(2) Bui Xuan Hai (Le Quy Don Technical University, Viet Nam)
(3) T. C. Phan (Le Quy Don Technical University, Viet Nam)
*corresponding author
AbstractIn this paper, the authors present a new method to synthesize an adaptive sliding controller for Twin Rotor MIMO System (TRMS) based on Synergetic Control Theory (SCT). This system represents a prototype of a helicopter with two degrees of freedom and is widely used in automatic control laboratories. The complexity of the control problem is due to the nonlinear cross-coupling between the main and tail rotors. Uncertainty in system parameters further increases the complexity of the control problem. In Synergetic Control Theory, manifolds are designed for each channel. The control law is found based on sequential manifolds and the Analytical Design of Aggregated Regulators (ADAR) method. The adaptive law when the parameters are uncertain is given based on the analysis of system stability thanks to the Lyapunov function of the first manifold. Finally, the effectiveness of the proposed controller is demonstrated by numerical simulation results and comparison with conventional Sliding Mode Control (SMC).
KeywordsTRMS; MIMO; Invariant Manifold; Adaptive Control; SMC; ADAR
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DOIhttps://doi.org/10.31763/ijrcs.v4i1.1307 |
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References
[1] A. Boubakir, S. Labiod, F. Boudjema, and F. Plestan, “Design and experimentation of a self-tuning pid control applied to the 3DOF helicopter,” Archives of Control Sciences, vol. 23, no. 3, pp. 311–331, 2013, http://dx.doi.org/10.2478/acsc-2013-0019 .
[2] J. -G. Juang, M. -T. Huang and W. -K. Liu, “PID Control Using Presearched Genetic Algorithms for a MIMO System,” IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), vol. 38, no. 5, pp. 716-727, 2008, http://dx.doi.org/10.1109/TSMCC.2008.923890.
[3] S. K. Pandey, V. Laxmi, “Optimal control of twin rotor mimo system using LQR technique,” Computational Intelligence in Data Mining-Volume 1: Proceedings of the International Conference on CIDM, pp. 11–21, 2014, http://dx.doi.org/10.1007/978-81-322-2205-7_2.
[4] E. V. Kumar, G. S. Raaja, J. Jerome, “Adaptive PSO for optimal LQR tracking control of 2 DOF laboratory helicopter,” Applied Soft Computing, vol. 41, pp. 77–90, 2016, https://doi.org/10.1016/j.asoc.2015.12.023.
[5] I. Ben Abdelwahed, A. Mbarek and K. Bouzrara, “Model Predictive Control of 2-DOF Helicopter Based on MIMO ARX-Laguerre Model,” 2019 6th International Conference on Electrical and Electronics Engineering (ICEEE), pp. 317-322, 2019, https://doi.org/10.1109/ICEEE2019.2019.00068.
[6] D. K. Saroj, I. Kar and V. K. Pandey, “Sliding mode controller design for Twin Rotor MIMO system with a nonlinear state observer,” 2013 International Mutli-Conference on Automation, Computing, Communication, Control and Compressed Sensing (iMac4s), pp. 668-673, 2013, https://doi.org/10.1109/iMac4s.2013.6526493.
[7] A. K. Ekbote, N. S. Srinivasan, 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, 2011, https://doi.org/10.3182/20110828-6-IT-1002.00645.
[8] M. Ilyas, N. Abbas, M. UbaidUllah, W. A. Imtiaz, M. A. Q. Shah, K. Mahmood, “Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy,” Discrete Dynamics in Nature and Society, vol. 2016, 2016, https://doi.org/10.1155/2016/2952738.
[9] M. Derakhshannia, S. B. F. Asl and S. S. Moosapour, “Backstepping Terminal Sliding Mode Control Design for a TRMS,” 2021 7th International Conference on Control, Instrumentation and Automation (ICCIA), pp. 1-5, 2021, https://doi.org/10.1109/ICCIA52082.2021.9403545.
[10] A. Boulkroune, M. M’Saad, and H. Chekireb, “Design of a fuzzy adaptive controller for MIMO nonlinear time-delay systems with unknown actuator nonlinearities and unknown control direction,” Information Sciences, vol. 180, no. 24, pp. 5041–5059, 2010, https://doi.org/10.1016/j.ins.2010.08.034.
