Robust Stabilization and Active Vibration Control of a Rigid-Flexible Multibody System Using Time-Varying Sliding Mode Algorithm

Document Type : Dynamics, Vibrations, and Control

Author

Assistant Professor, Department of Astronautic, Aerospace Research Institute (Ministry of Science, Research and Technology), Tehran, Iran

Abstract

This paper proposes robust hybrid sliding mode control with a time-varying sliding surface and active vibration control for a flexible spacecraft during attitude maneuver. The fully coupled nonlinear dynamic model of the rigid-flexible system includes the three-axis rotation of the rigid body in interaction with the transverse deformation of the smart PZT-mounted flexible appendages. The smooth control signal includes a hyperbolic tangent and a sharpness function to reduce the effects of chattering and high-frequency interactions of the flexible parts and external disturbances in interaction with the rigid body and controller. The structure of the variable sliding surface with time has made it possible to adjust the effect of attitude parameters (quaternions and angular velocities) on the control performance. Also, the residual vibrations during and after the reaching phase are suppressed using a robust active vibration control algorithm. The simulations in the form of a comparative study show the performance and superiority of the proposed approach compared to conventional sliding mode control approaches for systems with structural flexibility in the presence of external perturbations and uncertainties.

Keywords

Smiley face

References

 [1] Zhong C, Chen Z and Guo Y. Attitude control for flexible spacecraft with disturbance rejection. IEEE Transactions on Aerospace and Electronic Systems. 2017;53(1): 101-110.##
[2] Wei J, Cao D, Wang L, Huang H and Huang W. Dynamic modeling and simulation for flexible spacecraft with flexible jointed solar panels. International Journal of Mechanical Sciences. 2017;130: 558-570.##
[3] Azimi M, Shahravi M and Fard KM. Modeling and vibration suppression of flexible spacecraft using higher-order sandwich panel theory. International Journal of Acoustics and Vibration. 2017;22(2): 143-151.##
[4] Angeletti F, Gasbarri P, Sabatini M and Iannelli P. Design and performance assessment of a distributed vibration suppression system of a large flexible antenna during attitude manoeuvres. Acta Astronautica. 2020;176: 542-557.##
[5] Guo J, Geng Y, Wu B and Kong X. Vibration suppression of flexible spacecraft during attitude maneuver using CMGs. Aerospace Science and Technology. 2018;72: 183-192.##
[6] Ding S and Zheng WX. Nonsmooth attitude stabilization of a flexible spacecraft. IEEE Transactions on Aerospace and Electronic Systems. 2014;50(2): 1163-1181.##
[7] Sendi C and Ayoubi MA. Robust fuzzy tracking control of flexible spacecraft via a T–S fuzzy model. IEEE Transactions on Aerospace and Electronic Systems. 2017;54(1): 170-179.##
[8] Firuzi S and Gong S. Attitude control of a flexible solar sail in low Earth orbit. Journal of Guidance, Control, and Dynamics. 2018;41(8): 1715-1730.##
[9] Xiao Y, Ye D and Sun Z. Observer-based continuous finite-time attitude control for rigid–flexible coupling satellites. International Journal of Control. 2019;92(11): 2667-2680.##
[10] Shahravi M and Azimi M. A hybrid scheme of synthesized sliding mode/strain rate feedback control design for flexible spacecraft attitude maneuver using time scale decomposition. International Journal of structural Stability and dynamics. 2016;16(02): 1450101.##
[11] Miao Y, Wang F and Liu M. Anti-disturbance backstepping attitude control for rigid-flexible coupling spacecraft. IEEE Access. 2018;6: 50729-50736.##
[12] Chegini M, Sadati H and Salarieh H. Chaos analysis in attitude dynamics of a flexible satellite. Nonlinear Dynamics. 2018;93(3): 1421-1438.##
[13] Sahnehsaraei MA and Mahmoodabadi MJ. Approximate feedback linearization based optimal robust control for an inverted pendulum system with time-varying uncertainties. International Journal of Dynamics and Control. 2021;9(1): 160-172.##
[14] Burkan R and Mutlu A. Robust control of robot manipulators with an adaptive fuzzy unmodelled parameter estimation law. Robotica. 2022;40(7): 2365-2380.##
[15] Wu A-G, Dong R-Q, Zhang Y and He L. Adaptive sliding mode control laws for attitude stabilization of flexible spacecraft with inertia uncertainty. IEEE Access. 2018;7: 7159-7175.##
[16] Li Y, Ye D and Sun Z. Time efficient sliding mode controller based on Bang–Bang logic for satellite attitude control. Aerospace science and technology. 2018;75: 342-352.##
[17] Azimi M, Shahbahrami V and Alikhani A. Vibration Suppression of a Rotating Flexible Structure using Super Twisting-Nonsingular Terminal Sliding Mode Control with Uncertainty. Aerospace Mechanics Journal. 2022;18(1): 95-107.##
[18] Jia S and Shan J. Continuous integral sliding mode control for space manipulator with actuator uncertainties. Aerospace Science and Technology. 2020;106: 106192.##
[19] Qing L, Lei L, Yifan D, Shuo T and Yanbin Z. Twistor-based synchronous sliding mode control of spacecraft attitude and position. Chinese Journal of Aeronautics. 2018;31(5): 1153-1164.##
