi = 0(t t )i 2
A
exp
1
−ζω −ω
− ζ

i d itφ = ω
Ai and ti = The amplitudes and time locations of the
impulses

The residual single mode sway amplitude of the
impulse response is obtained at the time of the last
impulse, tN as:

2 2
1 2V V V= + (11)

Where:
n N i
N
(t t )i n
1 d i2
i 1
AV exp cos( t )
1
−ζω −
=
ω
= ω
− ζ∑

n N i
N
(t t )i n
2 d i2
i 1
AV exp sin( t )
1
−ζω −
=
ω
= ω
− ζ∑

To achieve zero sway after the last impulse, it is
required that both V1 and V2 in Eq. 11 are
independently zero. This is known as the zero residual
sway constraints. In order to ensure that the shaped
command input produces the same rigid body motion as
the unshaped reference command, it is required that the
sum of amplitudes of the impulses is unity. This yields
the unity amplitude summation constraint as:

N
i
i 1
A 1
=
=∑ (12)

In order to avoid response delay, time optimality
constraint is utilized. The first impulse is selected at
time t1 = 0 and the last impulse must be at the
minimum, i.e., min (tN). The robustness of the input
shaper to errors in natural frequencies of the system can
be increased by taking the derivatives of V1 and V2 to
zero. Setting the derivatives to zero is equivalent to
producing small changes in sway corresponding to the
frequency changes. The level of robustness can further
be increased by increasing the order of derivatives of
V1 and V2 and set them to zero. Thus, the robustness
constraints can be obtained as:

i i
1 2
i i
n n
d V d V0, 0
d d
= =
ω ω
(13)

Both the positive and modified SNA input shapers
are designed by considering the constraints Eq.s. The
design of the positive and modified SNA input shapers
is further discussed in this investigation.

Positive input shaper: 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 order to
increase the robustness of the input shaper to errors in
natural frequencies, the positive ZSDD input shaper is
designed by setting the second derivatives of V1 and V2
in Eq. 11 to zero. Simplifying 2 2i nd V dω yields:

n N i
n N i
2 N
(t t )21
i i d i2
i 1n
2 N
(t t )22
i i d i2
i 1n
d V A t e sin( t );
d
d V A t e cos( t )
d
−ζω −
=
−ζω −
=
= ω
ω
= ω
ω
∑
∑
(14)

The positive ZSDD input shaper, i.e., four-impulse
sequence is obtained by setting Eq. 11 and 14 to zero
and solving with the other constraint Eq.s. Hence, a
four-impulse sequence can be obtained with the
parameters as:

1 2 3 4
d d d
1 22 3 2 3
2 3
3 42 3 2 3
2 3
t 0, t , t , t
1 3KA ,A
1 3K 3K K 1 3K 3K K
3K KA ,A
1 3K 3K K 1 3K 3K K
pi pi pi
= = = =
ω ω ω
= =
+ + + + + +
= =
+ + + + + +
(15)

Where:
21K e
−ζpi
−ζ
=
2
d n 1ω = ω − ζ

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

246

ωn and ζ representing the natural frequency and damping
ratio respectively. For the impulses, tj and Aj are the time
location and amplitude of impulse j respectively.

Modified SNA input shapers: Input shaping
techniques based on positive input shaper have been
proved to be able to reduce sway of a system. In order
to achieve higher robustness, the duration of the shaper
is increased and thus, increases the delay in the system
response. By allowing the shaper to contain negative
impulses, the shaper duration can be shortened, while
satisfying the same robustness constraint.
To include negative impulses in a shaper requires
the impulse amplitudes to switch between 1 and -1 as:

i 1
iA ( 1) += − ; i = 1, …, n (16)

