Optimum structural design and robust active control using singular value constraints

Abstract

This paper introduces a methodology for simultaneously designing a minimum weight structure and robust active controls to reduce vibrations in an aircraft structure due to external disturbances. The design problem is posed as a mathematical optimization problem with the principal objective function being the weight of the structure. The robust control design is achieved by specifying appropriate constraints on singular values of the closed-loop transfer matrices. The control approach selected for this purpose is based on designing a dynamic compensator that simultaneously minimizes the upper bound of a quadratic performance index H ₂ and the H _∞ norm of a disturbance transfer function of a multi-input/multi-output system. The controller can tolerate both real parameter uncertainty in the structural frequencies and damping, and unmodelled dynamics. The design variables are the crosspsectional areas of the structure and the parameters used in the design of a control system. The method was applied to three structures idealized with membrane elements, shear panels and bar elements with embedded actuators and sensors simulating an active flexible aircraft wing.