Sensitivity analysis of smart structures Original Research Article

The simultaneous optimal design of adaptive structural systems has been formulated as a multi-objective programming problem with the structural variables and controller parameters as design variables. To construct a well-behaved algorithm for the solution of a problem of such complexity, accurate sensitivity information is essential. The purpose of this paper is to systematically evaluate the analytical expressions for the design gradients of the various objectives and constraints with respect to the continuous design variables. Kleinmanʹs Lemma and Bellmanʹs expansion are employed in the derivation, and as a result, the gradient of quadratic performance criterion with respect to the open-loop plant matrix is obtained. This result provides, along with previous results obtained by others, a complete sensitivity package for smart structural control and optimisation. With this sensitivity information, a truly simultaneous optimisation of a smart structure could be possible. Numerical results are presented as verification of the analytical derivations.