Simultaneous Optimum Design of Structural and Control Systems for Truss Structure.

Abstract

This paper proposes an optimum design problem of structural and control systems, taking a 2-D truss structure as an example. The structure is supposed to be subjected to initial static loads and disturbances. For the structure, FEM model is formed, and using modal transformation, the equation of motion is transformed into that of modal coordinate in order to decrease DOF of FEM model. The structure is controlled by an output feedback H∞ controller to suppress the effect of the disturbances. The design variables are the cross sectional areas of truss members. The structural objective function is the structural weight. As the control objective, we consider two types of performance indices. The first function is the H∞ norm, that is, the performance index for disturbance suppression. The second one is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been carried out. Through the consideration of structural weight and H∞ norm, an advantage of the simultaneous optimum design of structural and control systems is shown. More-over, while the performance index of control is almost kept, we can perform the design which is better also in structural strength.