Boundary control of container cranes from the perspective of controlling an axially moving string system

Abstract

The control objectives in this paper are to move the load of a container crane to its target position and to suppress the transverse vibration of the load. Owing to the fact that the load is hoisted up and down, the crane is modeled as an axially moving string system. The dynamics of the moving string are derived using Hamilton's principle for systems with changing mass. The Lyapunov function method is used in deriving a boundary control law, where the Lyapunov function candidate takes the form of the total mechanical energy of the system. The boundary control law utilizes the hoisting speed as well as the sway angle of the rope at the gantry side. Through experiment, the effectiveness of the proposed control law is demonstrated particularly in the lift-up process of the load.

Adaptive control of an axially moving system

“…As shown in Fig. 5, the same conclusion can be drawn from the comparison of the adaptive control law with the PD controller (19) under the same experimental conditions.…”

“…A typical assumption in the second approach is that the rope is perfectly flexible and inextensible. In this case, the dynamics of the crane system is expressed as a coupled ODE and partial differential equation (PDE): the trolley motion is given in the ODE form and the rope dynamics is given in the PDE form [15][16][17][18][19]. By using the PDE form, the payload as well as the rope motion is described exactly, especially when the rope length is very large and the payload is very heavy.…”

“…In [18], d'Andrea-Novel and Coron proposed a torque control to stabilize an overhead crane with a variable-length flexible cable. On the other hand, Kim et al [19] modeled a container crane as an axially moving string system and proposed a boundary control law utilizing the hoisting speed as well as the sway angle of the rope. In their work, the Lyapunov function approach was adopted in ensuring stability.…”

“…In this paper, an axially moving string model for container cranes with changing the rope length is firstly introduced [19]. Considering the variation of the rope length and the disturbance effect on the gantry motion, an adaptive control law is derived, in which the disturbance as rail friction, frame vibration, etc, is estimated.…”

Boundary control for flexible mechanical systems with input dead-zone

“…The stabilization problem is discussed for an overhead crane with flexible cable in [9], where the exponential stabilization is achieved by the proposed backstepping approach. In [10], a boundary control law is proposed for a container crane which is modeled as an axially moving string system to suppress the transverse vibration of the load based on the Lyapunov's direct method. In [11], boundary control is proposed for a flexible string system with input saturation, where an auxiliary system is employed to handle the input nonlinearity.…”