Optimal Command Shaping Design for a Liquid Slosh Suppression in Overhead Crane Systems

In many industries, liquid container transport is carried out by an overhead traveling crane. The operation of crane transferring liquid slosh containers required both operator experience and an automated control system. The goal of this research is to move the liquid inside a container in a short time and less spill for process effectiveness and safety. For controller design, a nonlinear mathematical model is developed to represent the actual system. A cost-effective, smooth continuous command shaper is presented to suppress sloshing vibration. The designed shaper is a multisine-wave function with adjustable and independent time maneuvering used to design the acceleration profile. The coefficients that control the shaper profile are obtained by solving a nonlinear constrained optimization problem using particle swarm algorithm. Simulation and experimental comparative results proved that the proposed command shaper can reduce transient peak slosh amplitudes. Moreover, it can simultaneously cancel both residual sloshing vibrations and container oscillations at the end of the transportation process which cannot be achieved using conventional zero-vibration (ZV), zero-vibration derivative (ZVD), and jerk-limited shaper. Furthermore, sensitivity analysis demonstrates that the proposed command shaper is robust to model parameters variation such as liquid depth, suspension length, or moving distance of the trolley.

Command Shaping for Sloshing Suppression of a Suspended Liquid Container

The residuals of liquid free-surface wave oscillations induced by a rest-to-rest crane maneuver of a suspended liquid container are eliminated using a command-shaped profile. The dynamics of liquid sloshing are modeled using an equivalent mechanical model based on a series of mass-spring-damper systems. The proposed model considers the excited frequencies of the container swing motion and liquid sloshing modes. The objective is to design a discrete-time shaped acceleration profile with a variable command length that controls the moving crane-jib, while suppressing the sloshing modes. Simulations are conducted to illustrate the command effectiveness in eliminating liquid sloshing with a wide variation range of system and command-designing parameters; liquid depth, cable length, command duration, and the employing of higher sloshing modes in representing the sloshing dynamics. The command sensitivity of the input command to changes of the system parameters are treated as well. A refined and smooth input command based on suppressing the residuals of multimodes is also introduced. Furthermore, the command effectiveness was supported by a comparison with the time-optimal flexible-body control and multimode zero vibration input shaper.

Command shaping with reduced maneuvering time for crane control

This study introduces a modified near-time–optimal rigid-body command that represents the fastest possible command profile based on using the full input capabilities of the system, considering rest-to-rest motion. The control objective is to have the shortest maneuvering time suitable for handling insensitive payloads. The rest-to-rest motion is divided into three stages. The first stage includes a quick response with maximum trolley acceleration. The second stage involves cruising at the maximum trolley velocity. The third stage provides deceleration, where both zero vibration and the zero vibration derivative are applied. The proposed shaper is simulated numerically for testing its performance. The theoretical findings were validated experimentally using a prototype crane. This study’s major finding demonstrates that the new technique succeeded in reducing the maneuvering time with zero vibration at the end of the motion. Moreover, the results show the insensitivity of the proposed shaper to variations in system parameters using a zero vibration derivative shaper.