Combined structures-controls optimization of lattice trusses

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The purpose of this paper is to demonstrate concretely the role that distributed parameter models can play in CSI, in particular in combined structures-controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy laboratory model and a real space structure we have chosen the lattice truss used in the earth pointing satellite (EPS). The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bound on the rms attitude error (tip response), using a co-located controller and sensors. Standard FEM, treating each bar as a truss element is used, while the continuum model is an anisotropic Timoshenko beam model. Performance criteria are derived for either model, except that for the distributed parameter model we obtain explicit closed form solutions. Numerical results obtained by the two models show complete agreement. Based on the continuum model we obtain a solution to the problem of optimal placement of actuators to minimize mean square attitude error. A canonical optimization problem is examined and shown to be trivial, and even capable of analytical solution, using the continuum model performance criteria formulas in contrast to the complex computer solutions based on FEM or truncated modal models currently in vogue.