# Modified Smith Input-Shaper Crane-Controller for Position Control and Sway Reduction
## 1 Introduction  
Crane systems greatly influence transport, as they are used to load and unload ship containers in the port. The time of loading and unloading of the containers significantly impacts the waiting time of the ships in the port, which depends on the speed of the crane automation system. The tasks imposed on this automation system are transferring cargo from the start to the desired location within a minimum time and maintaining system stability, achieved by maintaining the cargo sway within safe limits. The cargo transfer includes lifting and lowering the cargo, positioning the cargo, checking the space between adjacent containers, transferring the cargo from the start to the target location, and accelerating and decelerating the cargo. The number of cargo transfers per hour defines the crane speed. The ships' waiting time can be decreased by increasing the cranes at the terminal or the crane speed. An increased crane speed negatively affects its stability because it introduces cargo sway. A relevant control system must be installed to achieve fast transfer and eliminate the introduced cargo sway to increase the crane's speed. The crane system control methods [1] used by the automation system can be divided into open-loop [2, 3], closed-loop [4, 5, 6, 7, 8], and hybrid control, which use a combination of open- and closed-loop control [9, 10, 11, 12, 13, 14] and tuned mass-damper [15, 16] for vibration suppression of structures [17, 18]. Input shaping is mainly used for open-loop control. [PERSON], [PERSON], and [PERSON] [7] propose a scheme for fast point-to-point transportation of a portal crane, focusing on coupled luffing and rotation motions. They use a Bessel curveto design the transportation trajectory and implement a feedforward controller to guide the crane's movement. A feedback controller is also employed to stabilize motion and minimize swinging during operation. A Composite Trajectory Tracking control is proposed by [PERSON]. [PERSON] et al. [8] to improve crane precision and robustness. It utilizes feedback linearization combined with a generalized variable gain super-twisting sliding mode algorithm to manage disturbances and maintain continuous control. The nonlinear controller that [PERSON] et al. [19] propose is designed using the disturbance decoupling method. This controller addresses the disturbance problem without linearizing the crane model. Young's inequality is used to handle disturbance terms in the tower crane system. Experimental validation is given. [PERSON] et al. [6] present an adaptive PID control strategy to improve overhead cranes' positioning and anti-swing capabilities. The adaptive mechanism is achieved by a neural network-based controller and a seagull optimization algorithm to change parameters and initial weights effectively. A new ADRC-based control method is achieved in [20] by [PERSON], [PERSON] et al. to reduce payload swing in 3D overhead cranes during hoisting and lowering operations, improving nonlinear tracking differentiators and using a nonlinear extended state observer to estimate disturbances in the system; all of these were verified only by the simulation. A simulation of an open-loop input-shaper controller to control the swing of an overhead crane's payload is presented in [2] by [PERSON], [PERSON] et al. The study uses MATLAB/Simulink to test several input shaping techniques and evaluate their performance for different payload masses. The ZVDDD controller demonstrated the most significant reduction in payload swing, offering a 91% improvement in both cases, enhancing crane efficiency and safety. A disturbance-observer-based control approach for overhead crane systems, considering output feedback, input saturation, double-pendulum dynamics, and uncertainties, is developed by [PERSON], [PERSON] in the paper [14]. It incorporates a disturbance observer, virtual position signal, and Lyapunov function to enhance controller performance and stability.