[11] B. Wu, J. Wu, J. Zhang, G. Tang, Z. Zhao, “Adaptive Neural Control of a 2DOF Helicopter with Input Saturation and Time-Varying Output Constraint,” Actuators, vol. 11, no. 11, p. 336, 2022, https://doi.org/10.3390/act11110336.
[12] E. A. Abioye et al., “A review on monitoring and advanced control strategies for precision irrigation,” Computers and Electronics in Agriculture, vol. 173, p. 105441, 2020, https://doi.org/10.1016/j.compag.2020.105441.
[13] R. Patel, D. Deb, H. Modi and S. Shah, “Adaptive backstepping control scheme with integral action for quanser 2-dof helicopter,” 2017 International Conference on Advances in Computing, Communications and Informatics (ICACCI), pp. 571-577, 2017, https://doi.org/10.1109/ICACCI.2017.8125901.
[14] S. M. Schlanbusch and J. Zhou, “Adaptive Backstepping Control of a 2-DOF Helicopter System with Uniform Quantized Inputs,” IECON 2020 The 46th Annual Conference of the IEEE Industrial Electronics Society, pp. 88-94, 2020, https://doi.org/10.1109/IECON43393.2020.9254497.
[15] S. Mondal, 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, 2012, https://doi.org/10.1049/iet-cta.2011.0478.
[16] A. A. Kolesnikov, “Introduction of synergetic control,” 2014 American Control Conference, pp. 3013-3016, 2014, https://doi.org/10.1109/ACC.2014.6859397.
[17] A. A. Kolesnikov, A. A. Kuz’menko, “Sliding Mode Control Laws Design by the ADAR Method with Subsequent Invariant Manifolds Aggregation,” Mekhatronika, Avtomatizatsiya, Upravlenie, vol. 20, no. 8, pp. 451-460, 2019, https://doi.org/10.17587/mau.20.451-460.
[18] A. A. Kolesnikov and A. S. Mushenko, “Applied Theory of Nonlinear System Design: Method Comparison,” 2019 III International Conference on Control in Technical Systems (CTS), pp. 50-53, 2019, https://doi.org/10.1109/CTS48763.2019.8973304.
[19] A. A. Kolesnikov and A. A. Kuz’menko, “Forced Sliding Mode Control: Synergetic Approach,” 2020 2nd International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency (SUMMA), pp. 36-40, 2020, https://doi.org/10.1109/SUMMA50634.2020.9280620.
[20] C. X. Nguyen, A. D. Lukianov, T. D. Pham, A. D. Nguyen, “Synthesis of a nonlinear control law with efficiency energy for the self-balancing two wheeled vehicle,” IOP Conference Series: Materials Science and Engineering, vol. 900, no. 1, p. 012002, 2020, https://doi.org/10.1088/1757-899X/900/1/012002.
[21] C. X. Nguyen, S. V. Tran, 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, https://doi.org/10.17587/mau.24.395-402.
[22] C. N. Xuan and L. T. Thang, “Design of nonlinear controller based on ADAR method for wedge balancing,” 2022 22nd International Conference on Control, Automation and Systems (ICCAS), pp. 1372-1377, 2022, https://doi.org/10.23919/ICCAS55662.2022.10003732.
[23] L. T. Thang, T. V. Son, T. D. Khoa, 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, 2023, https://doi.org/10.11591/eei.v12i1.4363.
[24] E. Obukhova, G. E. Veselov, P. Obukhov, A. Beskopylny, S. A. Stel’makh, E. M. Shcherban, “Synergetic Synthesis of Nonlinear Laws of Throttle Control of a Pneumatic Drive,” Applied Science, vol. 12, no. 4, p. 1797, 2022, https://doi.org/10.3390/app12041797.
[25] A. A. Kuz’menko, “Robust Control of Permanent Magnet Synchronous Motor: Synergetic Approach,” Mekhatronika, Avtomatizatsiya, Upravlenie, vol. 21, no. 8, pp. 480-488, 2020, https://doi.org/10.17587/mau.21.480-488.
