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Optimal control of rigid body motion with the help of rotors using stereographic coordinates

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  • El-Gohary, Awad

Abstract

This paper considers the problem of optimal controlling the rotational motion of a rigid body using three independent control torques developed by three rotors attached with the principal axes of inertia of the body and rotate with the help of electric motors rigidly mounted on the body. The optimal control law is given as non-linear function of new parameterizations of the rotation group derived by using the stereographic projection of the Euler parameters. Given a cost function we seek for a stabilizing feedback control law that minimizes this cost and asymptotically stabilizes the rotational motion of the body. The stabilizing properties of the proposed controllers are proved by using the optimal Liapunov function. Numerical examples and simulation study are presented.

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  • El-Gohary, Awad, 2005. "Optimal control of rigid body motion with the help of rotors using stereographic coordinates," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1229-1244.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1229-1244
    DOI: 10.1016/j.chaos.2004.11.072
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    1. El-Gohary, Awad, 2005. "Optimal stabilization of an equilibrium position of a rigid body using rotors system with friction forces," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1585-1597.
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    Cited by:

    1. Ge, Zheng-Ming & Yang, Cheng-Hsiung, 2009. "Chaos synchronization and chaotization of complex chaotic systems in series form by optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 994-1002.
    2. Wang, Zheng & Chau, K.T., 2008. "Anti-control of chaos of a permanent magnet DC motor system for vibratory compactors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 694-708.

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