Abstract: The proportional–integral–derivative (PID) control systems, which have become a standard for technical and industrial applications, are the fundamental building blocks of classical and modern control systems. In this paper, a three-layer feed-forward neural network (NN) model trained to replicate the behavior of a PID controller is employed to stabilize control systems through a NN feedback controller. A novel bio-inspired weights-and-structure-determination (BIWASD) algorithm, which incorporates a metaheuristic optimization algorithm dubbed beetle antennae search (BAS), is used to train the NN model. More presicely, the BIWASD algorithm identifies the ideal weights and structure of the BIWASD-based NN (BIWASDNN) model utilizing a power sigmoid activation function while handling model fitting and validation. The results of three simulated trials on stabilizing feedback control systems validate and demonstrate the BIWASDNN model’s exceptional learning and prediction capabilities, while achieving similar or better performance than the corresponding PID controller. The BIWASDNN model is compared to three other high-performing NN models, and a MATLAB repository is accessible in public through GitHub to encourage and enhance this work.