General Approach to Active Structural Control

A general approach is proposed to be used in the active control of civil engineering structures. The approach aims at satisfying, simultaneously, the safety of the structure, the desired human comfort, and the feasibility of control. The problem is formulated as an optimal control problem subjected to equality and inequality constraints. These constraints represent, respectively, the structure’s model and the requirements on the controlled response. Since a solution of an optimal control problem becomes cumbersome for a high-order system, a method is offered to make the order of the system as small as desired. Also, an algorithm is offered that enables one to obtain a closed-loop control in the presence of the inequality constraints. It is shown that by using quadratic objective functions as performance indices and step penalty functions for the inequality constraints, an optimal feedback control law can be found. The approach is applied to the active tendon control of a two-story building frame.