The constraint in Eq. 16 yields useful shapers as
they can be used with a wide variety of inputs. For a
UM negative ZS shaper, i.e. the magnitude of each
impulse is |1|, the shaper duration is one-third of the
vibration period of an undamped system, while the
shaper duration for the positive shaper is half of the
vibration period. However, the increase in the speed of
system response achieved using the SNA input shapers
is at the expense of some tradeoffs and penalties. The
shapers containing negative impulses have tendency to
excite unmodeled high modes and they are slightly less
robust as compared to the positive shapers. Besides,
negative input shapers require more actuator effort than
the positive shapers due to high changes in the set-point
command at each new impulse time location.
To overcome the disadvantages, a modified SNA
input shaper is introduced, whose negative amplitudes
can be set to any value at the centre between each
normal impulse sequences. In this study, the previous
SNA input shaper[11] is modified by locating the
negative amplitudes at the centre between each positive
impulse sequences with even number of total impulses.
This will result the shaper duration as one-fourth of the
sway period of an undamped system as shown in Fig. 4.

c c
a a
-b -b
-d -d
0.5t2 1.5t2 2.5t2 3.5t2
0 t2 t3 t4


Fig. 4: Modified SNA-ZSDD shaper
The modified SNA-ZSDD shaper is proposed and
applied in this study to enhance the robustness
capability of the controller while increasing the speed
of the system response. By considering the form of
modified SNA-ZSDD shaper shown in Fig. 4, the
amplitude summation constraints Eq. can be obtained as:

2a + 2c – 2b – 2d = 1 (17)

The values of a, b, c and d can be set to any value
that satisfy the constraint in (17). However, the
suggested values of a, b, c and d are less than |1| to
avoid the increase of the actuator effort.

RESULTS

In this study, the proposed control schemes are
implemented and tested within the simulation
environment of the gantry crane and the corresponding
results are presented. In this study, positive ZSDD and
modified SNA-ZSDD are investigated as the input
shaping control schemes. The cart position of the gantry
crane is required to follow a trajectory within the range
of 4± m as shown in Fig. 5. System responses namely
the cart position, cart velocity and sway angle of the
hoisting rope are observed. To investigate the sway of
the system in the frequency domain, Power Spectral
Density (PSD) of the response at the sway angle is
obtained. The performances of the hybrid controllers
are assessed in terms of input tracking and sway
suppression in comparison to the PD-type Fuzzy logic
control. Moreover, robustness of the controllers to
variations in sway frequencies is also investigated. In
this case, 30% error tolerance in sway frequencies is
considered.



Fig. 5: The trajectory reference input

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

247


(a) (b)


(c) (d)

Fig. 6: Response of the gantry crane with PD-type Fuzzy Logic controller. (a) : Cart position; (b) : Cart velocity;
(c): Sway angle and (d): PSD of sway angle

PD-type Fuzzy Logic control: In this investigation, the
responses of the gantry crane system to the unshaped
trajectory reference input were analyzed in time-domain
and frequency domain (spectral density) as shown in
Fig. 6. These results were considered as the system
response to the unshaped input under tracking
capability and will be used to evaluate the performance
of the input shaping techniques. The steady-state cart
position trajectory of +4 m for the gantry crane was
achieved within the rise and settling times and
overshoot of 1.169 s, 2.506 s and 12.4 % respectively.
It is noted that the cart reaches the required position
from +4 m to -4 m within 2 s, with high overshoot.
However, a noticeable amount of swing angle
occurs during movement of the cart. It is noted from the
swing angle response with a maximum residual of ±1.3
rad. Moreover, from the PSD of the swing angle
response the swaying frequencies are dominated by the
first three modes, which are obtained as 0.3925, 1.177
and 1.962 Hz with magnitude of 27.27, -10.73 and
-29.55 dB respectively. The closed loop parameters
with the PD-type Fuzzy Logic control will subsequently
be used to design and evaluate the performance of
hybrid controllers with positive ZSDD and SNA-ZSDD
shapers.

