Optimal structural active control force, number and placement of controllers

A new method for optimizing the control force and the number and location of controllers of a closed–open loop control system has been developed. In the case of using some controllers, there is a need for determining the preference of stories for placement of controllers. The study of some shear buildings subject to different excitations, leads to a simple index for determining the sequence of stories. Knowing the preference of stories, the optimization of control force and number of controllers can be represented as a typical optimization problem. In a closed–open loop control system, applying control force is equivalent to making changes in the mass, damping and stiffness matrices of the structure and external force vector. Assuming these changes are linear and proportional to their initial values, the minimization of control force depends on the optimal values of the proportion coefficients. This idea leads to a constrained n-variable optimization problem, which has been solved by using the exterior penalty function method. The effectiveness of the proposed method is demonstrated using numerical examples. Optimizing the number of controllers using such a method requires a time-consuming trial and error procedure until the final result is achieved. Based on the results obtained by the proposed method, an artificial neural network has been trained such that considering the physical properties of structure and excitation, the optimal number and location of controllers may be yielded by the network with the least effort.