An improved Adam Algorithm for BP neural network feedforward compensation control

To address slow convergence speed and low convergence accuracy in the inverse model (IM) learning and training of the controlled object during BP neural network (BP-NN) feedforward compensation control for tracking a step signal, which results in poor dynamic and steady-state performance of the control system. This study introduces an improved Adam algorithm (IADAM)-enabled BP-NN feedforward compensation control method. This method introduces a dynamic learning rate adjustment mechanism based on the Adam algorithm, which adjusts the learning rate in phases based on the NN training parameter gradients. When the gradient exceeds a preset threshold, the learning rate is dynamically increased via an adjustment function to accelerate IM convergence. When the gradient is below the threshold, the maximum historical second-order moment estimate of the gradient is retained to keep the learning rate at a lower value, thereby improving IM convergence accuracy. The control system is composed of a PID controller, a neural network controller (NNC), and an IADAM-based neural network identifier (IADNNI). The PID controller provides online learning samples. The IADNNI learns the IM of the controlled system online, while the NNC shares the same structure and parameters as the IADNNI, generates real-time compensation control signals. Experimental results from a DC servo motor position control platform reveal that the proposed control method achieves zero overshoot in tracking both continuous step signals and square signals, while the settling time is reduced by 60.05% and 39.53%, respectively, compared to the ADAM + BP + PID control method. resulting in significant improvements in both dynamic and steady-state performance.