Nonlinear dynamics and attitude control of articulated and flexible space structures

Myung-Jin Baek

doi:10.17918/00000462

The present study is concerned with the development of a unified approach to the modeling and the design of an effective feedback linearizing and stabilizing nonlinear controller for multibody flexible and articulated systems. Modeling and control system design for such systems is of current interest. The principal objectives are to investigate the attitude regulation of rigid and/or flexible articulated multibody structures and to demonstrate how interacting nonlinear behaviors of flexible and articulated systems affect the stability and robustness properties of the controlled system. A systematic method for the formulation of the equations of motion for the nonlinear dynamics of flexible and articulated systems is employed based on a unified serial chain body algorithm, and this algorithm is integrated into Poincare's form of Lagrange's equations to formulate an innovative new approach to modeling of the system. The closed form solution of partial feedback linearization is derived using simple mathematical techniques and PFL compensation is applied as a general approach for the attitude decoupling and stabilization of the system having perfect knowledge of model uncertainties. The performance of a linear stabilizer, constructed on the same decoupling principle of the PFL stabilizer, is compared to that of PFL stabilizer with respect to attitude decoupling and stabilization. In the presence of model uncertainties, parameter adaptive control method is combined with PFL to enhance stability and robustness properties. Throughout these analyses, it is shown that (1) the developed modeling procedure is an effective tool in constructing feedback linearizing control laws, (2) with the perfect knowledge of parametric uncertainties, PFL controller yields excellent performance with respect to attitude decoupling and stabilization, (3) the domain of attraction of the linear controller applied to nonlinear systems is critically small, and the boundary of stability is explained as a subcritical Hopf bifurcation, and (4) the equilibrium point of the closed-loop adaptive control system is asymptotically stable, but the domain of attraction of adaptive PFL is limited due to nonlinear effects between flexible and articulated bodies.

Nonlinear dynamics and attitude control of articulated and flexible space structures

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Nonlinear dynamics and attitude control of articulated and flexible space structures

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