Robust Control of Nonlinear Multibody Flexible Space Structures

A generic nonlinear math model of a multibody flexible system is developed. Asymptotic stability of such systems using dissipative compensators is established. It is proved that, under certain conditions, this class of systems exhibit global asymptotic stability under dissipative compensation. The dissipative compensators considered are static as well as dynamic dissipative compensators. The stability proofs are based on passivity approaches, Lyapunov methods, as well as a key property of such systems, i.e., skew-symmetricity of certain matrix. The importance of the stability results obtained is that the stability is robust to parametric uncertainties and modeling errors. For static dissipative compensators, it is shown that stability is not only robust to parametric uncertainties and modeling errors but also to certain actuator and sensor nonlinearities. Actuator nonlinearities considered are (0, ∞) sector monotonically non-decreasing type, which include realistic nonlinearities such as the saturation nonlinearity. In the presence of dead-zone and hysteresis type nonlinearities, system trajectories do not approach equilibrium point asymptotically, however, it is shown that there is a compact region of ultimate boundedness and system trajectories do not go unbounded. The sensor nonlinearities considered are (0,$\infty$) sector nonlinearities. A more versatile class of dissipative compensators, called dynamic dissipative compensators, is next considered. A control designer has more design freedom with dynamic dissipative compensators than with the static dissipative type. The increased design degrees of freedom can be used to enhance the performance of the control system. The synthesis techniques for static as well as dynamic dissipative compensators for multibody, nonlinear, flexible systems are currently unknown and it is a topic of future research. The asymptotic stability property of a static dissipative controller for multibody, nonlinear, flexible space structures is demonstrated through a simulation example. The example system used consists of a flexible 10-bay truss structure with a flexible, 2-link manipulator arm attached at one end of the truss. This example system is representative of the class of spacecraft envisioned for the future missions. For dynamic dissipative compensators an application example is shown for a multibody planar system with an articulated member. The controller design is based on locally linearized models in the configuration space of the articulated member. This example also demonstrates the use of dissipative compensators in the integrated design framework