Design of general LQR-ANN-controller of „crane-load” system. Part 2

The second part of the article presents the training mechanism of an artificial neural network (ANN), the structure of which was developed in the previous study. A significant amount of training data (85451 training pairs), the size of the bach (2000), the number of training rounds (500000), as well as the depth of the ANN allowed us to obtain a fairly low training loss (1.52·10-6) and validation loss (1.99·10-6). In addition, for almost the entire test data the ANN showed a high-quality prediction of the coefficients of the optimal controller. This statement was supported with the maximum and root-mean-square prediction errors. However, individual values of the coefficient prediction errors doubt the quality of the optimal control of the system's motion. In order to assess this quality for these cases, the worst result in terms of prediction error was studied. This allowed us to establish that the deviation of the coefficients (the maximum value is 7.86%) does not cause a significant deviation of the dynamics of the “crane-load” system from that obtained by using the optimal coefficients of the linear-quadratic controller. For this purpose, graphical dependencies of the phase portrait of the pendulum oscillations of the load, the control function, the driving force, and the speed of the crane movement were built and analyzed. The article notes one of the advantages of the obtained ANN – the speed of obtaining optimal control. It follows from the fact that access to the ANN requires significantly fewer computational resources than those required for solving the Riccati equations. The final part of the article provides recommendations for implementing the obtained results in practice. They consist of the fact that the input vector, which contains the normalized values of the load mass, the length of the flexible suspension, and the control weight coefficient, is transmitted to the input of the ANN. This allows us to obtain the predicted values of the coefficients of the optimal controller. In the further, they are used to find the optimal control strategy. The latter, in turn, is implemented by means of controlled electric drive mechanisms of the crane.