Synthesis of an Orbit Tracking Controller for a 2DOF Helicopter based on Sequential Manifolds with Stabilization Time in the Presence of Disturbances
Received: 16 April 2024 | Revised: 2 May 2024 | Accepted: 18 May 2024 | Online: 2 August 2024
Corresponding author: Le Tran Thang
Abstract
This study presents the design of a controller for a two-degree-of-freedom (2-DOF) helicopter based on sequential invariant manifolds with exponential convergence. The system is decomposed into two subsystems for pitch and yaw angles, and exponentially stable manifolds are constructed for each subsystem. The control law is found based on sequential manifolds and the Analytical Design of Aggregated Regulators (ADAR) method. The controller is designed to increase the system's stability against disturbances while ensuring stability over a finite period of time. The response time of the system can be evaluated in advance through the parameters of the designed manifold. The robustness of the control law for external disturbances was proven using the Lyapunov function in the design process. Finally, the effectiveness of the proposed controller based on the synergetic control theory is demonstrated by numerical simulation results and a comparison with the backstepping controller.
Keywords:
sequential manifold, backstepping controller, SMC, 2-DOF helicopter, ADARDownloads
References
G. Yang, T. Zhu, F. Yang, L. Cui, and H. Wang, "Output feedback adaptive RISE control for uncertain nonlinear systems," Asian Journal of Control, vol. 25, no. 1, pp. 433–442, 2023.
B. Luo, H. N. Wu, and T. Huang, "Optimal Output Regulation for Model-Free Quanser Helicopter With Multistep Q-Learning," IEEE Transactions on Industrial Electronics, vol. 65, no. 6, pp. 4953–4961, Jun. 2018.
S. K. Kim and C. K. Ahn, "Performance-Boosting Attitude Control for 2-DOF Helicopter Applications via Surface Stabilization Approach," IEEE Transactions on Industrial Electronics, vol. 69, no. 7, pp. 7234–7243, Jul. 2022.
Z. Zhao, W. He, C. Mu, T. Zou, K. S. Hong, and H. X. Li, "Reinforcement Learning Control for a 2-DOF Helicopter With State Constraints: Theory and Experiments," IEEE Transactions on Automation Science and Engineering, vol. 21, no. 1, pp. 157–167, Jan. 2024.
B. Wu, J. Wu, J. Zhang, G. Tang, and Z. Zhao, "Adaptive Neural Control of a 2DOF Helicopter with Input Saturation and Time-Varying Output Constraint," Actuators, vol. 11, no. 11, Nov. 2022, Art. no. 336.
B. M. Kim and S. J. Yoo, "Approximation-Based Quantized State Feedback Tracking of Uncertain Input-Saturated MIMO Nonlinear Systems with Application to 2-DOF Helicopter," Mathematics, vol. 9, no. 9, Jan. 2021, Art. no. 1062.
P. Lambert and M. Reyhanoglu, "Observer-Based Sliding Mode Control of a 2-DOF Helicopter System," in IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society, Washington, DC, USA, Oct. 2018, pp. 2596–2600.
Q. Ahmed, A. I. Bhatti, S. Iqbal, and I. H. Kazmi, "2-sliding mode based robust control for 2-DOF helicopter," in 2010 11th International Workshop on Variable Structure Systems (VSS), Mexico City, Mexico, Jun. 2010, pp. 481–486.
S. Mondal and C. Mahanta, "Adaptive second-order sliding mode controller for a twin rotor multi-input–multi-output system," IET Control Theory & Applications, vol. 6, no. 14, pp. 2157–2167, Sep. 2012.
A. K. Ekbote, N. S. Srinivasan, and A. D. Mahindrakar, "Terminal Sliding Mode Control of a Twin Rotor Multiple-Input Multiple-Output System," IFAC Proceedings Volumes, vol. 44, no. 1, pp. 10952–10957, Jan. 2011.
P. Sodhi and I. Kar, "Adaptive Backstepping Control for A Twin Rotor MIMO System," IFAC Proceedings Volumes, vol. 47, no. 1, pp. 740–747, Jan. 2014.
R. Patel, D. Deb, H. Modi, and S. Shah, "Adaptive backstepping control scheme with integral action for quanser 2-dof helicopter," in 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI), Udupi, India, Sep. 2017, pp. 571–577.
