large number of elements and nodes thus becoming uneconomical, especially at this initial design phase when the structure and its associated systems are subject to modifications. Techniques presently used to study space lattice structures fall into three categories: (i) matrix methods, (ii) field techniques, and (iii) continuum modelling. The first consists of numerically solving a set of algebraic equations in a direct manner. The other two are analytical approaches. Numerical methods such as the finite element and finite difference procedures, use the matrix approach based on discrete element idealization. Field techniques attempt to describe lattice structures or a pattern of elements analytically. The popularity of this approach is due to the fact that the elemental nature of the lattice bay is preserved in the governing equilibrium equations. In comparison with the numerical methods, a field analysis does not increase the problem size as the number of bays in the truss structure is increased. The last method consists of approximating a repetitive lattice by an equivalent continuum. This ensures that the continuum model exhibits equivalent energy levels as the actual discrete lattice. Here qualitative decisions reduce the dimensionality of the mathematical model and physically identify the nature of the deformation (e.g. warping, bending, shear). Furthermore, as the number of repeating modules is increased, the accuracy of the response improves although the model size does not increase. This energy equivalence concept has been demostrated in a variety of investigations. For instance, continuous systems involving particular types of beam and plate type lattice structures have been developed by Berry et al., and Juang and Sun. Their studies suggest the necessity to model large truss structures by the geometrically nonlinear Timoshenko beams. While shear and rotary inertia lead to small corrections to the Bernoulli-Euler theory for the lower modes of long and thin beams, significant errors may be introduced if they are neglected when dealing with thicker beams, or for the higher modes of any beam. 9.2.2 Control The subject of attitude and vibration control in Large Space Structures (LSS) has received considerable attention and has evolved quite rapidly in the last thirty years. Balas and Meirovitch have presented an excellent overview of approaches to the control of LSS. Unlike the rigid Spacecraft design, LSS control is an interdisciplinary subject drawing on structural mechanics, continuum representation, optimization and identification. Issues in modelling and control design include control/structure interactions, actuator and sensor selection and placement, controllability and observability, control and observation spillover, sensitivity and robustness, modelling uncertainties and errors, to name a few. The primary requirement of the flight control system is to maintain the LSS attitude within 5 degrees with reference to the orbital frame. Control Momentum Gyros (CMGs) will be utilized as the primary actuating devices for most of the assembly sequence due to their greater torque capability for given weight and power consumption, as opposed to momentum wheels. However, they have limited momentum storage capabilities before reaching saturation. Therefore, a scheme for desaturation of the CMGs will have to be developed to remove secular momentum build-up. Desaturation methods include the use of magnetic torquer bars, aerodynamic torques, fluid desaturation, reaction control systems, and gravity gradient torques. When suppressing structural vibration, the closely spaced modal frequencies, coupled with the uncertainties in structural modelling, place stringent robustness requirements on the control system. A frequently used approach to ensuring robustness is to colocate the sensors and actuators, resulting in an energy dissipating configuration. However, because of physical limitations on hardware placement, this approach is often not feasible, resulting in unstable control/structure interactions. We describe now several design techniques, from the most common (Classical and Optimal- Quadratic) to others that either improve the description of the system (Nonlinear Control) or emphasize uncertainty of the system (Robust Control) at the expense of more complicated formulation and more computational effort.
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