# Physics-Guided Neural Network-Based Feedforward Control for Seamless Pipe Manufacturing Process
## 4 Discussion  
In this paper, a detailed methodology for the application of neural networks for feedforward control to a specific manufacturing process--seamless pipe production--was developed. Starting from the general nonlinear model of a hydraulic cylinder, used as an actuator in this industrial process, the unknown parameters of the mathematical model were identified. Although, in the realm of neural networks, precise knowledge of the system parameters is often unnecessary due to their universal approximator nature, this work emphasizes parameter identification as a step toward embedding knowledge of the dynamic system into the artificial intelligence workflow. Of course, neural networks could also have been used for the identification of the unknown parameters of the hydraulic actuator, as extensively covered in the existing literature [26]. However, such an approach would compromise the interpretability and the possibility of further simplifying the mathematical model--an essential step in coupling physical models with neural networks. It was demonstrated that, by using traditional identification methods, such as the least squares method, and based on straightforward experiments on real hardware (cylinder responses to step changes in valve openings), it is possible to determine unknown parameters with sufficient accuracy to capture the dominant system dynamics. Processes in heavy industry, such as seamless pipe manufacturing, are distinct from the perspective of control system synthesis due to the coupling between the dynamics of the actuators and the working material or the process itself. Therefore, to fully capture the system's dynamics, regardless of the required accuracy, it is essential to adopt a mathematical model that encompasses this interaction. We propose that such a model should be sufficiently rich to capture the phenomena that predominantly influence the controlled system, yet simple enough to preserve the concept of physical models that can be seamlessly integrated with neural networks. In this particular task, the dominant factors by which the production process influences the actuator's operation are friction and the behavior of the cast material under deformation. Therefore, this paper proposes a model of external force defined by two parameters: the pushing force threshold \(F_{yield}\) and the time constant \(\tau_{ext}\). These parameters can be identified using experimentally recorded data from the existing production process. Figure 23: Piston velocities during varying force setpoint tracking with different controller structures: PI controller; benchmark neural network feedforward; physics-guided neural network (PGNN) feedforward. A potential direction for future work could focus on the application of neural networks to emulate the material being pressed into the piercing mill. This approach would be beneficial as it would enable the simulation of the workpiece's impact using simplified hardware, such as the example of two coupled cylinders--one responsible for pushing the material and the other simulating the resistive force--thus allowing the control system to be tuned outside the industrial environment. With the finalized mathematical model of the entire production process, it becomes possible to proceed with its simplification as a preparation step for the formation of inversion-based models. The process model, represented by Equation (35), was derived using a reduced-order model of the hydraulic cylinder [25] and adopting justified assumptions specific to this production process: unidirectional material movement and a velocity high enough to neglect the static component of friction. It has been shown that the deviations resulting from the use of the reduced hydraulic cylinder model are around 30%, within the expected operating point range, which would lead to significant discrepancies if the obtained inversion-based model were the sole method used in generating the control signal.