Optimal selection of weighting matrices in integrated design of structures/controls

A methodology is developed for the optimal selection of state and input weighting matrices, Q and R, respectively, of the linear quadratic regulator (LQR) method in the integrated design of structures/controls. An optimal control problem is set up in such a way that design variables are the diagonal entries of Q and R; the objective function is the trace of the solution matrix to the algebraic Riccati equation of the LQR method, P matrix; and constraints are imposed on the closed-loop eigenvalues to satisfy minimum stability conditions for the control system. The procedure finds the optimal diagonal Q and R that enables the actively controlled system to meet the prespecified stability and performance bounds. Furthermore, the resulting Q and R yield the minimum possible performance index and hence the control effort is substantially reduced. The proposed method is integrated with a substructure decomposition scheme which results in substantial savings on the numerical computations with very little loss in the accuracy of original system response. It is found that for trusslike space structures, the proposed optimization scheme is mostly affected by the changes in the diagonal terms of R and the changes in the velocity diagonal terms of Q of the controlled system. The method is expected to be very useful for large-scale systems and is illustrated with the help of two example problems.