PID and LQR controllers applied to the inverse dynamics of a 3-DOF Manipulator / Controladores PID e LQR aplicados à dinâmica inversa de um Manipulador 3-GDL

Josias Guimarães Batista, Darielson Araújo de Souza, Laurinda Lúcia Nogueira dos Reis, Antônio Barbosa de Souza Júnior

Abstract


The application in the industrial manipulator robots has grown over the years making production systems increasingly efficient. Within this context, the need for efficient controllers is required to perform the control of these manipulators. In this work the PID controller (Proportional-Integral-Derivative) and LQR (Linear Quadratic Regulator) is presented from the inverse dynamics model of a RPP (Rotational - Prismatic - Prismatic) cylindrical manipulator. The inverse dynamic model which is modeled on Simulink together with a cascaded PID controller is presented. The PID and LQR results are also presented for joint independent and joint dependent control, i.e a controlled PID is used for each joint, controlling the trajectories and speeds at the same time. This paper has as main contributions the development of the manipulator dynamics model and the design of the LQR and PID controllers applied to the inverse dynamics model, which makes the system simpler to control.


Keywords


PID Controller, Inverse Dynamics, PID Cascade, Cylindrical Manipulator, LQR Controller.

References


Pinto, Milena F., et al. Modified approach using variable charges to solve inherent limitations of potential fields method. 2014 11th IEEE/IAS International Conference on Industry Applications. IEEE, 2014.

Herman, Przemyslaw. Inverse dynamics control in terms of unnormalized quasi-velocities. Journal of the Franklin Institute 342.1 (2005): 25-38.

Spong, Mark W., and Mathukumalli Vidyasagar. Robot dynamics and control. John Wiley & Sons, 2008.

Korkmaz, Ozan, and S. Kemal Ider. ”Hybrid force and motion control of flexible joint parallel manipulators using inverse dynamics approach.” Advanced Robotics 28.18 (2014): 1221-1230.

Szafranski, Grzegorz, and Roman Czyba. ”Different approaches of PID control UAV type quadrotor.” (2011).

Damic, Vjekoslav, and Maida Cohodar. ”Dynamic Analysis and Visualization of Spatial Manipulators with Closed Structure.” Annals of DAAAM & Proceedings 26.1 (2015).

Damic, Vjekoslav, Maida Cohodar, and Marko Tvrtkovic. ”Inverse Dynamic Analysis of Hobby Robot Uarm by Matlab/Simulink.” Annals of DAAAM & Proceedings 27 (2016).

Devi Handaya, S.Pd, M.T. Comparison Of Manipulator Control 2 Link Using The Inverse Dynamic Control Method With Outdoor Control Structure And The Second Method Of Lyapunov. Jurnal Ilmiah Technoscience Politeknik PGRI Banten Volume II No. 1, Januari - Juni 2016. ISSN: 977 2461086008.

Lashin, Manar, et al. ”Dynamic Modeling and Inverse Optimal PID with Feed-forward Control in H∞ Framework for a Novel 3D Pantograph Manipulator.” International Journal of Control, Automation and Systems 16.1 (2018): 39-54.

Pott, Peter Paul, et al. ”Inverse dynamic model and a control application of a novel 6-DOF hybrid kinematics manipulator.” Journal of Intelligent & Robotic Systems 63.1 (2011): 3-23.

Singh, Yogesh, et al. ”Inverse dynamics and control of a 3-DOF planar parallel (U-shaped 3-PPR) manipulator.” Robotics and Computer-Integrated Manufacturing 34 (2015): 164-179.

Das, Abhijit, Kamesh Subbarao, and Frank Lewis. ”Dynamic inversion with zero-dynamics stabilisation for quadrotor control.” IET control theory & applications 3.3 (2009): 303-314.

Sanz, Pedro. ”Robotics: Modeling, planning, and control (siciliano, b. et al; 2009)[on the shelf].” IEEE Robotics & Automation Magazine 16.4 (2009): 101-101.

Spong, Mark W. et al. Robot modeling and control. New York: Wiley, 2006.

Edge, Solid Software; Siemens Global Website; Siemens PLM Software: Stuttgart, Germany, 2020.

Batista, Josias, et al. Dynamic model and inverse kinematic identification of a 3-DOF manipulator using RLSPSO. Sensors, 2020, 20.2: 416.

Batista, Josias, et al. Trajectory planning using artificial potential fields with metaheuristics. IEEE Latin America Transactions, 2020, 18.05: 914-922.

Hartenberg, Richard, and Jacques Danavit. Kinematic synthesis of linkages. New York: McGraw-Hill, 1964.

Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2010). Robotics: modelling, planning and control. Springer Science & Business Media.

Potkonjak, V. Dynamics of manipulation robots: Theory and application. Berlin et al.: Springer, 1982.

Kozlowski, Krzysztof R. Modelling and identification in robotics. Springer Science & Business Media, 2012.

Sciavicco, Lorenzo, and Bruno Siciliano. Modelling and control of robot manipulators. Springer Science & Business Media, 2012.

Spong, Mark W., Seth Hutchinson, and Mathukumalli Vidyasagar. Robot modeling and control. 2006.

Das, Abhijit, Kamesh Subbarao, and Frank Lewis. ”Dynamic inversion with zero-dynamics stabilisation for quadrotor control.” IET control theory & applications 3.3 (2009): 303-314.

Astrom, K. J., & Hagglund, T. (1995). PID controllers: theory, design, and tuning (Vol. 2). Research Triangle Park, NC: Instrument society of America.

Su, Yuxin, and Chunhong Zheng. ”Global finite-time inverse tracking control of robot manipulators.” Robotics and Computer-Integrated Manufacturing 27.3 (2011): 550-557.

Moreno-Valenzuela, Javier, et al. ”Nonlinear PID-type controller for quadrotor trajectory tracking.” IEEE/ASME Transactions on Mechatronics 23.5 (2018): 2436-2447.

Teixeira, M. C. M., et al. ”Projeto de um controlador linear para variar o angulo de articulac¸ ˆ ao do ˜ joelho de um paciente paraplegico.” Brazilian Conference on Dynamics, Control and Their Applications. 2007.

Rosa Filho, Julio Estefano A.” Contribuic¸oes de controle ótimo.” Trabalho de Conclusão de Curso, Universidade Estadual de Londrina, Londrina (2011).

Pandey, Sumit Kumar, and Vijaya Laxmi. ”Optimal control of twin rotor MIMO system using LQR technique.” Computational Intelligence in Data Mining-Volume 1. Springer, New Delhi, 2015. 11-21.

Batista, J. G., Souza, D. A., dos Reis, L. L., Filgueiras, L. V., Ramos, K. M., Junior, A. B., & Correia, W. B. (2019, October). Performance comparison between the PID and LQR controllers applied to a robotic manipulator joint. In IECON 2019-45th Annual Conference of the IEEE Industrial Electronics Society (Vol. 1, pp. 479-484). IEEE.

Dias, E. V., Silva, C. G., Batista, J. G., Ramalho, G. L., Costa, J. R., Silva, J. L., & Souza, D. A. (2021). Prevenção de Colisão de um Manipulador SCARA utilizando Campos Potenciais Artificiais e Caminhos Probabilísticos. Brazilian Journal of Development, 7(1), 11252-11270.

Sampaio, D. D., & Silva, W. L. S. (2021). Sistema nebuloso para navegação autônoma de veículo aéreo não tripulado. Brazilian Journal of Development, 7(4), 34520-34536.




DOI: https://doi.org/10.34117/bjdv7n7-388

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