The first part of the article describes the research concept and presents the results, which in the future allow the development of a LQR-neurocontroller of the movement of the dynamic "crane-load" system. For this purpose, the the problem of optimal control was stated. It uses a mathematical model in which the control function is considered as the rate of driving force change. This increases the order of the system by one. For individual components of the integral criterion, the weight coefficients were chosen and the values of the initial conditions were substantiated. The original problem of the synthesis of a LQR-controller is reduced to the Riccati equation. For one case, a solution to the Riccati equation was obtained and graphic dependencies corresponding to the obtained optimal control were built. The analysis of graphical dependencies made it possible to establish the disadvantages and advantages of the obtained optimal control. Among the advantages are the smoothness of the movement of the system and the provision of a zero value of the driving force at the beginning of the movement. This makes it possible to reduce the dynamic forces of the drive of the crane movement mechanism and its metal structure. Among the disadvantages of optimal control is a significant rate of increase of the driving force at the beginning of the movement, which can cause difficulties in the implementation of optimal control in practice, as well as an overshoot of the crane velocity. Multiple solutions of the Riccati equation made it possible to obtain datasets for training, validation, and testing of an artificial neural network, which is considered as a universal approximator of Riccati equation solutions. The process of data normalization and formation of training pairs is described. All data regarding the optimal values of the controller coefficients were obtained for load masses that varied within 60...25,000 kg and lengths of flexible suspension that varied within 1.2...12 m. In addition, the power of the weight coefficient varied within -5...-30, which corresponds to the minimization of the driving force rate.
Read full abstract