Saturated regulation with derivative variable gain for robot manipulators

[EN] In this paper a family with a large number of hyperbolictype saturated regulators for robot manipulators, was presented. The proposed regulators consider a constant proportional gain while the derivative variable gain is self-tuned according to a function that depends on the position error, speed of motion and a damping factor, in order to modify the velocity of the transient response of the robot. The derivative control with variable gain enables reduced overshots, oscillations and ripple, enabling a smooth arrival to the steady state. The paper also proposes a strict Lyapunov function which enables the demonstration of asymptotic global stability of the closed-loop equation. In order to illustrate the performance and functionality of the proposed family of control schemes, an experimental comparison between seven control schemes was implemented. Five of these control schemes belong to the proposed family while two additional control schemes are well-known strategies such as the proportional-derivative (PD) and hyperbolic tangent (Tanh) control schemes. The experiments were performed by using a three degree-of-freedom, direct-drive robot manipulator.[ES] En este trabajo se presenta una familia grande de reguladores saturados tipo hiperbólicos para robots manipuladores. La propuesta considera a la ganancia proporcional constante y a la ganancia derivativa variable con sintonía automática definida en función del error de posición, velocidad de movimiento y un factor de inyección de amortiguamiento para modificar la velocidad de respuesta del robot. La acción de control derivativa con ganancia variable permite reducir sobreimpulsos, oscilaciones y rizo, tal que alcance el estado estacionario en forma suave. Asimismo, se presenta la propuesta de una función estricta de Lyapunov que permite demostrar la estabilidad asintótica global de la ecuación en lazo cerrado. Para mostrar el desempeño y funcionalidad de la familia propuesta de esquemas de control, un análisis comparativo experimental fue desarrollado entre siete estructuras de control, cinco reguladores pertenecen a la familia propuesta, y dos algoritmos de control bien conocidos como son el proporcional derivativo (PD) y tangente hiperbólico (Tanh). Los resultados experimentales fueron obtenidos con un robot manipulador de transmisión directa de tres grados de libertad.M.A. Limón-Díaz agradece por la beca # 351549 otorgada por CONACyT para estudios de doctorado.Limón-Díaz, MA.; Reyes-Cortés, F.; González-Galván, EJ. (2017). Regulacion Saturada con Ganancia Variable Derivativa de Robots Manipuladores. Revista Iberoamericana de Automática e Informática industrial. 14(4):434-445. https://doi.org/10.1016/j.riai.2017.06.001OJS434445144Armendariz, J., Parra-Vega, V., Garcia-Rodriguez, R., Hirai, S., 2012. Dynamic self-tuning pd control for tracking of robot manipulators. In: Decision and Control (CDC), 2012 IEEE 51st Annual Conference on. IEEE, pp. 1172- 1179. DOI: 10.1109/CDC.2012.6426562Åstrom, ¨ K. J., Wittenmark, B., 1973. On self tuning regulators. Automatica 9 (2), 185-199.Bai, E.-W., Huang, Y.-F., 2000. Variable gain parameter estimation algorithms for fast tracking and smooth steady state. Automatica 36 (7), 1001-1008.Canudas de Wit, C., Olsson, H., Astrom, K. J., Lischinsky, P., Mar 1995. A new model for control of systems with friction. IEEE Transactions on Automatic Control 40 (3), 419-425. DOI: 10.1109/9.376053Chavez, C., Reyes, F., Gonz ' alez, E., Mendoza, M., Bonilla, I., 2012. Experi- ' mental evaluation of parameter identification schemes on an anthropomorphic direct drive robot. International Journal of Advanced Robotic Systems 9. DOI: DOI: 10.5772/52190Chavez-Olivares, C. A., Reyes-Cort ' es, ' F., Gonzalez-Galv ' an, ' E. J., MendozaGutierrez, ' M. O., Bonilla-Gutierrez, I., 2012. Experimental ' evaluation of parameter identification schemes on a direct-drive robot. