Abstract
Attitude control of rigidflexible multibody systems by active stabilizers is studied in this paper. During slewing maneuvers, flexible members like solar panels may be excited to vibrate. These vibrations, in turn, produce oscillatory disturbing forces on other subsystems and consequently produce error in the spacecraft motion. Also, to develop a proper modelbased controller for such complicated system, the system dynamic model is derived. However, due to practical limitations and realtime control implementation, the system dynamic model should be structured such that low computations burden will be imposed on the modelbased controller. In this paper, in contrast to many accumulating dynamic modeling approach, a precise compact dynamic model for an active stabilized spacecraft (ASS) system with flexible members is derived. Toward this goal, the total system is virtually partitioned into two rigid and flexible portions. Moreover, the obtained model of these complicated systems is vigorously verified using ANSYS and ADAMS programs. Finally, based on the derived dynamics and a proper virtual damping parameter, an attitude control algorithm is then developed. The suggested controller structure takes the advantage of utilizing the piezoelectric smart materials to dissipate the vibration of solar panels. The obtained results reveal the merits and effectiveness of the proposed suggested modeling and control methods for reliable attitude maneuvering of the system. In addition, it will be shown that the undesired vibrations of the flexible solar panels result in disturbing forces on the ASS system which can be significantly eliminated by the proposed attitude control algorithm.
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Abbreviations
 \(\mathbf{B}_\mathrm{f}\) :

Virtual damping matrix of flexible member
 \(\mathbf{C}\) :

Vector of quadratic nonlinear terms of velocity
 \(\mathbf{H}\) :

Positive definition mass matrix of system
 \(\mathbf{J}_\mathrm{c} \) :

Jacobian matrix for the spacecraft
 \(\mathbf{J}_\mathrm{f} \) :

Jacobian matrix of the floating frame of each flexible body
 \(\mathbf{K}\) :

Stiffness matrix of flexible member
 \({\tilde{\mathbf{K}}}_\mathrm{p} ,{\tilde{\mathbf{K}}}_\mathrm{d} \) :

Gain matrix of controller for system in task space
 \(\mathbf{K}_{\mathrm{PZ}} \) :

Capacitances of the piezoelectric patches
 \(\mathbf{M}_\mathrm{f} \) :

Positive definition mass matrix of flexible member
 \({n}_\mathrm{b} \) :

Number of flexible members
 \(\mathbf{q}\) :

Entity vector of generalized coordinate of rigid system
 \({\bar{\mathbf{q}}}\) :

Entity vector of generalized coordinate of flexible body
 \({\bar{\mathbf{q}}}_\mathrm{f} \) :

Vector of elastic generalized coordinate of flexible body
 \({\bar{\mathbf{q}}}_\mathrm{r} \) :

Vector of reference or rigid generalized coordinate of flexible body
 \(\mathbf{Q}\) :

Vector of generalized forces
 \(\mathbf{Q}_\mathrm{e} \) :

Vector of generalized external forces of the flexible members
 \(\mathbf{Q}_{\mathrm{flex.}} \) :

Vector of generalized forces due to stimulation of the flexible members
 \({\tilde{\mathbf{Q}}}_\mathrm{m}\) :

Vector of control forces for endeffector motion
 \({\tilde{\mathbf{Q}}}_{\mathrm{supp.}}\) :

Vector of suppression forces in task space to control flexible member
 \(\mathbf{Q}_\mathrm{v}\) :

Quadratic velocity vector of flexible member
 \(\mathbf{v}_\mathrm{a} \) :

Vectors of the voltages at each flexible member actuators
 \(\left\{ \mathrm{i} \right\} \) :

Counter of flexible member
 \(\mathrm{f}\) :

Showing flexibility for a part of the system
 \(\mathrm{r}\) :

Showing rigidity for a part of the system
 \(\mathrm{0}\) :

