ANALYSIS OF THE NOMOTO SHIP MODEL RESPONSE TO

ANALYSIS OF THE NOMOTO SHIP MODEL RESPONSE TO COURSE CHANGES USING PID CONTROLLER IN MATLAB/SIMULINK Assani N. , Pavić I. , Vukša S. , Laušić M. Faculty of Maritime Studies Split Portorož, 2020. ICTS 2020 - Portorož, 17. -18. Sept. 2020

SUMMARY 1. Introduction 2. Basic ship motions 3. Nomoto ship model 4. Ship course control system 5. Simulations 6. Conclusion

1. INTRODUCTION • Nomoto model of ship and its response to course changes using regulation loop with PID controller was used to carry out simulations • Analysis had been conducted using Matlab/Simulink package with first order Nomoto model using real parameters of a fully loaded tanker • Results of an analysis had been used to conclude about characteristics of presented system and its response to course changes

2. BASIC SHIP MOTIONS • Equations describing basic ship motions were retrieved using XOYZ reference ship centered system shown on figure 1. • Pitching, rolling and heaving were ignored • Horizontal plane movements were considered Figure 1. Ship centered system [Fernandezm, C. , Kumar, S. B. ]

3. NOMOTO SHIP MODEL •

3. NOMOTO SHIP MODEL •

4. SHIP COURSE CONTROL SYSTEM • Ship course control system shown on figure 2 is a SISO (single input single output) system • Every block represents a subsystem Figure 2. Ship course control system block diagram [Authors]

5. SIMULATIONS • Fully loaded tanker of 350 m length overall is considered. • At speed of 8. 1 m/s, parameters K and T are -0. 019 and -153. 7 • Rudder angle limit is set to ± 30° , while rudder movement rate is limited to ± 2. 33°/s • Calculated PID parameters, assuming natural frequency 0. 03 rad/s and damping ratio 1 are: Kp = 7. 2805, Kd = 538 and Ki = 0. 0218 Figure 3. Ship control system block diagram in MATLAB/Simulink [Authors]

5. SIMULATIONS Figure 4. Systems response to desired course of 20° [Authors]

5. SIMULATIONS Figure 5. Systems response to desired course of 50° [Authors]

5. SIMULATIONS Figure 6. Systems response to desired course of 10°, 50° and 30° respectively [Authors]

6. CONCLUSION • Based on simulation results this model is applicable when there are no sudden course changes • On last figure, when simulating sudden course change, overshot of 17. 28° is evident which can be dangerous if ship is in vicinity of other ships or navigating through a narrow channel • Presented system can be expanded with additional parameters that affect ship course such as wind impact, waves, draft and more • Enhancement of such system using neural networks or fuzzy logic which would contribute to robustness of a PID controller used as autopilot for any kind of ship can be done

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