Performance analysis of a PID fractional order control in a differential mobile robot

[EN] This work deals with the tracking trajectory problem for a differential-drive mobile robot taking into account a dynamic extension from the kinematic model and, controlling a front point located at a certain distance perpendicular to the mid-axis of the wheels. Two controls are proposed, a PID fractional order controller (PIδDµ) and a PD fractional order controller (PDµ), both based on the tracking errors. The proposed controllers are obtained by means of the input-output linearization technique. On the other hand, the controller fractional terms are based on the Caputo’s operator. Numerical simulations with different fractional orders are presented and compared with the integer order PID controller, showing the variations that occurred when changing only the controller order.[ES] 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.División de Investigación y Posgrado (DINVP) de la Universidad IberoamericanaVázquez, U.; González-Sierra, J.; Fernández-Anaya, G.; Hernández-Martínez, EG. (2021). Análisis del desempeño de un control PID de orden fraccional en un robot móvil diferencial. Revista Iberoamericana de Automática e Informática industrial. 19(1):74-83. https://doi.org/10.4995/riai.2021.15036OJS7483191Al-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/s40313-015-0214-2Betourne, 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/v10175-012-0037-2Buslowicz, 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_3Campion, 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/10.1109/70.481750Contreras, 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/10.1109/72.701173Kanjanawanishkul, 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.2009.5152217Khalil, 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/CDC40024.2019.9029954Matignon, 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:1998004Miller, 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.22.5.16337Ovalle, 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.2019.01.002Park, 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.2008.922584Petrás, 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/10.1007/978-3-642-18101-6Petrás, 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.2007.10.033Rasheed, 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.2007.4282706Rojas-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.2017.8079683Sabatier, 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.2009.08.003Siegwart, 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.523Tawfik, 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/10.1007/978-3-319-52950-9Tepljakov, 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.2013.6663486Valerio, 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-1001.00904Yang, 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.2015.2457877Zhang, 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/10.1155/2020/9523549Zhao, 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.2016.753220

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