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 226 (10), 1419-1431. DOI: 10.1177/0959651812456795Davila, A., Moreno, ' J. A., Fridman, L., 2010. Variable gains super-twisting algorithm: a Lyapunov based design. In: American Control Conference (ACC), 2010. IEEE, pp. 968-973.Dehghani, A., Khodadadi, H., Oct 2015. Fuzzy logic self-tuning pid control for a single-link flexible joint robot manipulator in the presence of uncertainty. In: Control, Automation and Systems (ICCAS), 2015 15th International Conference on. pp. 186-191. DOI: 10.1109/ICCAS.2015.7364904Draou, A., Miloud, A., Miloud, Y., 2010. A variable gains PI speed controller in a simplified scalar mode control induction machine drive - Design and implementation -. In: Control Automation and Systems (ICCAS), 2010 International Conference on. pp. 2467-2471.Gonzalez, T., Moreno, J. A., Fridman, L., 2012. Variable gain super-twisting sliding mode control. Automatic Control, IEEE Transactions on 57 (8), 2100- 2105.Haj-Ali, A., Ying, H., 2004. Structural analysis of fuzzy controllers with nonlinear input fuzzy sets in relation to nonlinear PID control with variable gains. Automatica 40 (9), 1551-1559.Hussein, M. T., Soffker, D., 2012. Variable gain control of elastic crane using vision sensor data. In: Control Automation Robotics & Vision (ICARCV), 2012 12th International Conference on. IEEE, pp. 1783-1788.Jafarov, E., Parlakci, M., Istefanopulos, Y., 2005. A new variable structure PIDcontroller design for robot manipulators. Control Systems Technology, IEEE Transactions on 13 (1), 122-130.Kahn, L. R., 1953. Analysis of a limiter as a variable-gain device. Electrical Engineering 72 (12), 1106-1109. DOI: 10.1109/EE.1953.6438395Kay, H. S., Khalil, H. K., 2003. Universal integral controllers with variable gains. In: American Control Conference, 2003. Proceedings of the 2003. Vol. 1. IEEE, pp. 885-890.Kelly, R., Santibáñez, V., Reyes, F., 1996. On saturated-proportional derivative feedback with adaptive gravity compensation of robot manipulators. International Journal of Adaptive Control and Signal Processing 10, 465-479.Kiong, L. C., Rajeswari, M., Kiong, W. E., Rao, 2004. A self-learning nonlinear variable gain proportional derivative (pd) controller in robot manipulators. Pertanika Journal of Science & Technology 12 (2), 139-158.Koditschek, D., 1984. Natural motion for robot arms. In: Decision and Control, 1984. The 23rd IEEE Conference on. Vol. 23. pp. 733-735. DOI: 10.1109/CDC.1984.272106Kumar, P. P., Kar, I., Behera, L., 2006. Variable-gain controllers for nonlinear systems using the T-S fuzzy model. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 36 (6), 1442-1449.Llama, M. A., Kelly, R., Santibáñez, V., 2001. A stable motion control system for manipulators via fuzzy self-tuning. Fuzzy Sets and Systems 124 (2), 133-154. DOI: http://dx.doi.org/10.1016/S0165-0114(00)00061-0Llama, M. A., Kelly, R., Santibaáñz, V., 2010. An adaptive fuzzy controller for robot manipulators: Theory and experimentation. International Journal of Factory Automation, Robotics and Soft.Llama, M. A., Kelly, R., Santibáñez, V., February 2000. Stable computedtorque control of robot manipulators via fuzzy self-tuning. IEEE Systems, Man, and Cybernetics Society, 143-150.Mamdani, E. H., Assilian, S., 1975. An experiment in linguistic synthesis with a fuzzy logic controller. International journal of man-machine studies 7 (1), 1-13.Marton, L., Lantos, B., 2009. Control ' of mechanical systems with stribeck friction and backlash. Systems & Control Letters 58 (2), 141-147.Mendoza, M., Zavala-Río, A., Santibáñez, V., Reyes, F., Dec 2014. A pid-type global regulator with simple tuning for robot manipulators with bounded inputs. In: 53rd IEEE Conference on Decision and Control. pp. 6335-6341. DOI: 10.1109/CDC.2014.7040382Meza, J., Santibáñez, V., Soto, R., Llama, M., 2009. Stable fuzzy self-tuning pid control of robot manipulators. In: Systems, Man and Cybernetics, 2009. SMC 2009. IEEE International Conference on. pp. 2624-2629. DOI: 10.1109/ICSMC.2009.5346112Meza, J., Santibáñez, V., Soto, R., Llama, M., 2012. Fuzzy self-tuning pid semiglobal regulator for robot manipulators. Industrial Electronics, IEEE Transactions on 59 (6), 2709-2717. DOI: 10.1109/TIE.2011.2168789Monopoli, R., Subbarao, V., 1980. A new algorithm for model reference adaptive control with variable adaptation gains. Automatic Control, IEEE Transactions on 25 (6), 1245-1248.Moreno, J. A., Osorio, M., 2008. A Lyapunov approach to second-order sliding mode controllers and observers. In: Decision and Control, 2008. CDC 2008. 