Application of BP neural network tracking differentiator in maglev train suspension control

To improve the safety and stability of maglev train suspension operation, the train suspension control system was selected as the research object, the real-time adaptive adjustment of tracking differentiator (TD) parameters based on the BP neural network (BP-NN) was analyzed. To avoid nonlinear complex operations in the TD algorithm, a fastest control synthesis function with linear characteristics was constructed using the second-order fastest time system and the state backstepping method, and a discrete form of fastest TD (FST-TD) was proposed. Frequency domain and convergence analysis was rigorously conducted on the proposed algorithm. For the issue of delayed parameter adjustment when FST-TD encountered irregular input signals, the self-learning capability of BP-NN and the dynamic characteristics of the adaptive uncertain system were integrated to propose a FST-TD based on BP-NN (BP-FST-TD) algorithm. In this algorithm, BP-NN parameter adaptive adjustment was achieved through online updated weights by the backpropagation algorithm. FST-TD performed real-time tracking and filtering of complex, multi-condition input signals based on the adaptive parameters. To validate the algorithm's effectiveness and practicality, the real-time tracking and filtering performance of BP-FST-TD was examined using gap signals with random noise in the maglev train suspension control system. Research results show that FST-TD has decent filtering and differentiation capabilities. The convergence analysis reveals that it exhibits no oscillation or overshoot. Furthermore, this FST-TD structure, without complex nonlinear operation, is relatively straightforward in design. The FST-TD maintains ideal smoothness and phase integrity during the tracking of various input signals. Under working conditions 1 and 2, the BP-FST-TD reduces the mean absolute error (MAE) of the gap signals by 32.6% and 61.8% respectively compared to traditional TD algorithms. Besides, the integrals of time-weighted absolute error reduce by 51.8% and 70.2%, respectively. These findings substantiate the effective tracking and filtering performance of BP-FST-TD, and the algorithm effectively suppresses random noise from the gap sensors under various operational conditions of the maglev train. Thus, it can be concluded that the suspension control system based on BP-FST-TD effectively ensures the stable suspension operation of the train. The research results offer novel approaches and methods for TD control parameter optimization in other engineering domains.