Robustness characteristics of optimum structural/control design

Abstract

An optimization program has been developed to design a minimum-weight flexible structure with constraints imposed on the closed-loop damping parameters, eigenvalue distribution, and the robustness bounds of the control system to retain stability under structured uncertainties. The formulation of approximate analytical expressions for the derivatives of the robustness measure is presented. The optimization problem was solved by using a nonlinear mathematical optimization technique. The numerical results are presented for the Draper 1 tetrahedral truss structure to satisfy different design requirements. These results indicate that the constraints on the damping parameters have to be imposed in addition to the robustness measure in order to improve the dynamic response. HE traditional approach to the design of a structure and control system has been sequential. The structure is first designed to satisfy the constraints on the allowable stresses, displacements, frequencies, etc., and then the control system is designed on this fixed structure. The control design has to satisfy its design requirements such as performance, control effort, robustness, stability, etc. This sequential approach generally does not lead to an optimum performance of the structure and control system for a specific mission. The opti- mum structural design and optimum control design have de- veloped into mature fields. However, because of the stringent requirements in the design of future aerospace structures, there is currently considerable interest in developing al- gorithms for the simultaneous design of the structure and control system. The mathematical model representing a physical system in- evitably contains inaccuracies. This would compromise the performance of the control system, making the system un- stable if one does not allow for these modeling errors. The modeling uncertainties are generally divided into two broad categories. The first is the parametric or structured uncertain- ties that result due to the variations in the real and analytical frequencies of the structure. The second is due to the unmod- eled higher frequencies. The robust-control system is designed to maintain closed-loop stability and performance in the pres- ence of unknown or known structured and unstructured un- certainties. The order of the finite element model of a space structure is generally too high and this necessitates the use of a reduced-order model constructed by truncating the higher vibration modes to design a controller. This reduction in the dimensionality of the controller sometimes leads to the spill- over effect when it is used on a higher order structural model. There have been various approaches proposed by different investigators in order to reduce or prevent the spillover effect. The objective of this paper was to develop an optimization algorithm to design a structure and control system by taking into consideration a robustness parameter that defines the structural uncertainties in a closed-loop system. The linear quadratic regulator (LQR) with a full-order controller is used