Index of the spacecraft bus
References
 1.
Moosavian, S., Ali, A., Papadopoulos, E.: Freeflying robots in space: an overview of dynamics modeling. Plan. Control Robot. 25, 537–547 (2007)
 2.
Dwivedy, S.K., Eberhard, P.: Dynamic analysis of flexible manipulators, a literature review. J. Mech. Mach. Theory 41, 749–777 (2006)
 3.
Huang, T.C.: Stability and control of flexible satellitesII: control. Acta Astronaut. 9(12), 691–695 (1982)
 4.
Zarafshan, P., Moosavian, S., Ali, A.: Dynamics modeling and hybrid suppression control of space robots performing cooperative object manipulation. J. Commun. Nonlinear Sci. Numer. Simul. 18(10), 2807–2824 (2013)
 5.
Azadi, M., Fazelzadeh, S.A., Eghtesad, M., Azadi, E.: Vibration suppression and adaptiverobust control of a smart flexible satellite with three axes manoeuvrings. Acta Astronaut. 69, 307–322 (2011)
 6.
Budynasi, R., Polii, C.: Threedimensional motion of a large flexible satellite. Automatica 8, 275–286 (1972)
 7.
Wang, W., Menon, P.P., Bates, D.G., Bennani, S.: Robustness analysis of attitude and orbit control systems for flexible satellites. J. IET Control Theory Appl. 4(12), 2958–2970 (2010)
 8.
Simeon, B.: On Lagrange multipliers in flexible multibody dynamics. J. Comput. Methods Appl. Mech. Eng. 19(5), 6993–7005 (2006)
 9.
Yingying, L., Jun, Zh.: Fuzzy attitude control for flexible satellite during orbit maneuver. In: Proceedings of the IEEE International Conference on Mechatronics and Automation, China (2009)
 10.
Yingying, L., Lun, Zh. Dynamics model and simulation for flexible satellite with orbit control force. In: Proceedings of the IEEE International Conference on Mechatronics and Automation, China, pp. 227–230 (2010)
 11.
Wasfy, T.M., Noor, A.K.: Computational strategies for flexible multibody systems. J. Appl. Mech. 56(6), 553–613 (2003)
 12.
Ebrahimi, A., Moosavian, S., Ali, A., Mirshams, M.: Comparison between minimum and nearminimum time optimal control of a flexible slewing spacecraft. J. Aerosp. Sci. Technol. 3(3), 135–142 (2006)
 13.
Suleman, A.: Multibody dynamics and nonlinear control of flexible space structures. J. Vib. Control 10(11), 1639–1661 (2004)
 14.
Shao, Z., Tang, X., Wang, L., Chen, X.: Dynamic modeling and wind vibration control of the feed support system in FAST. J. Nonlinear Dyn. 67(2), 965–985 (2011)
 15.
Zarafshan, P., Moosavian, S., Ali, A.: Rigidflexible interactive dynamics modeling approach. J. Math. Comput. Model. Dyn. Syst. 18(2), 1–25 (2011)
 16.
Ge, X., Liu, Y.: The attitude stability of a spacecraft with two flexible solar arrays in the gravitational field. J. Chaos Solitons Fractals 37, 108–112 (2008)
 17.
Pratiher, B., Dwivedy, S.K.: Nonlinear dynamics of a flexible single link cartesian manipulator. Int. J. Non Linear Mech. 42, 1062–1073 (2007)
 18.
Ambrosio, J.A.C.: Dynamics of structures undergoing gross motion and nonlinear deformations: a multibody approach. J. Comput. Struct. 59(6), 1001–1012 (1996)
 19.
Schmitke, C., McPhee, J.: Using linear graph theory and the principle of orthogonality to model multibody, multidomain systems. J. Adv. Eng. Inf. 22(2), 147–160 (2008)
 20.
Sadigh, M.J., Misra, A.K.: Stabilizing tethered satellite systems using space manipulators. In: IEEE International Conference on Intelligent Robots and Systems, pp. 1546–1553 (1994)
 21.
Guana, P., Xi, Liub, Ji, Liub: Adaptive fuzzy sliding mode control for flexible satellite. J. Eng. Appl. Artif. Intell. 18, 451–459 (2005)
 22.
VuQuoc, L., Simo, J.C.: Dynamics of earthorbiting flexible satellites with multibody components. J. Guid. 10(6), 549–588 (1987)
 23.
Williams, P.: Deployment retrieval optimization for flexible tethered satellite systems. J. Nonlinear Dyn. 52, 159–179 (2008)
 24.
Chtiba, M.O., Choura, S., ElBorgi, S., Nayfeh, Ali H.: Confinement of vibrations in flexible structures using supplementary absorbers: dynamic optimization. J. Vib. Control 16(3), 357–376 (2010)
 25.
Yoshida, K., Nenchev, D.N., Vichitkulsawat, P., Kobayashi, H., Uchiyama, M.: Experiments on the pointtopoint operations of a flexible structure mounted manipulator system. J. Adv. Robot. 11(4), 397–411 (1996)
 26.
Yuan, J., Yang, D., and Wei, H.: Flexible satellite attitude manoeuvre control using pulsewidth pulsefrequency modulated input shaper. In: International Conference on Wireless Networks and Information Systems, pp. 1407–1412 (2009)
 27.
Shang, Y., Bouffanais, R.: Influence of the number of topologically interacting neighbors on swarm dynamics. Sci. Rep. 4, 4184 (2014)
 28.
Shang, Y., Bouffanais, R.: Consensus reaching in swarms ruled by a hybrid metrictopological distance. Eur. Phys. J. B 87(12), 1–7 (2014)
 29.
Moosavian, S., Ali, A., Papadopoulos, E.: Explicit dynamics of space freeflyers with multiple manipulators via SPACEMAPL. J. Adv. Robot. 18(2), 223–244 (2004)
 30.
Nanos, K., Papadopoulos, E.: On the dynamics and control of flexible joint space manipulators. Control Eng. Pract. 45, 230–243 (2015)
 31.
Shabana, A.A.: Dynamics of Multibody Systems, 3rd edn. Cambridge University Press, Cambridge (2005)
 32.
Piefort, V.: Finite Element Modeling of Piezoelectric Active Structures. PhD Thesis, Faculty of Applied Sciences, University of Libre De Bruxelles (2001)
 33.
Aglietti, G.S., Langley, R.S., Gabriel, S.B., Rogers, E.: A modeling technique for active control design studies with application to spacecraft microvibrations. J. Acoust. Soc. Am. 102(4), 2158–2166 (1997)
 34.
Katti, V.R., Thyagarajan, K., Shankara, K.N., Kiran Kumar, A.S.: Spacecraft technology. Curr. Sci. 93(12), 1715–1736 (2007)
 35.
Brennan, M.J., Bonito, J.G., Elliott, S.J., David, A., Pinnington, R.J.: Experimental investigation of different actuator technologies for active vibration control. J. Smart Mater. Struct. 8, 145–153 (1999)
Acknowledgments
The authors would like to thank the financial support provided by Islamic Azad University, Qazvin branch for accomplishing this research.
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Alipour, K., Zarafshan, P. & Ebrahimi, A. Dynamics modeling and attitude control of a flexible space system with active stabilizers. Nonlinear Dyn 84, 2535–2545 (2016). https://doi.org/10.1007/s110710162663y
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Keywords
 Rigidflexible multibody systems
 Reaction wheel
 Piezoelectric patch
 Attitude control