Optimization of the joint startup of the boom and load hoisting mechanisms of a jib crane

During the joint motion of the boom and load hoisting mechanisms, dynamic loads increase, leading to additional energy consumption, which subsequently contributes to the deterioration of the crane’s structure. The aim of the research was to enhance the efficiency of the jib crane by optimising the joint startup modes of the boom and load hoisting mechanisms, which will minimise energy consumption. To achieve this aim, methods of analytical mechanics, variational calculus, and a modified particle swarm optimisation metaheuristic method were used. As a result of using these methods, the joint startup of the boom and load hoisting mechanisms was optimised. The joint motion of the crane mechanisms is represented by a dynamic model with four degrees of freedom, which accounts for the main motion of the mechanisms, as well as the elastic oscillations of the load hoisting mechanism’s drive and low-frequency oscillations of the load on a flexible suspension. Based on the dynamic model, a mathematical model in the form of a system of second-order differential equations was constructed, which was then reduced to a system of two fourth-order equations. The synthesis of the optimal startup mode of the mechanisms was carried out according to the criterion of the root mean square value of the total power of the drives, taking into account the constraints on the driving torques of the drives. The constrained optimisation problem was reduced to an unconstrained optimisation problem by developing a generalised criterion. The nonlinear problem of optimising the joint startup mode for the boom and load hoisting mechanisms of the crane was solved using a modified particle swarm optimisation metaheuristic method. As a result of the optimisation, startup modes for the boom and load hoisting mechanisms were obtained that minimise the total power of the drives and eliminate low- and high-frequency oscillations of the crane’s structural elements, which leads to increased reliability and reduced energy consumption. This mode is recommended for use in the control systems of crane boom and load hoisting mechanisms