Optimal Direct Output Feedback of Structural Control

Abstract

An algorithm to calculate optimal direct output feedback gain is developed in a simple fashion such that a certain prescribed performance index is minimized. With the introduction of a special matrix operation, optimal feedback gain is obtained systematically by solving simultaneously linear algebraic equations iteratively. Control forces are then calculated from the multiplication of output measurements by a time‐invariant feedback gain matrix. Numerical verification is illustrated through the control of single‐degree‐of‐freedom and three‐degree‐of‐freedom structures subjected to real earthquake excitation. It is shown that the number of sensors and controllers may be very small compared with the dimension of states. A small number of sensors and controllers, and simple on‐line calculation, make the proposed control algorithm favorable to real implementation. Since the full‐order mathematical model of the structure is considered throughout the derivation, the spillover effect in control and observation due to modal control is eliminated. Hence, if the structure is well described by the mathematical model, system stability is guaranteed. Finally, the optimal allocation pattern of sensor and controller is suggested.