Shape of stiffest controlled structures under unknown loads

This paper discusses the optimal geometry for maximum stiffness of controll ed truss-type structures subjected to a class of unknown disturbances, unde r a constant volume constraint. The stiffness is defined by a quadratic fun ction of the worst distortion at the controlled degrees of freedom after ap plying optimal control. The disturbance is arbitrary but is limited by a qu adratic bound. Herein, the design variables are the spatial coordinates of a predetermined set of nodes. Based on earlier publications, it is indicate d that if the structure is controlled by N-c ideal actuators this min- max problem is equivalent to minimizing the Nc+1 th singular value of the distu rbance influence matrix. This implies that the first N-c singular modes are taken care of by the control system. Consequently the designed structures are often highly unstable without control. A methodology is presented to de sign sub-optimal structures which addresses this problem. In order to allev iate the effects of a possible failure of the control system, limits on the levels of the lower singular values are incorporated in the design process . Numerical examples illustrate the approach and indicate clearly the benef icial effect of this technique which increases the stiffness of the structu re while maintaining stability in the case of a breakdown of the control sy stem. (C) 2001 Published by Elsevier Science Ltd.