Hybrid control: Figure 7 shows a block diagram of
the proposed hybrid control scheme where the PD-
type FLC is combined with the input shaping control
schemes. The positive ZSDD and modified SNA-
ZSDD shapers were designed based on the dynamic
behavior of the closed-loop system obtained using
only the PD-type FLC. As demonstrated in PSD
result, the natural frequencies of the sway angle were
0.3925, 1.177 and 1.962 Hz for the first three sway
modes. With exact natural frequencies, the time
locations and amplitudes of the impulses for positive
ZSDD shaper were obtained by solving Eq. 15.

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

248



Fig. 7: Block diagram of the hybrid control schemes
configuration

Moreover, the amplitudes of the modified SNA-ZSDD
shaper were deduced as [0.3 -0.1 0.5 -0.2 0.5 -0.2 0.3 -
0.1] and the time locations of the impulses were chosen
at the half of the time locations of positive ZSDD
shaper as shown in Fig. 4. For evaluation of robustness,
input shapers with erroneous natural frequencies were
also evaluated. With 30% error in natural frequency, the
system sways were considered at 0.5103, 1.5301 and
2.551 Hz for the three modes of sway. Similarly, the
amplitudes and time locations of the input shapers with
30% erroneous natural frequencies for both the positive
and modified SNA-ZSDD shapers were calculated.
For digital implementation of the input shaper,
locations of the impulses were selected at the nearest
sampling time. The developed input shaper was then
used to pre-process the input reference shown in Fig. 5.
Figure 8 shows the shaped inputs using both the
positive and modified SNA-ZSDD shapers with exact
natural frequencies. It is noted that the shaped input
with the modified SNA shaper is not as smooth as
compared to the positive shaper. This is due to higher
number of switching of the actuator.
Figure 9 shows the system responses of the gantry
crane using the hybrid controllers with exact natural
frequencies. Table 2 shows the levels of sway reduction
of the system responses at the first three modes in
comparison to the PD-type Fuzzy Logic control. It is
noted that the proposed hybrid controllers are capable
of reducing the system sway while maintaining the
input tracking performance of the cart position.
Similar cart position and cart velocity responses were
observed as compared to the PD-type FLC. Moreover,
a significant amount of sway reduction was
demonstrated at the sway angle of the hoisting rope
with both control schemes. With the positive ZSDD
and modified SNA-ZSDD shapers, the maximum
sway angles were obtained at ±0.20 and ±0.16 rad
respectively. These are seven-fold and eight-fold
improvements as compared to PD-type FLC. This is
also evidenced in the PSD of the sway angle residual
that shows lower magnitudes at the resonance modes.


Fig. 8: Shaped inputs with exact natural frequencies
using positive ZSDD and modified SNA-ZSDD
shapers

Table 2: Level of sway angle reduction of the rope and
specifications of the cart trajectory response for the hybrid
control schemes
Attenuation (dB) Specifications of cart
of sway angle of trajectory response
the rope ---------------------------
Types of -------------------------- Rise Settling Over
shaper Mode Mode Mode time time shoot
Frequency (ZSDD) 1 2 3 (s) (s) (%)
Exact Positive 36.16 39.20 39.10 3.071 4.866 0.63
Modified 22.99 34.11 32.01 3.492 4.607 2.15
SNA
Error Positive 19.93 26.56 24.21 2.431 3.901 3.30
Modified 26.86 14.22 12.23 2.661 3.615 2.90
SNA

The corresponding rise time, settling time and
overshoot of the cart response using PD-type FLC with
positive and modified SNA ZSDD shapers with exact
natural frequencies is shown in Table 2. The simulation
results show that the cart position reaches the required
trajectory position of +4 m within the settling times of
4.866 s and 4.607 s with positive ZSDD and modified
SNA-ZSDD respectively. It is noted with the feed-
forward controller, a slower settling time as compared
to the PD-type Fuzzy Logic controller was achieved.
To examine the robustness of the hybrid
controllers, the shapers with 30% error in sway
frequencies were designed and implemented to the
gantry crane system. Figure 10 shows the response of
the gantry crane with the hybrid controllers with
erroneous natural frequencies. Table 2 shows the
levels of sway reduction with erroneous natural
frequencies in comparison to the PD-type FLC. The
time response specifications of the cart position with
error in natural frequencies are also shown in Table 2.

