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. 2010 11th Int. Conf. Control, Automation, Robotics and Vision Singapore, 7-10th December 2010 532