Simultaneous Optimum Design of Structural and Control Systems. Application of Sliding Mode Control.

Abstract

In this paper, a method for simultaneous optimum design of a structure and its control system is proposed. A beam is considered as an example, which is subjected to initial loads and a time-varying disturbance. Sliding mode control method is chosen because it is insensitive to disturbance and uncertainty if a matching condition is met, after giving a switching hyperplane. In this paper, an optimization method is used to design the switching hyperplane. The objective function of the optimum switching hyperplane is adopted as the objective function of the simultaneous design. The total weight of the structure is treated as a constraint condition, and the cross sectional areas of beam are all adoped as the design variables. This problem is a nonlinear programming problem. In this paper, the sequential linear programming method is adopted to solve it. In the example, after the optimum design the effect of attenuating vibrations has been improved obviously. Moreover, light design of the structure becomes possible by using the relationship between the structural weight and control objective function.