47th IEEE Conference on. IEEE, pp. 2856-2861.Palm, R., 1997. Model based fuzzy control: fuzzy gain schedulers and sliding mode fuzzy controllers. Springer.Salas, F., Llama, M., Santibáñez, V., May 2013. A stable self-organizing fuzzy pd control for robot manipulators. International Journal of Innovative Computing, Information and Control 9 (5), 2065-2086. URL: http://www.ijicic.org/ijicic-12-02104.pdfSalas, F. G., Llama, M. A., 2010. Self-organizing fuzzy pid tracking control for a 2 d.o.f. robotic arm. In: Congreso Anual 2010 de la Asociación de México de Control Automático. Puerto Vallarta, Jalisco, México.Salas, F. G., Santibáñez, V., Llama, M. A., 2012a. Variable gains PD tracking control of robot manipulators: Stability analysis and simulations. In: World Automation Congress (WAC), 2012. IEEE, pp. 1-6.Salas, F. G., Santibáñez, V., Llama, M. A., 2012b. Variable gains pd tracking control of robot manipulators: Stability analysis and simulations. In: World Automation Congress (WAC), 2012. IEEE, pp. 1-6.Santibáñez, V., Kelly, R., April 1997. Strict lyapunov functions for control of robot manipulators. Automatica 33, 675-682.Santibáñez, V., Kelly, R., Llama, M. A., 2002. Asymptotic stable tracking for robot manipulators via sectorial fuzzy control1/2. In: 15th Triennial World Congress. Barcelona, SpainSantibáñez, V., Kelly, R., Llama, M. A., 2004. Global asymptotic stability of a tracking sectorial fuzzy controller for robot manipulators. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 34 (1), 710- 718.Sifuentes-Mijares, J., Santibanez, V., Medina, J. L. M., Aug 2014. A globally asymptotically stable nonlinear pid regulator with fuzzy self-tuned pd gains, for robot manipulators. In: 2014 World Automation Congress (WAC). pp. 573-578. DOI: 10.1109/WAC.2014.6936049Slotine, J. J. E., Li, W., et al., 1991. Applied nonlinear control. Vol. 199. Prentice hall New Jersey.Takegaki, M., Arimoto, S., June 1981. A new feedback method for dynamic control of manipulators. ASME J. Dyn. Syst. Meas. Control 103, 119-125.Tomei, P., 1991. Adaptive pd controller for robot manipulators. IEEE Transactions on Robotics and Automation, 565-570.Wang, L., 1994. Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Electrical engineering. PTR Prentice Hall. URL: http://books.google.com.mx/books?id=spIeAQAAIAAJWhitcomb, L. L., Rizzi, A. A., Koditscheck, D. E., February 1993. Comparative experiments with a new adaptive controller for robot arms. IEEE Transactions on Robotics and Automation 9 (1).Xiaobo, G., Aiguo, S., Yan, Z., 2008. Neural Network Control for Telerehabilitation Robot based on Variable Gain. BioMedical Engineering and Informatics, International Conference on 2, 778-782.Ying, H., 1993a. A two-input two-output fuzzy controller is the sum of two nonlinear PI controllers with variable gains. In: Fuzzy Systems, 1993., Second IEEE International Conference on. pp. 35-37 vol.1. DOI: 10.1109/FUZZY.1993.327467Ying, H., 1993b. The simplest fuzzy controllers using different inference methods are different nonlinear proportional-integral controllers with variable gains. Automatica 29 (6), 1579-1589. DOI: 10.1016/0005-1098(93)90025-OYing, H., 1998a. Constructing nonlinear variable gain controllers via the Takagi-Sugeno fuzzy control. Fuzzy Systems, IEEE Transactions on 6 (2), 226-234.Ying, H., 1998b. The Takagi-Sugeno fuzzy controllers using the simplified linear control rules are nonlinear variable gain controllers. Automatica 34 (2), 157-167.Ying, H., 2001. Conditions on general Mamdani fuzzy controllers as nonlinear, variable gain state feedback controllers with stability analysis. In: IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th. Vol. 3. IEEE, pp. 1265-1270