Análisis del desempeño de un control PID de orden fraccional en un robot móvil diferencial

Ulises Vázquez; Jaime González-Sierra; Guillermo Fernández-Anaya; Eduardo Gamaliel Hernández-Martínez

doi:10.4995/riai.2021.15036

Autores/as

Ulises Vázquez Tecnológico Nacional de México/I.T. La Laguna
Jaime González-Sierra Universidad Politécnica de Pachuca https://orcid.org/0000-0001-9141-0061
Guillermo Fernández-Anaya Universidad Iberoamericana
Eduardo Gamaliel Hernández-Martínez Universidad Iberoamericana

DOI:

https://doi.org/10.4995/riai.2021.15036

Palabras clave:

Control fraccionario, Robot diferencial, Control de seguimiento, Control PID

Resumen

Este trabajo aborda el problema de seguimiento de trayectorias de un robot móvil tipo diferencial considerando una extensión dinámica del modelo cinemático y, controlando un punto frontal situado a una cierta distancia perpendicular al eje medio de las ruedas. Se proponen dos tipos de controladores, un controlador PID de orden fraccionario (PIdeltaDmu) y un controlador PD fraccionario (PDmu), ambos basados en errores de seguimiento. Los controladores propuestos se obtienen empleando la técnica de linealización entrada-salida. Por otra parte, los términos fraccionarios del controlador se basan en el operador de Caputo. Se presentan simulaciones numéricas con diferentes órdenes fraccionarios y se comparan con el controlador PID de orden entero, mostrando las variaciones ocurridas al cambiar únicamente el orden del controlador.

Descargas

Los datos de descargas todavía no están disponibles.

Biografía del autor/a

Guillermo Fernández-Anaya, Universidad Iberoamericana

Departamento de Física y Matemáticas

Eduardo Gamaliel Hernández-Martínez, Universidad Iberoamericana

Instituto de Investigación Aplicada y Tecnología

Citas

Al-Mayyahi, A., Wang, W., Birch, P., 2016. Design of fractional-order controller for trajectory tracking control of a non-holonomic autonomous ground vehicle. Journal of Control, Automation and Electrical Systems 27 (1), 29-42. https://doi.org/10.1007/s40313-015-0214-2

Betourne, A., Campion, G., 1996. Dynamic modelling and control design of a class of omnidirectional mobile robots. In Proceedings of IEEE International Conference on Robotics and Automation 3, 2810-2815.

Buslowicz, M., 2012. Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders. Bulletin of the Polish Academy of Sciences. Technical Sciences 60 (2), 279-284. https://doi.org/10.2478/v10175-012-0037-2

Buslowicz, M., 2013. Frequency domain method for stability analysis of linear continuous-time state-space systems with double fractional orders. In Advances in the Theory and Applications of Non-integer Order Systems, Springer, Heidelberg, 31-39. https://doi.org/10.1007/978-3-319-00933-9_3

Campion, G., Bastin, G., Dandrea-Novel, B., 1996. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE transactions on robotics and automation 12 (1), 47-62. https://doi.org/10.1109/70.481750

Contreras, J., Herrera, D., Toibero, J., Carelli, R., 2017. Controllers design for differential drive mobile robots based on extended kinematic modeling. In 2017 European Conference on Mobile Robots, 1-6.

Fierro, R., Lewis, F., 1998. Control of a nonholonomic mobile robot using neural networks. IEEE transactions on neural networks 9 (4), 589-600. https://doi.org/10.1109/72.701173

Kanjanawanishkul, K., Zell, A., 2009. Path following for an omnidirectional mobile robot based on model predictive control. In 2009 IEEE International Conference on Robotics and Automation, 3341-3346. https://doi.org/10.1109/ROBOT.2009.5152217

Khalil, H., Grizzle, J., 2002. Nonlinear systems. Upper Saddle River, NJ: Prentice hall 3.

Martínez, E., Ríos, H., Mera, M., Gonzalez-Sierra, J., 2019. A robust tracking control for unicycle mobile robots: An attractive ellipsoid approach. In 2019 IEEE 58th Conference on Decision and Control (CDC), 5799-5804. https://doi.org/10.1109/CDC40024.2019.9029954

Matignon, D., 1996. Stability results for fractional differential equations with applications to control processing. In IMACS Multiconference on Computational engineering in systems applications 2 (1), 963-968.

Matignon, D., 1998. Stability properties for generalized fractional differential systems. In ESAIM: Proceedings 5, 145-158. https://doi.org/10.1051/proc:1998004

Miller, K., Ross, B., 1993. An introduction to the fractional calculus and fractional differential equations.

