This paper aims to explain the design of a novel time-varying sliding mode control of variable parameter (VP-TVSMC), which can effectively solve the anti-swing and positioning problem of distributed-mass double pendulum bridge crane system with its quick responsiveness and strong robustness to external interference. More specifically, this model initiates with the establishment of the dynamic equation of double pendulum crane model based on distributed-mass, then followed by the design of a time-varying parameter to realize the dynamic adjustment of the sliding mode surface and enhance the adjustment ability of the sliding mode surface, which is conducive to the global robustness of the double pendulum crane system under VP-TVSMC. With Lyapunov method and LaSalle’s invariance principle, the asymptotic stability of the system can be sufficiently proved. Finally, the adoption of three kinds of external interference signals and uncertain system parameters successfully verified the preeminent control performance and global robustness against external interference of the proposed controller. The simulation results indicate that compared with the conventional CSMC and PDSMC, the proposed control method can reduce the driving force of the trolley, ensure the rapid and precise positioning of the trolley, as well as restrain the load swing angle within 5° in an effective manner. In addition, compared with the symbolic function sgn( $S$ ), the designed continuous function th( $S$ ) possesses a better anti-chattering effect, thus strengthening of the control performance of VP-TVSMC.

In this study, an improved African vulture optimization algorithm (IAVOA) that combines the African vulture optimization algorithm (AVOA) with both quasi-oppositional learning and differential evolution is proposed to address specific drawbacks of the AVOA, including low population diversity, bad development capability, and unbalanced exploration and development capabilities. The improved algorithm has three parts. First, quasi-oppositional learning is introduced in the population initialization and exploration stages to improve population diversity. Second, a differential evolution operator is introduced in the local search position update of each population to improve exploration capability. Third, adaptive parameters are introduced to the differential evolution operator, thus balancing the algorithm exploration and development. A numerical simulation experiment based on 36 different types of benchmark functions showed that while the IAVOA can enhance the convergence speed and solution accuracy of the basic AVOA and two variants of AVOA, IAVOA outperforms the other 7 swarm intelligence algorithms in the mean and best values of 33 benchmark functions.

For the multi-rope structure of the container crane system and its large mass payload anti-swing positioning problem, an equivalent double-swing model based on radial spring-dampers is established and a time-varying PD sliding mode controller (TVPD-SMC) with improved transient performance is proposed. In particular, the dynamics of the container crane system are first analyzed using the Lagrange method, and an equivalent double pendulum dynamics model of the crane is established. Compared with the traditional double pendulum model, this model ensures the accuracy of modeling without measuring the second pendulum angle. On this basis, an enhanced coupled time-varying sliding mode control method is designed to eliminate the sliding mode control method’s reaching phase and improves the robustness of the controller. Finally, the convergence and stability of the closed-loop system are proved using the Lyapunov technique and the Lasalle invariance theorem, and the simulation results demonstrate the effectiveness of the method.

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.