# Modified Smith Input-Shaper Crane-Controller for Position Control and Sway Reduction
## 1 Introduction
Simulations confirm the approach's effectiveness and robustness, and theoretical analysis proves the system's state convergence. In the paper [21], [PERSON], [PERSON] et al. propose an active wave compensation strategy for offshore crane ships, which addresses the challenges of hysteresis and nonlinearity in the compensation platform. To enhance the stability and accuracy of crane operations under wave-induced motion, the method combines PI modelling, backstepping control, and sliding-mode control. [PERSON], [PERSON] et al. [22] propose a multi-variable state-constrained controller to address control challenges in tower cranes with varying cable lengths. It introduces auxiliary terms to manage actuated and underactuated variables, which ensures precise cargo positioning and suppressing swing. The feasibility and robustness of the method and operational efficiency are validated by a simulation. A sliding-mode controller to stabilize a gantry crane system and reject external disturbances during transportation, proposed by [PERSON], [PERSON] et al. [23], was tested within the simulation. Its effectiveness is proven by semigroup theory and asymptotic stability analysis using the Krasovskii-LaSalle principle. In this paper [24], [PERSON] et al. give an amplitude-saturated nonlinear output feedback controller for five-degree-of-freedom (5-DOF) underactuated tower cranes, addressing challenges such as lack of velocity measurement and variable rope length. It aims to improve crane safety and efficiency by ensuring asymptotic stability at the target position, even without velocity feedback. The system's stability is proven using [PERSON]'s theorem and [PERSON]'s invariance principle, and the effectiveness of the proposed control method is experimentally demonstrated. A time-optimal trajectory planning method for the double-pendulum bridge crane system, addressing the complexities that arise when the load volume or hook weight is significant, is given in [25] by [PERSON] and [PERSON] Their approach transforms the system's kinematic model and then converts the optimization problem into a nonlinear programming problem, considering constraints like swing angles, trolley speed, and acceleration limits. The time-optimal trajectory planning method provides effective control performance confirmed by a simulation. For 5-DOF tower crane systems, a controller that does not rely on velocity signals, addressing key issues like crane swing and vibration, is proposed by [PERSON] et al. [26]. The controller employs an adaptive output feedback method with online gravity compensation, overcoming challenges such as velocity unavailability, noise amplification, and steady-state error employed by their controller. In their paper, [PERSON] and [PERSON] [27] propose a model-free control method for multi-lift overhead cranes, addressing inaccurate modeling and system uncertainty. An iterative learning, a time-varying sliding-mode surface, and adaptive super-twisting are used to improve system convergence, robustness, and performance. Lyapunov stability analysis confirms the system's stability, and using simulation results, the effectiveness of their synchronization control scheme is verified. A nonlinear optimal control method for boom cranes mounted on vessels, utilizing Taylor series expansion for linearization, is given by [PERSON] [28]. An H-infinity feedback controller is designed, with feedback gains computed using an algebraic Riccati equation at each step. The control approach ensures fast and accurate tracking, with stability proven through Lyapunov analysis. A nonlinear energy-based controller and Lyapunov-based MPC for shipboard boom cranes addresses state constraints and ship roll influences in the paper [29] by [PERSON], [PERSON] and [PERSON]. Barrier Lyapunov functions (BLFs) and a contractive constraint are introduced to improve control performance and ensure stability in the Lyapunov-based MPC.