[26] A. J. Humaidi, I. K. Ibraheem, A. T. Azar, M. E. Sadiq, “A New Adaptive Synergetic Control Design for Single Link Robot Arm Actuated by Pneumatic Muscles,” Entropy, vol. 22, no. 7, p. 723, 2020, https://doi.org/10.3390/e22070723.
[27] N. X. Chiem, L. T. Thang and N. C. Dinh, “Synthesis of stable control law for ball and beam system robust to disturbances based on synergetic control theory,” 2023 12th International Conference on Control, Automation and Information Sciences (ICCAIS), pp. 466-470, 2023, https://doi.org/10.1109/ICCAIS59597.2023.10382309.
[28] N. X. Chiem, P. X. Thuy, “Synthesis of control laws for magnetic levitation systems based on serial invariant manifolds,” IAES International Journal of Robotics and Automation (IJRA), vol. 11, no. 4, pp. 333-342, 2022, http://doi.org/10.11591/ijra.v11i4.pp333-342.
[29] K. I. Usmanov, N. S. Yakubova, V. T. Urmanova, G. E. Abdurasulova, “Synthesis of a control system for the process of diesel fuel hydropuring with the Adar method,” E3S Web of Conferences, vol. 458, p. 01025, 2023, https://doi.org/10.1051/e3sconf/202345801025.
[30] P. C. Tran, H. T. Nguyen, A. Q. Nguyen, T. T. Le, H. N. Phan, C. X. Nguyen, “Design control system for Pan-Tilt Camera for Visual Tracking based on ADAR method taking into account energy output,” E3S Web of Conferences, vol. 279, p. 02007, 2021, https://doi.org/10.1051/e3sconf/202127902007.
[31] M. S. Mahmoud, A. Alameer, M. M. Hamdan, “An Adaptive Sliding Mode Control for Single Machine Infinite Bus System under Unknown Uncertainties,” International Journal of Robotics and Control Systems, vol. 1, no. 3, pp. 226-243, 2021, https://doi.org/10.31763/ijrcs.v1i3.351.
[32] M. S. Mahmoud, A. H. AlRamadhan, “Optimizing the Parameters of Sliding Mode Controllers for Stepper Motor through Simulink Response Optimizer Application,” International Journal of Robotics and Control Systems, vol. 1, no. 2, pp. 209-225, 2021, https://doi.org/10.31763/ijrcs.v1i2.345.
[33] A. Ma’arif, M. A. M. Vera, M. S. Mahmoud, E. Umoh, A. J. Abougarair, S. N. Rahmadhia, “Sliding Mode Control Design for Magnetic Levitation System,” Journal of Robotics and Control (JRC), vol. 3, no. 6, pp. 848-853, 2022, https://doi.org/10.18196/jrc.v3i6.12389.
[34] A. Ma’arif, A. Çakan, “Simulation and Arduino Hardware Implementation of DC Motor Control Using Sliding Mode Controller,” Journal of Robotics and Control (JRC), vol. 2, no. 6, pp. 582-587, 2021, https://doi.org/10.18196/jrc.26140.
[35] E. Samsuria, Y. M. Sam, F. Hassan, “Enhanced Sliding Mode Control for a Nonlinear Active Suspension Full Car Model,” International Journal of Robotics and Control Systems, vol. 1, no. 4, pp. 501-522, 2021, https://doi.org/10.31763/ijrcs.v1i4.473.
[36] M. G. Ghogarea, A. R. Laware, S. L. Patil, C. Y. Patil, “Design and Analysis of Decentralized Dynamic Sliding Mode Controller for TITO Process,” International Journal of Robotics and Control Systems, vol. 2, no. 2, pp. 277-296, 2022, https://doi.org/10.31763/ijrcs.v2i2.648.
[37] Y. Zahraouia, M. Moutchoua, S. Tayanea, C. Fahassab, S. Elbadaoui, “Induction Motor Performance Improvement using SuperTwisting SMC and Twelve Sector DTC,” International Journal of Robotics and Control Systems, vol. 4, no. 1, pp. 50-68, 2024, https://doi.org/10.31763/ijrcs.v4i1.1090.
