Submit Manuscript | http://medcraveonline.com Introduction Industries and services such as heavy industry, construction work, loading/unloading the harbor and automotive industries widely use overhead cranes. The main purpose of the overhead crane is to transport the heavy workpiece to the target position. However, the swing of the processed object must be eliminated at the target position for better performance and productivity. To increase the productivity of the overhead crane, fast accelerated and decelerated operations are required. However, fast acceleration and deceleration motions create a dangerous situation by shaking the workpiece suspended from the hoist. If heavy workloads are shaken too much, the facilities and infrastructure around the overhead crane can be destroyed or, in severe cases, the crane itself can be broken and may cause people to suffer serious injuries. The most important part of crane work is horizontal transport, which moves the workpiece horizontally to the goal position after lifting it. In this horizontal motion task, the trolley and workpiece must reach the desired goal position quickly while keeping a small swing angle. When the trolley reaches the target position, the swing angle is suppressed to zero. The following two main approaches are necessary to reach the above-mentioned requirement. The frst one consists of designing a proper trajectory for the trolley (i.e., motion planning). The second approach involves designing an anti-swing controller (i.e., control design). In the frst approach, the reference trajectory of the overhead crane has a general motion control velocity profle. That is, it is composed of three stages of acceleration, constant velocity, and deceleration. The accelerating and decelerating time and shape in the frst and third phases increase the swing angle to its maximum value before decreasing the angle to zero. Consequently, the swing angle is zero in the constant velocity phase. 1 The second approach has attracted the interest of researchers. Numerous control methods have also been studied for overhead cranes. Several controllers can be listed as linear, gain schedule, nonlinear, partial feedback linearization, sliding mode, adaptive, fuzzy logic, and so on. 2–12 Each controller has its own advantages and disadvantages, the details of which can be found. 13 A combination of control methods is considered by several authors (e.g., adaptive and adaptive fuzzy sliding-mode controls). 14–19 These combinations produce complex controllers with parameters that do not guarantee system stability. Design methods based on the energy and passivity of the system has been studied. This control approach can be applied not only to fully actuated systems, but also to under-operating systems such as under-operated actuators, 20,21 overhead cranes, 4 and ball- beam systems. 22 The aforementioned method exhibits simplicity in designing a controller from energy-storage function, which adopts mechanical, kinetic, and potential energies. The additional energy affects the control performance. Based on the aforementioned studies, we utilize passivity to generalize the controller design for under actuated overhead crane systems. Five controllers, including linear and nonlinear controllers, are designed based on the total energy of an overhead crane. The Lyapunov candidate function is chosen by a combination of the system energy and the kinetic and potential energies. The origin of the closed-loop system is proven asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. Energy-based controllers guarantee the asymptotic stability of the system; however, the choice of control parameters is an ad hoc issue. Another disadvantage of these controllers is that the swing angle converges slowly to zero. Therefore, the linear optimal controller in this study is switched on when the trolley reaches a point close to the destination. The system response is signifcantly improved by applying this technique. The remainder of this paper is organized as follows. Section 2 introduces the nonlinear dynamics of an overhead crane with two degrees of freedom (DOFs), as well as the useful properties of a dynamic system. Sections 3 presents an energy-based control design in which fve controllers based on Lyapunov theory are derived. Section 4 shows the numerical and experimental verifcations of the controllers. Section 5 concludes. Dynamic model and its properties Dynamic model The control problem of the crane during the horizontal transportation phase is addressed in this section. The rope has constant length, and the system has two DOFs. The following assumptions are established to obtain the dynamic model of the system: Int Rob Auto J. 2018;4(3):197‒203. 197 © 2018 Won et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and build upon your work non-commercially. Comparative study of energy-based control design for overhead cranes Volume 4 Issue 3 - 2018 In-Sik Won, 2 Nguyen Quang Hoang, 1 Soon- Geul Lee, 2 Jae Kwan Ryu 3 1 Hanoi University of Science and Technology,Vietnam 2 Kyung Hee University, South Korea 3 LIG Nex1 Co. Ltd, South Korea Correspondence: Soon-Geul Lee, Kyung Hee University, South Korea, Tel +82-31-2012506, FAX +82-31-2021204, Email sglee@khu.ac.kr Received: May 04, 2018 | Published: June 08, 2018 Abstract This paper presents a position control problem for an under actuated overhead crane system, which has two degrees of freedom with only one actuator for trolley driving. An overhead crane transfers a work piece to a desired position while keeping the swing angle of the work piece small during this process. The rope should not have a swing angle at the load destination. In this paper, fve controllers (i.e., linear and nonlinear controllers) are derived based on the passivity of the system. The total energy of the system and its square are used in a Lyapunov candidate function to design the controllers. The equilibrium point of the closed loop is proven asymptotically stable by the Lyapunov technique and LaSalle invariance theorem. The optimal linear controller is combined to force the swing angle to converge rapidly to zero by reaching the trolley location. Numerical simulations and experiments are conducted by using the test bed model to evaluate the controllers. Keywords: under actuated nonlinear systems, overhead crane, energy-based control International Robotics & Automation Journal Research Article Open Access