Improved control design variable linking for optimization of structural/control systems

A method is presented to integrate the design space for structural/control system optimization problems in the case of linear state feedback control. To make the truly simultaneous optimization of structural/control systems tractable, without increasing the number of control design variables, the conventional structural design variable linking idea is extended to the control system feedback gain matrix. In this paper a new control design variable linking scheme based on representing the feedback gain matrix as the linear combination of component matrices corresponding to different modes is introduced. The original nonlinear mathematical programming problem based on a finite element formulation and linear state feedback is replaced by a sequence of explicit approximate problems exploiting various approximation concepts such as structural and control design variable linkings, temporary constraint deletion, and first-order Taylor series expansion of nonlinear behavior constraints in terms of intermediate design variables. Examples that involve a variety of dynamic behavior constraints (including constraints on closed-loop eigenvalues, peak transient displacements, and peak actuator forces) are effectively solved by using the improved control design variable linking scheme presented.