[38] A. T. Hafez, A. A. Sarhan and S. Givigi, “Brushless DC Motor Speed Control Based on Advanced Sliding Mode Control (SMC) Techniques,” 2019 IEEE International Systems Conference (SysCon), pp. 1-6, 2019, https://doi.org/10.1109/SYSCON.2019.8836754.
[39] N. A. Alawad, A. J. Humaidi, A. S. Alaraji, “Observer Sliding Mode Control Design for lower Exoskeleton system: Rehabilitation Case,” Journal of Robotics and Control (JRC), vol. 3, no. 4, pp. 476-482, 2022, https://doi.org/10.18196/jrc.v3i4.15239.
[40] F. Gopmandal, A. Ghosh, “LQR-based MIMO PID control of a 2-DOF helicopter system with uncertain cross-coupled gain,” IFAC PapersOnLine, vol. 55, no. 22, pp. 183-188, 2022, https://doi.org/10.1016/j.ifacol.2023.03.031.
[41] R. G. Subramanian, V. K. Elumalai, “Robust MRAC augmented baseline LQR for tracking control of 2 DoF helicopter,” Robotics and Autonomous Systems, vol. 86, pp. 70-77, 2016, https://doi.org/10.1016/j.robot.2016.08.004.
[42] B. M. Kim, 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, p. 1062, 2021, https://doi.org/10.3390/math9091062.
[43] M. Reyhanoglu, M. Jafari, M. Rehan, “Simple Learning-Based Robust Trajectory Tracking Control of a 2-DOF Helicopter System,” Electronics, vol. 11, no. 13, p. 2075, 2022, https://doi.org/10.3390/electronics11132075.
[44] S. I. Abdelmaksoud, M. Mailah and A. M. Abdallah, “Practical Real-Time Implementation of a Disturbance Rejection Control Scheme for a Twin-Rotor Helicopter System Using Intelligent Active Force Control,” IEEE Access, vol. 9, pp. 4886-4901, 2021, https://doi.org/10.1109/ACCESS.2020.3046728.
[45] R. C. Romana, R. E. Precupa, R. C. David, “Second Order Intelligent Proportional-Integral Fuzzy Control of Twin Rotor Aerodynamic Systems,” Procedia Computer Science, vol. 139, pp. 372–380, 2018, https://doi.org/10.1016/j.procs.2018.10.277.
[46] E. C. V. González, D. M. Rivera and E. J. Gómez, “Model and Observer-Based Controller Design for a Quanser Helicopter with Two DOF,” 2012 IEEE Ninth Electronics, Robotics and Automotive Mechanics Conference, pp. 267-271, 2012, https://doi.org/10.1109/CERMA.2012.50.
[47] G. G. Neto, F. dos Santos Barbosa and B. A. Angélico, “2-DOF helicopter controlling by pole-placements,” 2016 12th IEEE International Conference on Industry Applications (INDUSCON), pp. 1-5, 2016, https://doi.org/10.1109/INDUSCON.2016.7874535.
[48] P. Wen and Y. Li, “Twin rotor system modeling, de-coupling and optimal control,” 2011 IEEE International Conference on Mechatronics and Automation, pp. 1839-1842, 2011, https://doi.org/10.1109/ICMA.2011.5986259.
[49] A. Tastemirov, A. Lecchini-Visintini, R. M. Morales, “Complete dynamic model of a twin rotor MIMO System (TRMS) with experimental validation,” Control Engineering Practice, vol. 66, pp. 89-98, 2017, https://doi.org/10.1016/j.conengprac.2017.06.009.
[50] A. Rahideh, M. H. Shaheed, H. J. C. Huijberts, “Dynamic modelling of a TRMS using analytical and empirical approaches,” Control Engineering Practice, vol. 16, no. 3, pp. 241-259, 2008, https://doi.org/10.1016/j.conengprac.2007.04.008.
[51] S. M. Ahmad, A. J. Chipperfield, M. O. Tokhi, “Dynamic modelling and linear quadratic Gaussian control of a twin-rotor multi-input multi-output system,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 217, no. 3, pp. 203-227, 2003, https://doi.org/10.1177/095965180321700304.Refbacks
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