Verhead Crane Anti-Swing System Based on the Pontryagin’s Maximum Principle

Abstract

Overhead cranes are widely used at industrial enterprises for transportation of materials and products. They are successfully adaptable to technological processes used at an enterprise and their exploitation is inexpensive; in addition, the price of cranes is relatively low. However, extension of requirements set for technological processes results in shortened time for transportation and stiffened requirements for accuracy of cargo delivery and cargo safety. In the attempts to satisfy the latter requirements, particular attention is paid to swings of the cargo-holding rope. There is a number of factors that cause increased requirements for the control system of the crane drive. The slewing movement affects the total system of the crane and aggravates the crane movement control. In modern overhead cranes, the abilities and qualification of an operator (who is assisted by a certain anti-swing system) predetermine the cargo swings and the accuracy of its positioning. The said circumstance latterly caused a particular attention to computerisation of overhead crane control. However, a nonlinearity of the mechanical system of a crane and complicated control of swings often cause undesirable swings, in particular in the beginning and the end of cargo transporting process, thus reducing the efficiency of usual crane control systems. In addition, it should be taken into account that the parameters of a crane, as a controlled mechanical system, depend on the cargo and the conditions of its transportation. Consequently, a development of an effective cargo swing reduction system is a currently topical engineering problem.

Further Research on an Anti-Swing Control System for Overhead Cranes

“…Simulation model of the overhead crane was developed using MATLAB/Simulink software [21]. Previous research works [22] showed that significant load swing occurs during transportation by the overhead crane.…”

“…During the creation of the mathematical model, experience of industrial enterprise Vilniaus kranai AB was evaluated claiming that rope angular deviation from the vertical does not exceed 5 degrees. Obtained after appropriate processing in accordance with techniques presented in [23] equations and used coordinates are presented in [21]. Modeling of the mechanical system was carried out with the following parameters (data obtained from the experiments carried out at Vilniaus kranai AB): standard gravity g=9.81m/s 2 , load mass M=1000kg, trolley mass M x =5000kg, mass of the trolley and the bridge M y =10000kg, damping coefficient at the rope attachment point H 2 =1Nms/rad, rope damping coefficient H 1 =1000Ns/m, initial rope tension stiffness C 1 =1716000N/m, damping coefficient of the trolley along axis X H x =1000Ns/m, damping of the crane along axis Y H y =2000Ns/m.…”

Behavior and Optimization of Pneumatic Damping System

“…However, an experimental way cannot be the only technique for investigating all possible combinations of operating parameters due to high costs and time spent for determining the optimal values. Mathematical modeling of a physical system employing numerical methods has become an effective alternative (Bogdevičius and Vitkūnas 2016;Andrikaitis and Fedaravičius 2014;Najafi and Ahmadzadeh 2014;Skrickij et al 2016;Spruogis et al 2015;Dyakov and Prentkovskis 2008;Moezi et al 2015;Bogdevičius et al 2015;Dönmez Demir et al 2015;Khatir et al 2014;Ahmadi et al 2015;Zhang et al 2015;Simonović 2015;Allali et al 2015). The paper is aimed on proposing mathematical model for the pneumatic damping system.…”

Vehicle Driving Cycle Optimisation on the Highway

“…The solution to such a global problem can be found by methods of variations, including using the Pontryagin maximum principle, providing that the system of equations 5 is differentiated by variables x 1 , x 2 , and that the corresponding Hamiltonian should reach a maximum at the range t o ... T [11]. This problem, for the route with a constant resistance of driving, has been solved before [14].…”