Position and Motor Control of a 3-DoF RRR Robotic Manipulator Using PID and Sliding Mode Control

Abstract

This study investigates the position and motor control of a 3-degree-of-freedom (3-DoF) RRR robotic manipulator. The research focuses on developing and comparing two control strategies: Proportional-Integral-Derivative (PID) control and Sliding Mode Control (SMC). Kinematic modeling of the manipulator is performed using Denavit-Hartenberg parameters, while dynamic modeling is achieved through the Lagrangian ormulation. The effectiveness of both control methods is evaluated through simulations conducted in MATLAB/Simulink, with a focus on assessing their stability and error performance. Results indicate that the PID tuning process significantly improves the manipulator's dynamic characteristics, leading to enhanced stability, reduced overshoot, and reliable reference tracking. Furthermore, the implementation of SMC demonstrates considerable efficacy in managing system uncertainties and attenuating disturbances, ensuring stable and precise control of the robotic system even under challenging conditions. This research validates the robustness and precision offered by these control methodologies for robotic manipulator applications.

Keywords

• RRR robotic manipulator
• sliding mode control
• PID control
• kinematic modeling
• dynamic modeling

Kaynakça

1. [1] Z. Kuang, X. Zhang, L. Sun, H. Gao, and M. Tomizuka, “Feedback-based Digital Higher-order Terminal Sliding Mode for 6-DoF Industrial Manipulators,” arXiv (Cornell University), Jan. 2021, doi: 10.48550/arxiv.2102.03531.
2. [2] K. Jayaswal, D. K. Palwalia, and S. Kumar, “Performance investigation of PID controller in trajectory control of two-link robotic manipulator in medical robots,” Journal of Interdisciplinary Mathematics, vol. 24, no. 2, p. 467, Feb. 2021, doi: 10.1080/09720502.2021.1893444.
3. [3] G. Sherif, S. Ahmad, M. Saad, and G. Fayez, “Dynamic Modelling with a Modified PID Controller of a Three Link Rigid Manipulator,” International Journal of Computer Applications, vol. 179, no. 34, p. 37, Apr. 2018, doi: 10.5120/ijca2018916772.
4. [4] S. Hasan, “A Realistic Model Reference Computed Torque Control Strategy for Human Lower Limb Exoskeletons,” arXiv (Cornell University), Sep. 2024, doi: 10.48550/arxiv.2410.07200.
5. [5] C. Ma and Z. Zhang, “Predictive reinforcement learning based adaptive PID controller,” 2025, doi: 10.48550/ARXIV.2506.08509.
6. [6] V. T. Aghaei, A. Seyyedabbasi, J. Rasheed, and A. M. Abu‐Mahfouz, “Sand cat swarm optimization-based feedback controller design for nonlinear systems,” Heliyon, vol. 9, no. 3, Feb. 2023, doi: 10.1016/j.heliyon.2023.e13885.
7. [7] J. Shanbhag et al., “Methods for integrating postural control into biomechanical human simulations: a systematic review,” Journal of NeuroEngineering and Rehabilitation, vol. 20, no. 1. BioMed Central, Aug. 21, 2023. doi: 10.1186/s12984-023-01235-3.
8. [8] A. Ashoori, B. Moshiri, A. K. Sedigh, and M. Bakhtiari, “Optimal control of a nonlinear fed-batch fermentation process using model predictive approach,” Journal of Process Control, vol. 19, no. 7, p. 1162, Apr. 2009, doi: 10.1016/j.jprocont.2009.03.006.

9. [9] N. Gafurov, S.-Y. Lee, U. Ali, M. Irfan, I. Kim, and T. Lee, “AI-driven digital twin for autonomous web tension control in Roll-to-Roll manufacturing system,” Scientific Reports, vol. 15, no. 1, Jul. 2025, doi: 10.1038/s41598-025-09813-2.
10. [10] P. Saraf, M. Gupta, and A. M. Parimi, “A Comparative Study Between a Classical and Optimal Controller for a Quadrotor,” 2021 IEEE 18th India Council International Conference (INDICON), p. 1, Dec. 2020, doi: 10.1109/indicon49873.2020.9342485.
11. [11] N. Sitapure and J. S. Kwon, “Require Process Control? LSTMc is all you need!,” arXiv (Cornell University), Jan. 2023, doi: 10.48550/arxiv.2306.07510.
12. [12] G. Bujgoi and D. Şendrescu, “Tuning of PID Controllers Using Reinforcement Learning for Nonlinear System Control,” Processes, vol. 13, no. 3, p. 735, Mar. 2025, doi: 10.3390/pr13030735.
13. [13] K. M. S. Mamani and A. Prado, “Integrating Model Predictive Control with Deep Reinforcement Learning for Robust Control of Thermal Processes with Long Time Delays,” Processes, vol. 13, no. 6, p. 1627, May 2025, doi: 10.3390/pr13061627.
14. [14] K. J. Åström and T. Hägglund, “The future of PID control,” Control Engineering Practice, vol. 9, no. 11, p. 1163, Nov. 2001, doi: 10.1016/s0967-0661(01)00062-4.
15. [15] R. Wu, J. Ai, and T. Li, “InstructMPC: A Human-LLM-in-the-Loop Framework for Context-Aware Control,” 2025, doi: 10.48550/ARXIV.2504.05946.
16. [16] W. Shen, X. Chen, M. Pons, and J. Corriou, “Model predictive control for wastewater treatment process with feedforward compensation,” Chemical Engineering Journal, vol. 155, p. 161, Jul. 2009, doi: 10.1016/j.cej.2009.07.039.
17. [17] Pandey, B. Bohara, R. Pungaliya, S. C. Patwardhan, and R. Banerjee, “A thermal comfort-driven model predictive controller for residential split air conditioner,” Journal of Building Engineering, vol. 42, p. 102513, Apr. 2021, doi: 10.1016/j.jobe.2021.102513.
18. [18] L. Zollo, E. Lopez, L. Spedaliere, N. García-Aracil, and E. Guglielmelli, “Identification of Dynamic Parameters for Robots with Elastic Joints,” Advances in Mechanical Engineering, vol. 7, no. 2, Dec. 2014, doi: 10.1155/2014/843186.
19. [19] M. Božić, M. Vasiljević-Toskić, M. Bodić, and V. Rajs, “Advantages of a combination of PD and PID controller over PID controller in the example of quadcopter control and stabilization,” IJEEC - INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING AND COMPUTING, vol. 4, no. 1, Jan. 2020, doi: 10.7251/ijeec2001043b.
20. [20] M. Fliess and C. Join, “An alternative to proportional‐integral and proportional‐integral‐derivative regulators: Intelligent proportional‐derivative regulators,” International Journal of Robust and Nonlinear Control, vol. 32, no. 18, p. 9512, Jul. 2021, doi: 10.1002/rnc.5657.
21. [21] L. A. Tuấn and S. Lee, “3D cooperative control of tower cranes using robust adaptive techniques,” Journal of the Franklin Institute, vol. 354, no. 18, p. 8333, Nov. 2017, doi: 10.1016/j.jfranklin.2017.10.026.