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

249


(a) (b)


(c) (d)

Fig. 9: Response of the gantry crane with hybrid controllers with exact natural frequencies. (a) : Cart position;
(b): Cart velocity; (c): Sway angle and (d): PSD of sway angle


(a) (b)


(c) (d)

Fig. 10: Response of the gantry crane with hybrid controllers with erroneous natural frequencies. (a): Cart position;
(b): Cart velocity; (c): Sway angle and (d): PSD of sway angle

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

250

Similar to the case with exact frequencies, the proposed
hybrid controllers are capable of reducing the system
sway while maintaining the input tracking performance
of the cart position. Moreover, the sways of the system
were considerable reduced as compared to the response
with PD-type FLC. However, the level of sway
reduction is slightly less than the case with exact
natural frequencies.

DISCUSSION

The simulation results show that performance of
the hybrid controller with positive ZSDD control
scheme is better than SNA-ZSDD scheme in sway
suppression of the gantry crane. This is further
evidenced in Fig. 11 that demonstrates the level of sway
reduction of the gantry crane with the hybrid controllers
as compared to the PD-type FLC. It is noted that higher
sway reduction is achieved with positive ZSDD at the
first, second and third resonance modes, which are the
most dominant modes. Almost less than two-fold
improvement in the sway reduction was observed as
compared to SNA-ZSDD. Comparisons of the cart
position responses show that the hybrid controller with
SNA-ZSDD shaper is faster than the case using the
positive ZSDD shaper. The result reveals that the speed
of the system responses can be improved by using
negative impulses input shaper.
Comparison of the results shown in Fig. 11 reveals
that both hybrid controllers with the positive and SNA
input shapers can successfully handle errors in natural
frequencies. Moreover, almost similar performance in
sway reduction of the gantry crane was achieved with
both control schemes. As positive ZSDD performs
better than SNA-ZSDD with exact frequencies, the
results demonstrate that, the modified SNA-ZSDD is
capable of improving the robustness of the controller to
uncertainty in sway frequencies. Comparisons of the
cart position response with the hybrid controllers show
a similar pattern as the case with exact natural
frequencies. With the new proposed SNA shaper, it is
shown that the robustness of the controller can be
improved while increasing the speed of the response.
The research thus developed and reported in this study
forms the basis of design and development of hybrid
control schemes for input tracking and sway
suppression of boom and 3-D gantry crane systems and
can be extended to and adopted in practical
applications.


Fig. 11: Level of sway reduction with exact and
erroneous natural frequencies with hybrid
controllers

CONCLUSION

The development of hybrid control schemes based
on PD-type Fuzzy Logic control with positive and
negative input shapers for input tracking and sway
suppression of a gantry crane has been presented. The
proposed control schemes have been implemented and
tested within simulation environment of an overhead
gantry crane derived using the Euler-Lagrange
formulation. The performances of the control schemes
have been evaluated in terms of input tracking
capability, level of sway reduction and robustness.
Acceptable performance in input tracking control and
sway suppression has been achieved with both control
strategies. Moreover, a significant reduction in the
system sways has been achieved with the hybrid
controllers regardless of the polarities of the shapers. A
comparative assessment of the hybrid control schemes
has shown that the PD-type FLC with positive ZSDD
shaper provides higher level of sway reduction of the
gantry crane as compared to the PD-type FLC with
SNA-ZSDD shaper. By using the PD-type FLC with
modified SNA-ZSDD, robustness of the controller can
be improved as similar level of robustness as positive
ZSDD is achieved. Moreover, with SNA -ZSDD, the
speed of the response is slightly increased at the
expenses of decrease in the level of sway reduction.