M. Derakhshannia, S. B. F. Asl, and S. S. Moosapour, "Backstepping Terminal Sliding Mode Control Design for a TRMS," in 2021 7th International Conference on Control, Instrumentation and Automation (ICCIA), Tabriz, Iran, Feb. 2021, pp. 1–5.
M. Ilyas, N. Abbas, M. UbaidUllah, W. A. Imtiaz, M. A. Q. Shah, and K. Mahmood, "Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy," Discrete Dynamics in Nature and Society, vol. 2016, Jul. 2016, Art. no. 2952738.
M. Reyhanoglu, M. Jafari, and M. Rehan, "Simple Learning-Based Robust Trajectory Tracking Control of a 2-DOF Helicopter System," Electronics, vol. 11, no. 13, Jan. 2022, Art. no. 2075.
Z. Gao and G. Guo, "Fixed-time sliding mode formation control of AUVs based on a disturbance observer," IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 2, pp. 539–545, Mar. 2020.
X. You, C. Hua, K. Li, and X. Jia, "Fixed-Time Leader-Following Consensus for High-Order Time-Varying Nonlinear Multiagent Systems," IEEE Transactions on Automatic Control, vol. 65, no. 12, pp. 5510–5516, Sep. 2020.
J. Liu, Y. Yu, H. He, and C. Sun, "Team-Triggered Practical Fixed-Time Consensus of Double-Integrator Agents With Uncertain Disturbance," IEEE Transactions on Cybernetics, vol. 51, no. 6, pp. 3263–3272, Jun. 2021.
S. B. Fazeli Asl and S. S. Moosapour, "Adaptive backstepping fast terminal sliding mode controller design for ducted fan engine of thrust-vectored aircraft," Aerospace Science and Technology, vol. 71, pp. 521–529, Dec. 2017.
K. Behih and H. Attoui, “Backstepping Terminal Sliding Mode MPPT Controller for Photovoltaic Systems,” Engineering, Technology & Applied Science Research, vol. 11, no. 2, pp. 7060–7067, Apr. 2021.
R. Sangrody and S. M. Shariatmadar, “A Lyapunov Function for Vector Control Drives in Induction Machines,” Engineering, Technology & Applied Science Research, vol. 6, no. 5, pp. 1167–1174, Oct. 2016.
H. Abouri, F. E. Guezar, H. Bouzahir, S. E. Chehaidia, and A. N. Vargas, "Integral Backstepping Sliding Mode Control for Maximizing the Power Production of Wind Turbines," Engineering, Technology & Applied Science Research, vol. 14, no. 1, pp. 12950–12958, Feb. 2024.
A. A. Kolesnikov, Synergetics control theory. Moscow, Russia: Energoatomizdat, 1994.
A. A. Kolesnikov and A. S. Mushenko, "Applied Theory of Nonlinear System Design: Method Comparison," presented at the 2019 III International Conference on Control in Technical Systems (CTS), St. Petersburg, Russia, Oct. 2019.
A. A. Kolesnikov, "Introduction of synergetic control," in 2014 American Control Conference, Portland, OR, USA, Jun. 2014, pp. 3013–3016.
C. X. Nguyen, S. V. Tran, and H. N. Phan, "Control Law Synthesis for Flexible Joint Manipulator Based on Synergetic Control Theory," Mekhatronika, Avtomatizatsiya, Upravlenie, vol. 24, no. 8, pp. 395–402, 2023.
C. N. Xuan and L. T. Thang, "Design of nonlinear controller based on ADAR method for wedge balancing," in 2022 22nd International Conference on Control, Automation and Systems (ICCAS), Jeju, Korea (South), Nov. 2022, pp. 1372–1377.
L. T. Thang, T. V. Son, T. D. Khoa, and N. X. Chiem, "Synthesis of sliding mode control for flexible-joint manipulators based on serial invariant manifolds," Bulletin of Electrical Engineering and Informatics, vol. 12, no. 1, pp. 98–108, Feb. 2023.
Downloads
How to Cite
License
Copyright (c) 2024 Nguyen Xuan Chiem, Le Tran Thang
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement 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 acknowledgement 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) after its publication in ETASR with an acknowledgement of its initial publication in this journal.
