Design of an Adaptive Super-Twisting Control for the Cart-Pole Inverted Pendulum System
DOI:
https://doi.org/10.26555/jiteki.v7i1.20420Keywords:
Inverted pendulum system, Stabilization control, Sliding mode control, Adaptive super-twisting algorithm, Open dynamic engine simulation, anyKode Marilou simulationAbstract
A cart-pole inverted pendulum system is one of the underactuated systems that has been used in many applications. This research aims to study the design and the effectiveness of the Adaptive Super-Twisting controller to stabilize the system by comparing it with other previous control methods. A stabilization control of the pendulum upright using the Adaptive Super-Twisting algorithm (ASTA), was investigated. The proposed controller was designed based on the decoupling algorithm method to solve the coupled control input in the system model. We then compared the proposed stabilizing controller with first-order sliding mode control (FOSMC) and Super-Twisting algorithm (STA) in Matlab/Simulink simulation and realistic computer simulation. We developed the computer simulation using anyKode Marilou software, which adopted Open-Dynamic Engine (ODE) as a physics engine. In Matlab/Simulink simulation, we considered three different scenarios: a nominal system, a system with uncertainty, and a disturbed system. Meanwhile, in a computer simulation, we only presented the comparison of different controllers' performances for the realized system. Both results showed that the three controllers could stabilize the pendulum upright with a 0.1 rad initial angular position around the vertical axis. Under the same conditions, the ASTA and STA controllers had similar performances; they both have less chattering and faster convergence than the FOSMC approach. However, the FOSMC approach had the least energy delivered and smallest errors than the other two approaches.References
D. Ashtiani Haghighi and S. Mobayen, "Design of an adaptive super-twisting decoupled terminal sliding mode control scheme for a class of fourth-order systems," ISA Trans., pp. 216–225, 2018. https://doi.org/10.1016/j.isatra.2018.02.006
Y. Rizal, C.-T. Ke, and M.-T. Ho, "Point-to-point motion control of a unicycle robot: Design, implementation, and validation," in IEEE International Conference Robotics and Automation, 2015, pp. 4379–4384. https://doi.org/10.1109/ICRA.2015.7139804
A. Rizky Octavia, D. Nathanlius, and T. Agustinus Tamba, “Implementasi Kontrol Umpan Balik Keluaran Berbasis Tapis Kalman dan Regulator Kuadratik Linier pada Sistem Pendulum Terbalik,†J. Otomasi Kontrol dan Instrumentasi, vol. 11, no. 2, pp. 81–93, 2019. https://doi.org/10.5614/joki.2019.11.2.2
A. U. Sambo, F. S. Bala, N. M. Tahir, and A. Y. Babawuro, "Optimal control of inverted pendulum on cart system," J. Phys. Conf. Ser., vol. 1502, no. 1, pp. 1–8, 2020. https://doi.org/10.1088/1742-6596/1502/1/012024
S. Hanwate, Y. V. Hote, and A. Budhraja, "Design and implementation of adaptive control logic for cart-inverted pendulum system," Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., vol. 233, no. 2, pp. 164–178, 2019. https://doi.org/10.1177/0959651818788148
L. Ovalle, H. RÃos, and M. Llama, "Robust output-feedback control for the cart–pole system: A coupled super-twisting sliding-mode approach," IET Control Theory Appl., vol. 13, no. 2, pp. 269–278, 2019. https://doi.org/10.1049/iet-cta.2018.5249
A. Kukker and R. Sharma, "Genetic Algorithm-Optimized Fuzzy Lyapunov Reinforcement Learning for Nonlinear Systems," Arab. J. Sci. Eng., vol. 45, no. 3, pp. 1629–1638, 2020. https://doi.org/10.1007/s13369-019-04126-9
