An Enhanced Coupling Adaptive Sliding Mode Control Method for Casting Cranes Based on Radial Spring Damping

Abstract

During the transference of a ladle by the casting crane, the antiswing control of the ladle is particularly difficult due to liquid sloshing, so we designed a model based on a radial spring damper. During the ladle swings, the centrifugal force causes the spring damper to move radially, thereby generating a Coriolis force that inhibits the sloshing of the liquid. In addition, a sloshing analysis of the liquid in the ladle is carried out, and a double-pendulum casting crane model based on viscous damping and radial spring damper is established. On the basis of this model, the Enhanced Coupled Adaptive Sliding Mode Control (ECASMC) method is proposed. By introducing an enhanced coupling variable and constructing a new coupling deviation signal, we enhance the relationship among state quantities. Then, a new type of sliding surface is designed based on the enhanced coupling deviation signal, and adaptive technology is used to adjust the sliding mode parameters, which enhances the system's robustness for system parameter variations and external disturbances. Using LaSalle's invariance principle and Lyapunov theorem, we prove that the casting crane system is asymptotically stable near the desired equilibrium point. The simulation results verify the effectiveness and superior control performance of the proposed method even in the presence of uncertainties.

A Time-Varying PD Sliding Mode Control Method for the Container Crane Based on a Radial-Spring Damper

“…According to the motion characteristics and constraints of the multi-rope container crane, it is considered to be the double pendulum model as shown in Figure 2 [10]. In addition, a radial spring-damped anti-swing device is designed by combining a spring oscillator and a dampener [28]. Figure 2 shows that θ stands for the angle between the trolley and the hook barycenter.…”

“…r a is the radial spring damper, where K and C represent the spring coefficient and damping coefficient, respectively. The payload will generate a radial tension in the direction of the rope during the motion, causing deformation of the spring oscillator with deformation variable r. The assumptions of the container crane system are described as follows [28]:…”

“…Inspired by literature [33] and [34], a time-varying function is added to the sliding surface of this paper, which eliminates the reaching phase of the sliding mode and makes the controller globally robust. The detailed expression of this time-varying function is shown in Equation (28).…”