Orman, K., Basci, A., Derdiyok, A., 2016. Speed and direction angle control of four wheel drive skid-steered mobile robot by using fractional order pi controller. Elektronika ir Elektrotechnika 22 (5), 14-19. https://doi.org/10.5755/j01.eie.22.5.16337

Ovalle, L., Ríos, H., Llama, M., Dzul, V. S. A., 2019. Omnidirectional mobile robot robust tracking: Sliding-mode output-based control approaches. Control Engineering Practice 85, 50-58. https://doi.org/10.1016/j.conengprac.2019.01.002

Park, B., Yoo, S., Park, J., Choi, Y., 2008. Adaptive neural sliding mode control of nonholonomic wheeled mobile robots with model uncertainty. IEEE Transactions on Control Systems Technology 17 (1), 207-214. https://doi.org/10.1109/TCST.2008.922584

Petrás, I., 2008. Stability of fractional-order systems with rational orders. Fractional Calculus and Applied Sciences 10.

Petrás, I., 2011. Fractional-order nonlinear systems: Modeling, analysis and simulation. Nonlinear Physical Science Book Series, Springer. https://doi.org/10.1007/978-3-642-18101-6

Petrás, I., Dorcák, L., 1999. The frequency method for stability investigation of fractional control systems. J. of SACTA 2 (1-2), 75-85.

Podlubny, I., 1998. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier, 340.

Radwan, A., Soliman, A., Elwakil, A., Sedeek, A., 2009. On the stability of linear systems with fractional-order elements. Chaos, Solitons & Fractals 40 (5), 2317-2328. https://doi.org/10.1016/j.chaos.2007.10.033

Rasheed, L., Al-Araji, A., 2017. A cognitive nonlinear fractional order pid neural controller design for wheeled mobile robot based on bacterial foraging optimization algorithm. Engineering and Technology Journal 35 (3), 289-300.

Rodriguez-Cortes, H., Aranda-Bricaire, E., 2007. Observer based trajectory tracking for a wheeled mobile robot. In 2007 American Conference Control, 991-996. https://doi.org/10.1109/ACC.2007.4282706

Rojas-Moreno, A., Perez-Valenzuela, G., 2017. Fractional order tracking control of a wheeled mobile robot. IEEE XXIV International Conference on Electronics, Electrical Engineering and Computing, 1-4. https://doi.org/10.1109/INTERCON.2017.8079683

Sabatier, J., Moze, M., Farges, C., 2010. Lmi stability conditions for fractional order systems. Computers & Mathematics with Applications 59 (5), 1594-1609. https://doi.org/10.1016/j.camwa.2009.08.003

Siegwart, R., Nourbakhsh, I., Scaramuzza, D., 2011. Introduction to autonomous mobile robots. MIT press.

Sira-Ramírez, H., López-Uribe, C., Velasco-Villa, M., 2013. Linear observer-based active disturbance rejection control of the omnidirectional mobile robot. Asian Journal of Control 15 (1), 51-63. https://doi.org/10.1002/asjc.523

Tawfik, M., Abdulwahb, E., Swadi, S., 2014. Trajectory tracking control for a wheeled mobile robot using fractional order piadb controller. Al-Khwarizmi Engineering Journal 10 (3), 39-52.

Tepljakov, A., 2017. Fractional-order modeling and control of dynamic systems; fomcon: Fractional-order modeling and control toolbox. Springer Theses, 107--129. https://doi.org/10.1007/978-3-319-52950-9

Tepljakov, A., Petlenkov, E., Belikov, J., Finajev, J., 2013. Fractional-order controller design and digital implementation using fomcon toolbox for matlab. IEEE Conference on Computer Aided Control System Design, 340--345. https://doi.org/10.1109/CACSD.2013.6663486

Valerio, D., Costa, J. D., 2013. An introduction to fractional control. IET 91, 32-208.

Vázquez, J., Velasco-Villa, M., 2008. Path-tracking dynamic model based control of an omnidirectional mobile robot. IFAC Proceedings Volumes 41 (2), 5365-5370. https://doi.org/10.3182/20080706-5-KR-1001.00904

Yang, H., Fan, X., Shi, P., Hua, C., 2015. Nonlinear control for tracking and obstacle avoidance of a wheeled mobile robot with nonholonomic constraint. IEEE Transactions on Control Systems Technology 24 (2), 741-746. https://doi.org/10.1109/TCST.2015.2457877

Zhang, L., Liu, L., Zhang, S., 2020. Design, implementation, and validation of robust fractional-order pd controller for wheeled mobile robot trajectory tracking. Complexity 2020, 1-12. https://doi.org/10.1155/2020/9523549

Zhao, Y., Chen, N., Tai, Y., 2016. Trajectory tracking control of wheeled mobile robot based on fractional order backstepping. In 2016 Chinese Control and Decision Conference, 6730-6734. https://doi.org/10.1109/CCDC.2016.7532208