E. Susanto, A. Surya Wibowo, and E. Ghiffary Rachman, "Fuzzy Swing Up Control and Optimal State Feedback Stabilization for Self-Erecting Inverted Pendulum," IEEE Access, vol. 8, pp. 6496–6504, 2020. https://doi.org/10.1109/ACCESS.2019.2963399
Y. Zheng, X. Li, and L. Xu, "Balance Control for the First-order Inverted Pendulum Based on the Advantage Actor-critic Algorithm," Int. J. Control. Autom. Syst., vol. 18, no. 12, pp. 3093–3100, 2020. https://doi.org/10.1007/s12555-019-0278-z
Y. Rizal, J.-W. Syu, and M.-T. Ho, "Balance control of an inverted pendulum system using second-order sliding mode control," in International Automatic Control Conference, 2014, pp. 191–196. https://doi.org/10.1109/CACS.2014.7097186
M. Ashok Kumar and S. Kanthalakshmi, "H∞ tracking control for an inverted pendulum," JVC/Journal Vib. Control, vol. 24, no. 16, pp. 3515–3524, 2018. https://doi.org/10.1177/1077546317750977
M. Ramirez-Neria, Z. Gao, H. Sira-Ramirez, R. Garrido-Moctezuma, and A. Luviano-Juarez, "Trajectory Tracking for an Inverted Pendulum on a Cart: An Active Disturbance Rejection Control Approach," in American Control Conference, 2018, vol. 2018-June, pp. 4881–4886. https://doi.org/10.23919/ACC.2018.8431712
A. K. Jayaprakash, K. B. Kidambi, W. Mackunis, S. V. Drakunov, and M. Reyhanoglu, "Finite-time state estimation for an inverted pendulum under input-multiplicative uncertainty," Robotics, vol. 9, no. 4, pp. 1–26, 2020. https://doi.org/10.3390/robotics9040087
R. G. Guerra, R. Iriarte, J. Eduardo, V. Velázquez, and L. Fridman, "Robust output trajectory linearisation control for a class of linear time-varying systems," IET Control Theory Appl., no. December 2020, pp. 877–889, 2021. https://doi.org/10.1049/cth2.12090
S. Mobayen, "Adaptive global sliding mode control of underactuated systems using a super-twisting scheme: an experimental study," JVC/Journal Vib. Control, vol. 25, no. 16, pp. 2215–2224, 2019. https://doi.org/10.1177/1077546319852257
R. Olfati-Saber, "Global configuration stabilization for the VTOL aircraft with strong input coupling," IEEE Trans. Automat. Contr., vol. 47, no. 11, pp. 1949–1951, 2002. https://doi.org/10.1109/TAC.2002.804457
R. Olfati-saber, "Normal forms for underactuated mechanical systems with symmetry," IEEE Trans. Automat. Contr., vol. 47, no. 2, pp. 305–308, 2002. https://doi.org/10.1109/9.983365
H. L. Pham, B. V. Adorno, V. Perdereau, and P. Fraisse, "Set-point control of robot end-effector pose using dual quaternion feedback," Robot. Comput. Integr. Manuf., vol. 52, pp. 100–110, 2018. https://doi.org/10.1016/j.rcim.2017.11.003
E. Coevoet et al., "Software toolkit for modeling, simulation, and control of soft robots," Adv. Robot., vol. 31, no. 22, pp. 1208–1224, 2017. https://doi.org/10.1080/01691864.2017.1395362
F. M. Noori, D. Portugal, R. P. Rocha, and M. S. Couceiro, "On 3D simulators for multi-robot systems in ROS: MORSE or Gazebo?," in 15th IEEE International Symposium on Safety, Security and Rescue Robotics, Conference, 2017, pp. 19–24. https://doi.org/10.1109/SSRR.2017.8088134
K. J. Gucwa and H. H. Cheng, "RoboSim: a simulation environment for programming virtual robots," Eng. Comput., vol. 34, no. 3, pp. 475–485, 2018. https://doi.org/10.1007/s00366-017-0553-7
Y. Rizal, "Computer Simulation of Human-Robot Collaboration in the Context of Industry Revolution 4.0," in Future of Robotics - Becoming Human with Humanoid or Emotional Intelligence, InTech, 2019. https://doi.org/10.5772/intechopen.88335
