The first stage of the research addresses the problem of tuning the coefficients of the PID-controller for the control of the "crane-load" system. Мodified particle swarm optimization (ME-D-PSO) method application brought solutions for various sets of system parameters: load mass m2 ranging from 500 kg to 20000 kg with a step of 500 kg and flexible suspension length l ranging from 2 to 12 meters with a step of 1 meter. As a result, 451 sets of coefficients KP, KI, KD of the PID-controller were obtained. Based on this data, an algorithm was developed that allows calculating the values of the PID-controller coefficients for a wide range of load mass and flexible suspension length. The algorithm first step determines the upper and lower bounds of the parameters m2 and l, for which the
coefficients KP, KI, KD of the PID-controller are searched. Then, initial approximations of the coefficient values are set, and using the ME-D-PSO method, individual values of each coefficient are determined. The algorithm allows tuning the PID-controller, that ensures elimination of load oscillations. The problems of synthesizing an optimal controller for acceleration, deceleration, and full-cycle crane motion with a load on the flexible suspension were solved. As a result of the calculations, the following coefficients of the linear controller were obtained: without load positioning component К1=-1898126, K2=611392, K3=25709; with load positioning requirement taken into account K1=3,171·10^5, K2=-1·10^6, K3=-1·10^6; K4=2,127·10^6. A program for conducting experimental research was developed. The program consists of 3 modules, totaling 16 experiments. These experiments include independent factors such as the presence of external disturbances on load motion, initial conditions of load motion, load mass, flexible suspension length, and the specified distance of the trolley final position. The analysis of experimental data revealed the following results: the smallest deviations between experimental and theoretical data were observed in experiment № 3. The relative error in crane final position is 0,09 %, the error in crane movement velocity is 19,5 %, the error in load oscillation amplitude is 5,9 %, and the error in load oscillation velocity is 4,5 %. The largest deviations between experimental and theoretical data were observed in experiments № 5, 7, and 11. The relative error in crane final position is 2,3 %, the error in crane movement velocity is 70 %, the error in load oscillation amplitude is 27,7 %, and the error in load oscillation velocity is 24,6 %. The first set of experiments showed minor deviations from theoretical data because there were no external impacts on the load during these experiments. The most significant deviations were observed in experiments where external impacts were applied to the load. Overall, the crane motion control system successfully eliminates pendulum oscillations of the load and ensures crane movement over a specified distance with high positioning accuracy in minimal time. A structural scheme for optimal control of crane motion with a flexible suspension system was developed, which effectively eliminates pendulum oscillations of the load and improves the operational features of the crane, such as work capacity, energy efficiency, and safety. Based on the analysis of technical characteristics, recommendations were made regarding the selection of hardware components for the optimal control system (programmable microcontroller, crane position sensors, length of the flexible load suspension, deviation angle of the load from the vertical, and frequency converter). It was established that the implementation of the optimal crane motion control system allows achieving economic efficiency via increased work capacity. Economic efficiency calculations were conducted for several types of cranes, including the Weihua MG25t gantry crane, Aicrane AQ-NLH bridge crane, and 60/12,5 t semi-gantry crane. For these cranes, the annual economic efficiency ranges from 28,521 to 67,550 hryvnias per year in 2023 prices.
