Simultaneous Optimum Design of Structural and Control Systems. Representation by Descriptor Forms and Use of LMI.

Abstract

A simultaneous optimum design problem of structural and control systems is discussed taking a 3-dimensional truss structure as an object. We use descriptor forms for a controlled object and a generalized plant because the structural parameters appear naturally in these forms. We consider minimum weight design problem for structural system and suppression problem of the effect of disturbances for control system as the purpose of the design. The structural objective function is the structural weight and the control objective function is H∞ norm from the disturbance input to the controlled output in the closed-loop system. The design variables are cross sectional areas of the truss members. The conditions for the existence of controller are expressed in terms of linear matrix inequalities (LMI). By minimizing the linear sum of the normalized structural objective function and control objective function, it is possible to make optimum design by which the balance of structural weight and control performance is taken. We consider in this paper the validity of simultaneous optimum design of structural and control systems.