OPTIMUM STRUCTURAL DESIGN AND ROBUST ACTIVE CONTROL USING SINGULAR-VALUE CONSTRAINTS

This paper introduces a methodology for simultaneously designing a min imum weight structure and robust active controls to reduce vibrations in an aircraft structure due to external disturbances. The design prob lem is posed as a mathematical optimization problem with the principal objective function being the weight of the structure. The robust cont rol design is achieved by specifying appropriate constraints on singul ar values of the closed-loop transfer matrices. The control approach s elected for this purpose is based on designing a dynamic compensator t hat simultaneously minimizes the upper bound of a quadratic performanc e index H-2 and the H-infinity norm of a disturbance transfer function of a multi-input/multi-output system. The controller can tolerate bot h real parameter uncertainty in the structural frequencies and damping , and unmodelled dynamics. The design variables are the cross-sectiona l areas of the structure and the parameters used in the design of a co ntrol system; The method was applied to three structures idealized wit h membrane elements, shear panels and bar elements with embedded actua tors and sensors simulating an active flexible aircraft wing.