978-1-4244-7815-6/10/$26.00 ©2010 IEEE ICARCV2010
Active Sway Control of a Single Pendulum Gantry
Crane System using Output-Delayed Feedback
Control Technique
Rajeeb Dey, Nishant Sinha, Priyanka Chaubey
Dept. of Electrical & Electronics Engineering,
Sikkim Manipal University, Sikkim, India.
E-mail: rajeeb_de@ieee.org ,
Tele: +91-9475078606.
S. Ghosh and G. Ray
Dept. of Electrical Engineering, National Institute of
Technology, Rourkela Orissa, India.
Dept. of Electrical Engg., Indian Institute of Technology,
Kharagpur, West Bengal, India.
Abstract— This paper investigates the implementation of
output-delayed feedback control (ODFC) technique for
controlling the sway angle of single pendulum gantry crane
(SPGC) system. Linearized mathematical model of the SPGC in
state space form is considered for the investigation. The designed
ODFC has undergone complete stability analysis for a given
controller gain.
Keywords— Anti-Sway control, Output-delayed feedback
control (ODFC), LQR Control, Single pendulum Gantry Crane
(SPGC).
I. INTRODUCTION
A SPGC system is a crane carrying the cart with a movable
or fixed hoisting mechanism, they are required in modern
industrial environment to transport heavy payloads from one
position to another as fast and as accurately as possible with
out collision with other equipments. The basic motions of
SPGC system involves crane traversing, load hoisting and load
lowering. We consider an SPGC which is of fixed hoist model.
In case of fast crane traversing, a large sway of the hoisting
mechanism takes place. The objective of this work is to design
ODFC for controlling sway angle of the hoisting mechanism.
This control problem is similar to vibration control problem
dealt in [1,4,6,9]. Finding control methods that will eliminate
vibration or oscillations from wide range of physical systems is
of interest for past few decades [1], and one such application of
vibration control of industrial significance is sway control of
gantry crane. The active vibration control strategies for
controlling vibration in physical structures or systems
[1,2,4,6,8,10,9] is the principle used here, thus calling it as
active sway control.
In [4,10] shaped input control method have been used,
this method has the effect of placing zeros at the locations of
the flexible poles of the original system, but being a feed-
forward control strategy control is not robust to external
disturbances. In [1,6] and references there in, it is found that
time-delay control (TDC) is another approach for active
vibration (oscillation) control. The inclusion of time-delay in
the system dynamics makes the system an infinite dimensional
[3,7,13-15] thus direct computation of the characteristic roots
and consequently deciding about stability is a difficult task.
A detailed review of the research on time-delay stability
and stabilization issues using both frequency domain
technique and time domain methods can be found in [3,7,15].
The former technique for assessing the stability of TDS can be
found in the literature [1,5,6,7,9,11,12], this technique
provides exact stability analysis for time-invariant delay and
hence TDC has been used in many control applications [1,6,9]
and references there in to suppress vibration or oscillations of
the system. The later technique can treat both the natures of
delay, time-variant and time-invariant, a numerically tractable
algorithm exist to solve the problem, but provides
conservative analysis compared to the former technique
[3,7,13,15]. In this paper, to control this under-damped system
a signal is derived from the position sensor which is then
combined with the delayed output signal from the same sensor
and fed back to the system, thus calling it output-delayed
feedback controller (ODFC). This design involves priori
knowledge of the controller gain for which the time-delay is
treated as design parameter. The frequency domain technique
of [11] is adopted for this design to compute the delay time for
a pre-selected gain value.
II. DYNAMIC MODEL OF SPGC
The two-dimensional single pendulum gantry crane
system with its payload considered in this work is shown in
the Fig.1. The payload is suspended from the point of
suspension S, which denotes the centre of gravity of the cart.
The downward vertical position of the payload is taken as
reference position. The centre point G denotes the centre of
gravity of the payload and the direction of the velocity of the
payload with its components in X and Y Cartesian coordinates
are represented in the Fig.1.
x
F represents the force causing
translational motion of the crane. The nomenclatures along
with the values of the physical parameter are given in Table 1.
The dynamic model of SPGC can be found in [2,8].
Following simplification apply in this model, (i) Model does
not include hoisting drive, thus rod length is fixed (ii) trolley
or payload is assumed to be point mass (iii) trolley and
payload assumed to move in X-Y plane and (iv) force on
trolley due to pendulum swing is neglected.
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