###### Abstract  
An anti-swaying or swaying-reduction effect for a container crane is key for improving the rapidity and safety of container handling operations. By analyzing the structure of a container crane hydraulic anti-swaying system, a dynamic system model was developed in the time domain, and the changing law of the load swaying angle was studied. In order to study the attenuation effect of the load swaying angle and the different working states of the anti-swaying system, the frequency domain equation of the load swaying angle was developed in the frequency domain. A time domain study on the dynamic model shows that the structure parameter is the key parameter that affects the load anti-swaying effect, and a larger structure parameter produces a better anti-swaying effect. A study regarding the load swaying angle in the frequency domain shows that the container crane hydraulic anti-swaying system works in a critical-damping state when the structure parameter load ratio is equal to twice the system frequency, and in this case, the hydraulic anti-swaying system has good load swaying-reduction effect and a small dependence on changes in the hoisting rope length. The longitudinal and transverse installation distances of the anti-swaying fixed pulleys jointly affect the structure parameter. In engineering applications, the longitudinal and transverse distances can be selected according to size near that of a standard container. To obtain a good swaying-reduction effect, data such as the hoisting load mass, the hoisting rope length, and the hoisting load swaying speed can be obtained in real-time and used to calculate the required pressure adjustments for the relief valve of the hydraulic anti-swaying system. c 20  
trolley or the crane so that the load always swings with a small swaying angle during the process of moving from a stationary position to the target position [21; 22; 23]. The other method is to take passive measures to reduce the swaying angle; that is, when the swaying angle is large, the trolley or the crane is passively controlled to reduce the swaying angle; thus, it is within a smaller range in the shortest possible time [24; 25]. Cranes are typical representatives of symmetry-underactuated systems [26]. There is much literature about active anti-swaying measures. A finite-time regulation controller was designed for an underactuated crane system in two-dimensional (2D) space with both constant cable length and varying cable length in [27]. The finite-time technique was used to achieve simultaneous motion regulation and load swing suppression and elimination within a finite time. A dynamic differential evolutionary algorithm-based sliding-mode controller (DDE-SMC) was designed for an under-actuated crane system [28]. A model-free adaptive controller (MFAC) using feedback linearization and an adaptive fuzzy sliding mode controller (AFSMC) using fuzzy approximation were designed and employed to control an underactuated overhead crane system [29]. A time-varying gain extended state observer (ESO)-based moving sliding mode control method was proposed for anti-sway and positioning control of two-dimensional underactuated overhead cranes [30]. An accurate model-free trajectory tracking controller subject to finite time convergence for overhead crane systems was proposed based on the suitably defined non-singular terminal sliding vector [31]. A control method based on linear active disturbance rejection control (LADRC) and differential flatness theory was proposed to realize accurate trolley positioning and effective load anti-swing for the under-actuated overhead cranes in [32]. [PERSON] et al. [33] proposed an improved input shaping for minimizing the payload swing of an overhead crane with payload hoisting and payload mass variations. [PERSON] et al. [34] proposed an optimal performance control scheme for the control of a three-dimensional (3D) crane system, including a zero-vibration shaper that considers two control objectives concurrently.