Cfd-based pı/pıd controller for velocıty and headıngcontrol of the darpa suboff

Abstract

This thesis presents a control approach developed through Computational Fluid Dynamics (CFD) to maintain the underwater route of submarines in a stable and consistent manner. The main focus of the study is the DARPA SUBOFF model with the E1619 model propeller, a widely used standard hull form in international hydrodynamic research. The study investigates the heading control performance of this model at various velocities and heading angles under free-running conditions. Compared to surface vessels, submerged bodies are exposed to significantly more external influences—such as currents, pressure fluctuations, and vortex structures around the hull—which complicate directional stability. Therefore, more precise and responsive control systems are necessary. The CFD framework was based on the incompressible Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations discretized using the Finite Volume Method (FVM) to ensure conservation across control volumes. A segregated solver with SIMPLE coupling and the Shear Stress Transport (SST) k–ω turbulence model was employed for stability and near-wall accuracy. The y+ wall treatment ensured proper resolution of near-wall turbulence effects. A Dynamic Fluid-Body Interaction (DFBI) method was employed for maneuvering motions to simulate dynamic interactions and control inputs. Propeller rotation and rudder motion were modeled using the Moving Reference Frame (MRF) and Rotating Body Motion (RBM) methods enabling efficient quasi-steady simulations with reduced computational cost and maintained accuracy. Thus, the adopted CFD setup enabled efficient and accurate prediction of key hydrodynamic phenomena (such as flow separation, vortex shedding, and pressure distribution) essential for maneuvering and propulsion analysis. This study presents a CFD-integrated classical PID controller for submarine heading control, selected for its proven stability and interpretability in marine applications. Unlike conventional methods that rely on empirical tuning or simplified analytical models, the control gains in this work are systematically derived from high-fidelity CFD-based free-running maneuvering simulations. A custom Java-based macro was seamlessly embedded into the CFD solver, enabling real-time dynamic control and capturing the physical interaction between the vehicle and the surrounding flow field with high fidelity. To verify the accuracy and reliability of the developed CFD model, a comprehensive Verification and Validation (V&V) study was conducted. The verification process was conducted through free-running self-propulsion simulations, where the Grid Convergence Index (GCI) method was employed to assess mesh uncertainty, resulting in an uncertainty level of less than 1.1%. In the validation step, the computed rotation rate, thrust and torque coefficients at a velocity of 2.75 m/s were compared with benchmark experimental and CFD data, showing strong agreement and confirming the model's numerical accuracy and predictive capability. Prior to implementing active heading control, the intrinsic course-keeping ability of the DARPA SUBOFF model was assessed. A free-running simulation without any rudder input (δ=0.0 deg) was performed, and the resulting steady-state yaw rate (r^\prime) was measured to be approximately 0.308. The elevated yaw rate indicates limited inherent course-keeping ability of the hull, highlighting the necessity of an active control system to maintain stable and accurate heading under realistic conditions. The study consists of two main simulation stages. In the first stage, self-propulsion points were determined at three different velocities (2.750 m/s, 6.096 m/s, and 9.152 m/s). These points indicate where propeller thrust balances the hull resistance. A custom-designed Proportional–Integral (PI) controller was implemented to precisely identify the self-propulsion points, ensuring that propeller thrust accurately balanced the hull's resistance forces. This specialized PI controller provided precision, crucial for establishing a stable propulsion baseline. The resulting propeller rotation rates (n) were compared with benchmark experimental and CFD data in the literature, showing a discrepancy of less than 0.22%, thus confirming the reliability and precision of the propulsion model. In the second stage, 10/10-degree zigzag maneuvers were performed. Parameters such as heading angle (ψ), yaw rate, and rudder angle (δ) were recorded during these tests. These data were used to extract the K (maneuvering gain) and T (hydrodynamic time constant) coefficients of the Nomoto model, which describes the relationship between rudder input and yaw response in submarine steering dynamics. This model is widely used in marine control applications to simplify and quantify the dynamics of course-keeping behavior, including heading control system design, autopilot tuning, and maneuvering performance analysis. The developed PID control system continuously measured heading deviations and dynamically updated the rudder angle, effectively minimizing deviations from the desired course at target heading angles of 0.0, 5.0, and 15.0 degrees. Even at higher velocities, the controller maintained performance with low overshoot. In the simulation environment, a low-pass filter was applied to the rudder commands, and both rudder angles and rotation rates were constrained within specified physical limits. This ensured both physically meaningful motion and numerical stability. In conclusion, this thesis demonstrates that PID controllers integrated with CFD can be effectively used for submarine heading control tasks. It enables the determination of control parameters during the design phase, potentially eliminating the need for expensive and time-consuming sea trials. Moreover, it provides a robust, energy-efficient, and environmentally adaptable heading control solution for autonomous underwater vehicles. A notable contribution of this study is the seamless integration of the control system into the CFD environment via a custom Java-based macro, enabling real-time rudder control without external processing. Furthermore, a key innovation lies in achieving dynamic, physically consistent heading control by directly coupling CFD-derived force responses with the control system. This approach significantly enhances the system's adaptability to varying flow and operating conditions. For future work, it is recommended to extend this approach to six degrees of freedom (6-DOF) simulations, include environmental effects such as different operating conditions (fully submerged, snorkel, and surface navigation) and ocean currents, and perform comparative analyses with artificial intelligence-based control algorithms. This would contribute to the development of smarter, faster-responding, and more environmentally adaptable autonomous submarine systems.