# Physics-Guided Neural Network-Based Feedforward Control for Seamless Pipe Manufacturing Process
###### Abstract
To address the limitations of standard NN approaches, physics-informed neural networks (PINNs) have been introduced. PINNs embed physical laws, often expressed as partial differential equations (PDEs), directly into the network's training process [14]. This integration reduces the dependence on extensive datasets and enhances the generalization of the model across varying operating conditions. [PERSON] et al. [15] demonstrated the application of PINNs in feedforward control, showing improved robustness and interpretability under diverse scenarios. Building upon the foundation of PINNs, physics-guided neural networks (PGNNs) represent a significant step forward in control system design. PGNNs not only incorporate physical insights into the training process but also embed structured physical models directly into the neural network architecture [16]. This structured approach enhances the interpretability, ensures compliance with system dynamics, and improves the robustness against varying operating conditions. This fusion allows for a reduced dependence on large datasets, especially in scenarios where data availability is limited or where the system operates outside the conditions used for training. In the context of feedforward control, PGNNs have demonstrated their effectiveness in predicting and compensating for system disturbances and nonlinearities. [PERSON] et al. [17] successfully applied PGNNs as feedforward controllers in hybrid stepper motors, and [PERSON] et al. [18] applied PGNNs as feedforward controllers in precision mo tion control systems, both demonstrating improved tracking accuracy and performance. [PERSON] et al. [19] demonstrated the effectiveness of PGNNs in addressing nonlinearities and parasitic effects within industrial systems, specifically when applied in feedforward control architectures requiring precise compensation and preemptive adjustments. Previous studies on PGNNs have predominantly focused on electromechanical actuator systems, where feedforward controllers are primarily used to compensate for friction. These systems benefit from the relatively isolated nature of their dynamics, allowing the PGNN to focus on accurately modeling the actuator's behavior. Although this approach has proven to be effective, it overlooks the critical influence of coupled dynamics in systems where the actuator interacts directly with the processed material in the production processes in heavy industry. In hydraulic actuators, this coupling becomes particularly significant due to the inherent relationship between the movement of the actuator's rods, the resulting pressure changes, and the corresponding actuation forces. Unlike electromechanical systems, where the force generation mechanism is more straightforward, hydraulic systems must contend with dynamic interactions between the actuator and the load. These interactions are further complicated in industrial applications where the production process itself introduces additional resistive forces and disturbances that must be accounted for in the control strategy. To address this, our work extends the application of PGNNs to hydraulic actuators, marking, to the best of our knowledge, the first attempt to incorporate this methodology in such systems. We innovatively couple the dynamics of the hydraulic actuator with the dynamics of the production process within the physical part of the PGNN. By doing so, we create a more comprehensive and robust feedforward structure that is able to capture the interactions between the actuator and the production process. We also address the significant challenge in industrial applications, which has traditionally been the lack of hardware platforms capable of executing such neural networks in real time within the control loop. In earlier implementations, such as those described by [PERSON] and [PERSON] [20], neural networks were executed on external computers, with communication to PLCs managed via OPC protocols.