[20] Ahmed S, Wang H and Tian Y. Adaptive fractional high‐order terminal sliding mode control for nonlinear robotic manipulator under alternating loads. Asian Journal of Control. 2021;23(4): 1900-1910.##
[21] Sun H, Zhang S, Quan Q, Liu Z, Wang G, and Lian W. Trajectory Tracking Robust Control Method Based on Finite-Time Convergence of Manipulator with Nonsingular Fast Terminal Sliding Mode Surface. Journal of Control Science and Engineering. 2022;2022.##
[22] Qiao J, Li Z, Xu J and Yu X. Composite nonsingular terminal sliding mode attitude controller for spacecraft with actuator dynamics under matched and mismatched disturbances. IEEE Transactions on Industrial Informatics. 2019;16(2): 1153-1162.##
[23] Alipour M, Malekzadeh M and Ariaei A. Practical fractional-order nonsingular terminal sliding mode control of spacecraft. ISA transactions. 2021.##
[24] Yu X and Zhihong M. Fast terminal sliding-mode control design for nonlinear dynamical systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 2002;49(2): 261-264.##
[25] Feng Y, Yu X and Man Z. Non-singular terminal sliding mode control of rigid manipulators. Automatica. 2002;38(12): 2159-2167.##
[26] Ye D and Sun Z. Variable structure tracking control for flexible spacecraft. Aircraft Engineering and Aerospace Technology: An International Journal. 2016.##
[27] Liu C, Sun Z, Ye D and Shi K. Robust adaptive variable structure tracking control for spacecraft chaotic attitude motion. IEEE Access. 2018;6: 3851-3857.##
[28] Lee D, Vukovich G and Gui H. Adaptive variable-structure finite-time mode control for spacecraft proximity operations with actuator saturation. Advances in Space Research. 2017;59(10): 2473-2487.##
[29] Khalil HK, Nonlinear systems. 2002, Patience Hall. p. 469-499.##
[30] Lossouarn B, Aucejo M, Deü J-F and Cunefare KA. Design of a passive electrical analogue for piezoelectric damping of a plate. Journal of Intelligent Material Systems and Structures. 2018;29(7): 1301-1314.##
[31] Jeon J-Y. Passive vibration damping enhancement of piezoelectric shunt damping system using optimization approach. Journal of Mechanical Science and Technology. 2009;23(5): 1435-1445.##
[32] Xie C, Wu Y and Liu Z. Modeling and active vibration control of lattice grid beam with piezoelectric fiber composite using fractional order PDμ algorithm. Composite Structures. 2018;198: 126-134.##
[33] Tian J, Guo Q and Shi G. Laminated piezoelectric beam element for dynamic analysis of piezolaminated smart beams and GA-based LQR active vibration control. Composite Structures. 2020;252: 112480.##
[34] Shivashankar P and Gopalakrishnan S. Review on the use of piezoelectric materials for active vibration, noise, and flow control. Smart Materials and Structures. 2020;29(5): 053001.##
[35] Zhang S, Schmidt R and Qin X. Active vibration control of piezoelectric bonded smart structures using PID algorithm. Chinese Journal of Aeronautics. 2015;28(1): 305-313.##
[36] Vasques C and Rodrigues JD. Active vibration control of smart piezoelectric beams: comparison of classical and optimal feedback control strategies. Computers & structures. 2006;84(22-23): 1402-1414.##
[37] Stavroulakis GE, Foutsitzi G, Hadjigeorgiou E, Marinova D and Baniotopoulos C. Design and robust optimal control of smart beams with application on vibrations suppression. Advances in Engineering Software. 2005;36(11-12): 806-813.##
[38] Raju V, Maheswari D and Patnaik S. Active vibration control of piezo actuated cantilever beam using PSO. in 2012 IEEE Students' Conference on Electrical, Electronics and Computer Science. 2012. IEEE.##
[39] Qiu Z-c and Wang T-x. Fuzzy neural network vibration control on a piezoelectric flexible hinged plate using stereo vision detection. Journal of Intelligent Material Systems and Structures. 2019;30(4): 556-575.##
[40] Abdeljaber O, Avci O and Inman DJ. Active vibration control of flexible cantilever plates using piezoelectric materials and artificial neural networks. Journal of sound and Vibration. 2016;363: 33-53.##
[41] Li L, Song G and Ou J. Nonlinear structural vibration suppression using dynamic neural network observer and adaptive fuzzy sliding mode control. Journal of Vibration and Control. 2010;16(10): 1503-1526.##
[42] Meirovitch L. Hybrid state equations of motion for flexible bodies in terms of quasi-coordinates. Journal of Guidance, Control, and Dynamics. 1991;14(5): 1008-1013.##
[43] Hu Q, Shao X and Guo L. Adaptive fault-tolerant attitude tracking control of spacecraft with prescribed performance. IEEE/ASME Transactions on Mechatronics. 2017;23(1): 331-341.##
[44] Chen M, Ge SS and Ren B. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints. Automatica. 2011;47(3): 452-465.##
[45] Krstic M, Kokotovic PV and Kanellakopoulos I, Nonlinear and adaptive control design. 1995: John Wiley & Sons, Inc.##
[46] Song G, Schmidt SP and Agrawal BN. Experimental study of active vibration suppression of flexible structure using modular control patch. in 1998 IEEE Aerospace Conference Proceedings (Cat. No. 98TH8339). 1998. IEEE.##
Aerospace Mechanics
Volume 18, Issue 4 - Serial Number 70
Serial No. 70, Winter Quarterly
December 2022
Pages 49-63

Files

History

  • Receive Date: 03 July 2022
  • Revise Date: 28 July 2022
  • Accept Date: 14 August 2022
  • Publish Date: 22 December 2022

Share

How to cite

Statistics