Y. Xu, C. Yang, J. Zhong, N. Wang, and L. Zhao, "Robot teaching by teleoperation based on visual interaction and extreme learning machine," Neurocomputing, vol. 275, pp. 2093–2103, 2017. https://doi.org/10.1016/j.neucom.2017.10.034
G. G. Gentiletti, J. G. Gebhart, R. C. Acevedo, O. Yáñez-Suárez, and V. Medina-Bañuelos, “Command of a simulated wheelchair on a virtual environment using a brain-computer interface,†IRBM, vol. 30, no. 5–6, pp. 218–225, 2009. https://doi.org/10.1016/j.irbm.2009.10.006
J. Zhao and M. W. Spong, "Hybrid control for global stabilization of the cart–pendulum system," Automatica, vol. 37, no. 12, pp. 1941–1951, 2001. https://doi.org/10.1016/S0005-1098(01)00164-9
S. Mahjoub, F. Mnif, and N. Derbel, "Second-order sliding mode control applied to inverted pendulum," in International Conference on Sciences and Techniques of Automatic Control and Computer Engineering, 2013, pp. 269–273. https://doi.org/10.1109/STA.2013.6783142
S. Mahjoub, F. Mnif, and N. Derbel, "Second-order sliding mode approaches for the control of a class of underactuated systems," Int. J. Autom. Comput., vol. 12, no. 2, pp. 134–141, 2015. https://doi.org/10.1007/s11633-015-0880-3
M. Yue, C. An, L. Ding, and Y. Zhou, "MPC motion planning-based sliding mode control for underactuated WPS vehicle via Olfati transformation," IET Control Theory Appl., vol. 12, no. 4, pp. 495–503, 2018. https://doi.org/10.1049/iet-cta.2017.0298
A. Hfaiedh, A. Chemori, and A. Abdelkrim, "Disturbance Observer-Based Super-Twisting Control for the Inertia Wheel Inverted Pendulum," in Proceedings of the 17th International Multi-Conference on Systems, Signals and Devices, SSD 2020, 2020, pp. 747–752. https://doi.org/10.1109/SSD49366.2020.9364233
B. Lu, Y. Fang, and N. Sun, "Continuous Sliding Mode Control Strategy for a Class of Nonlinear Underactuated Systems," IEEE Trans. Automat. Contr., vol. 63, no. 10, pp. 3471–3478, 2018. https://doi.org/10.1109/TAC.2018.2794885
S. Rajappa, C. Masone, H. H. Bulthoff, and P. Stegagno, "Adaptive Super Twisting Controller for a quadrotor UAV," in IEEE International Conference on Robotics and Automation, 2016, pp. 2971–2977. https://doi.org/10.1109/ICRA.2016.7487462
M. Derbeli, M. Farhat, O. Barambones, and L. Sbita, "Control of PEM fuel cell power system using sliding mode and super-twisting algorithms," Int. J. Hydrogen Energy, vol. 42, no. 13, pp. 8833–8844, 2017. https://doi.org/10.1016/j.ijhydene.2016.06.103
A. R. Babaei, M. Malekzadeh, and D. Madhkhan, "Adaptive super-twisting sliding mode control of 6-DOF nonlinear and uncertain air vehicle," Aerosp. Sci. Technol., vol. 84, no. September, pp. 361–374, 2019. https://doi.org/10.1016/j.ast.2018.09.013
J. Liu and J. Liu, "Chapter 9 – Sliding mode control for underactuated system with decoupling algorithm," in Sliding Mode Control Using MATLAB, Academic Press, 2017, pp. 307–327. https://doi.org/10.1016/B978-0-12-802575-8.00009-6
Z. Feng and J. Fei, "Design and analysis of adaptive Super- Twisting sliding mode control for a microgyroscope," J. Pone, vol. 13, no. 1, pp. 1–18, 2018. https://doi.org/10.1371/journal.pone.0189457
A. Levant, "Sliding order and sliding accuracy in sliding mode control," Int. J. Control, vol. 58, no. 6, pp. 1247–1263, 1993. https://doi.org/10.1080/00207179308923053
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with JITEKI agree to the following terms:
- Authors retain copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
This work is licensed under a Creative Commons Attribution 4.0 International License