REFERENCES

1. Auernig, J. and H. Troger, 1987. Time optimal
control of overhead cranes with hoisting of the
load. Automatica, 23: 437-447. DOI:
10.1016/0005-1098(87)90073-2

Am. J. Engg. & Applied Sci., 2 (1): 241-251, 2009

251

2. Karnopp, B.H., F.E. Fisher and B.O. Yoon, 1992.
A strategy for moving mass from one point to
another. J. Frankl Ins., 329: 881-892.
http://hdl.handle.net/2027.42/29888
3. Teo, C.L., C. J. Ong and M. Xu, 1998. Pulse input
sequences for residual vibration reduction. J.
Sound Vibrat., 211: 157-177. DOI:
10.1006/jsvi.1997.1360
4. Singhose, W.E., L.J. Porter and W. Seering, 1997.
Input shaped of a planar gantry crane with hoisting.
Proceeding of the American Control Conference,
June 4-6, IEEE Xplore, USA., pp: 97-100. DOI:
10.1109/ACC.1997.611762
5. Feddema, J.T., 1993. Digital filter control of
remotely operated flexible robotic structures.
Proceeding of the American Control Conference,
(ACC’93), San Francisco, CA., pp: 2710-2715.
6. Noakes, M.W. and J.F. Jansen, 1992. Generalized
inputs for damped-vibration control of suspended
payloads. Robot. Autonom. Syst., 10: 199-205.
DOI: 10.1016/0921-8890(92)90026-U
7. Singer, N., W. Singhose and E. Kriikku, 1997. An
input shaping controller enabling cranes to move
without sway. Proceeding of the ANS 7th Topical
Meeting on Robotics and Remote Systems,
Augusta, GA.,
http://www.osti.gov/bridge/servlets/purl/491559-
NFLqr9/webviewable/491559.PDF
8. Kress, R.L., J.F. Jansen and M.W. Noakes, 1994.
Experimental Implementation of a Robust
Damped-Oscillation Control Algorithm on a Full
Sized, Two-DOF, AC Induction Motor- Driven
Crane. Proceeding of the 5th International
Symposium on Robotics and Manufacturing, Aug.
14-18, Maui, HI., pp: 585-92.
http://adsabs.harvard.edu/abs/1994roma.symp...14K
9. Singhose, W., N.C. Singer and W.P. Seering, 1994.
Design and implementation of time-optimal
negative input shapers. Proceedings of the
Congress and Exposition on International
Mechanical Engineering, (CEIME’94), Chicago,
pp: 151-157.
http://www.me.gatech.edu/inputshaping/Papers/W
AM94.pdf








10. Singhose, W. and B.W. Mills, 1999. Command
generation using specified-negative-amplitude
input shapers. Proceedings of the American Control
Conference, June 2-4, IEEE Xplore, San Diego,
California, pp: 61-65.
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumbe
r=00782740
11. Mohamed, Z., A.K. Chee, A.W.I. Mohd Hashim,
M.O. Tokhi, S.H.M. Amin and R. Mamat, 2006.
Techniques for vibration control of a flexible
manipulator. Robotica, 24: 499-511. DOI:
10.1017/S0263574705002511
12. Belanger, N.M., 1995. Control Engineering: A
Modern Approach. 1st Edn., Oxford University
Press, Inc., New York, USA., ISBN:0030134897,
pp: 494.
13. Omar, H. and A.H. Nayfeh, 2004. Gain scheduling
feedback control of tower cranes with friction
compensation. J. Vibrat. Control, 10: 269-289.
DOI: 10.1177/1077546304035610
14. Lee, H.H. and S.K. Cho, 2001. A New fuzzy logic
anti-swing control for industrial three-dimensional
overhead crane. Proceedings of the IEEE
International Conference on Robotic and
Automation, (IICRA’01), IEEE Xplore, USA.,
pp: 2958-2961.
http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumbe
r=00933070
15. Alam, M.S. and M.O. Tokhi, 2008. Hybrid fuzzy
logic control with genetic optimisation for a single-
link flexible manipulator. Eng. Appl. Artif. Intell.,
21: 858-873. DOI: 10.1016/j.engappai.2007.08.002