Abstract: Expansion loops are critical components in piping systems, designed to manage stress caused by thermal expansion and contraction, thereby ensuring the system's durability and safety. This study investigates innovative approaches to optimizing expansion loop design, focusing on improving the performance and reliability of piping systems under various operational conditions. The research examines multiple configurations, including alterations in loop length, shape modifications, and the incorporation of additional loops, to assess their impact on stress distribution within the system. While the primary focus of this study is on static stress analysis, transient operational factors, such as water hammer, were also considered in the analysis to provide a more comprehensive understanding of the loop configurations' performance under various conditions. The findings demonstrate that while increasing the loop length can effectively reduce stress, alternative designs, such as double loops or modified shapes, offer superior stress management, particularly in space-constrained environments. The study concludes that optimal expansion loop design should accommodate thermal expansion and provide robustness against potential transient effects, contributing to a more reliable piping system. These insights provide valuable guidelines for the design and optimization of piping systems across various industrial applications.
Abstract: Expansion loops are critical components in piping systems, designed to manage stress caused by thermal expansion and contraction, thereby ensuring the system's durability and safety. This study investigates innovative approaches to optimizing expansion loop design, focusing on improving the performance and reliability of piping systems under variou...Show More
Abstract: The stabilization of the non-linear inverted pendulum system requires a robust control strategy, as this system is inherently unstable and sensitive to disturbances. This research utilizes Lagrangian mechanics, a powerful technique in analytical dynamics, to derive the mathematical representation of the system. By applying the principles of Lagrangian dynamics, we can accurately model the energies involved and derive the equations of motion that govern the pendulum’s behavior. Following this, state-space feedback is employed to determine the Proportional, Integral, and Derivative (PID) values essential for effective control. This control strategy is particularly useful due to its ability to minimize error over time and ensure stability. To further enhance the control process, a comprehensive mathematical model is developed to establish the transfer function that correlates the pendulum's angle with the displacement of the cart. This relationship is crucial for understanding how changes in the cart's position affect the pendulum's stability. To validate the proposed control law, extensive simulations are conducted, allowing for comparative analysis against an Integer Order Controller. These simulations not only highlight the effectiveness of the PID controller but also provide insights into the dynamic behavior of the system under various conditions. The results demonstrate significant improvements in settling time and overshoot, showcasing enhanced performance metrics for the selected objective functions. This research contributes to the broader field of control systems engineering, suggesting that advanced control strategies can effectively manage complex, non-linear systems.
Abstract: The stabilization of the non-linear inverted pendulum system requires a robust control strategy, as this system is inherently unstable and sensitive to disturbances. This research utilizes Lagrangian mechanics, a powerful technique in analytical dynamics, to derive the mathematical representation of the system. By applying the principles of Lagrang...Show More