# Physics-Guided Neural Network-Based Feedforward Control for Seamless Pipe Manufacturing Process
###### Abstract  
Artificial intelligence (AI) is increasingly being utilized in the industrial sector, revolutionizing traditional manufacturing processes with advanced automation systems. Despite their potential, neural networks have seen limited adoption in industrial control systems due to their lack of interpretability compared to traditional methods. The recently introduced physics-guided neural networks (PGNNs) address this limitation by embedding physical knowledge directly into the network structure, enhancing the interpretability and robustness. This study proposes a novel feedforward control framework that integrates a reduced-order physics-based model of a hydraulic actuator with a data-driven correction term for accurate force control in the seamless pipe manufacturing process. The coupled dynamics of the actuator and the continuously cast material being pushed into the piercing mill are identified through experimental data, and reduced-order models are developed for integration into the PGNN structure. The training of the networks is performed on a dataset from a scaled industrial hydraulic system, with the validation of the proposed methods conducted on a neural processing unit (NPU), a specialized industrial-grade platform for AI, operating within a PLC environment. The results demonstrate real-time execution with excellent force tracking, even with a limited training dataset--a typical constraint in industrial processes--while providing safer and more predictable behavior compared to traditional neural-network-only solutions. optimal results. Precise control of the piercing force is essential because any deviations can lead to defects, such as uneven wall thicknesses, off-center holes, and surface irregularities, compromising the integrity of the final pipe. In modern variations of this process, a continuously cast material is often used instead of traditional billets, offering improved efficiency by eliminating the intermediate steps of casting and reheating [2]. To ensure smooth and precise operation during the piercing process, an entrance device is employed to continuously guide the cast material into the piercing mill. This device commonly consists of hydraulic actuators that provide the desired pushing force needed to maintain consistent material feeding. The accurate control of this force is important in preventing issues that can negatively impact the quality of the final product. Feedforward control is a widely used technique in control system design, particularly effective in addressing predictable disturbances and ensuring precise trajectory tracking. By leveraging a model of the system or process, feedforward controllers generate control actions based on reference inputs, proactively mitigating deviations before they occur [3,4]. This approach complements feedback control, which reacts to errors after they are detected, reducing the burden on feedback loops and enabling faster system responses--especially in dynamic and complex industrial environments [5]. Traditional feedforward control techniques often rely on mathematical models derived from system dynamics or empirical data obtained through experiments [6,7]. However, classical methods face challenges in handling model uncertainties, nonlinearities, and unforeseen disturbances [8]. In response to these challenges, neural networks (NNs) have emerged as a powerful tool for the design of feedforward controllers due to their universal approximation capabilities [9]. Neural networks can learn complex, nonlinear relationships directly from experimental data, bypassing the need for highly accurate mathematical models. [PERSON] [10] demonstrated the efficacy of NN-based feedforward control in managing nonlinear system dynamics, while [PERSON] et al. [11] applied adaptive NN feedforward strategies to dynamically substructured systems. Despite their flexibility and ability to model complex behaviors, NN-based approaches often require large datasets spanning the full operating range to ensure reliable performance [12,13].