# Modified Smith Input-Shaper Crane-Controller for Position Control and Sway Reduction
## 1 Introduction
Theoretical analysis guarantees asymptotic stability, and simulation results validate the improved performance of the Lyapunov-based MPC over the energy-based controller. The importance of using the anti-sway system is given by a human factor study conducted by [PERSON], [PERSON] and [PERSON] in [30] where participants showed up to 49.1% improvement in tracking desired payload targets when using the anti-sway system in a virtual-reality simulator. It provided motion compensation in two coordinate frames. This paper also emphasizes the importance of an anti-swing algorithm in the crane's control systems. Hybrid configurations of input-shaping control (ISC) and fuzzy-logic control (FLC) for tower crane systems to improve positioning and anti-swing control were explored by [PERSON], [PERSON] et al. in [31]. Three configurations of ISC + FLC were tested, and the results showed a 150% improvement in ISC response and a 72% reduction in oscillation. Compared to full-state feedback controllers, the hybrid ISC + FLC control method is more cost-effective and computationally efficient, using minimal feedback, which is position only. A fault-tolerant control method for tower cranes is presented by [PERSON], [PERSON] in [32] using an adaptive backstepping technique, overcoming the need for redundant actuators. The fixed-time convergence optimized backstepping controller ensures smooth operation and updates fault parameters in case of sudden faults. Comparison tests demonstrate that the proposed controller performs excellently in position accuracy, swing elimination, and fault tolerance. Input-shaping techniques for sway control in tower cranes were used in [33] by [PERSON], [PERSON] et al. with a model derived using the Lagrange equation and validated through simulations. Zero Vibration (ZV) and Zero Vibration Derivative (ZVD) shapers were developed and tested to reduce oscillations during payload hoisting. [PERSON], [PERSON] et al. in paper [15] introduce a control approach for anti-sway in container cranes modelled as a hybrid PDE-ODE system with a flexible cable. Based on [PERSON]'s second method, a control law is derived to suppress transverse vibrations, using time-varying control force and active mass damper. The system's exponential stability is proven, and simulations show the effectiveness of the proposed control laws in suppressing sway. A newer study [16] by [PERSON], [PERSON] et al. proposes a vibration suppression feedforward control for stacker cranes, which also uses an active mass damper (AMD). The method aims to match the carriage acceleration with the travel unit acceleration to reduce excessive vibrations during high-speed operation. This paper presents a control structure that eliminates the sway induced by cargo acceleration and deceleration. It uses the input shaper technique. The input shaper technique has the benefit of reducing the sway but introduces a negative effect on the position controller of the cargo [34]. It introduces a decrease in the phase reserve and shifts the control structure to the unstable region. The negative effect is proportional to the natural frequency of cargo. The proposed structure uses [PERSON]'s predictive algorithm [35], which needed to be modified so that it can be used in a crane to eliminate this adverse effect. This predictive algorithm uses a model of the crane to calculate the control vector one step ahead instead of \(N\) steps ahead and inject it into the system. Using this calculation of control is simplified, and cheaper hardware can be used to run this control algorithm. The suggested controller is compared with the PD position controller without the sway reduction to show the impact of acceleration and deceleration on the cargo sway and the PD position controller with the input shaper technique. The advantage of using this predictive algorithm with the input shaper is shown within the simulation and experimentally on the laboratory crane.