This work developed the optimal and active control algorithms applicable to structural control for earthquake resistance. [Lewis, F. L., Vrabie, D. and Syrmos, V. L. [2012] Optimal Control (John Wiley & Sons)] developed a rigorous and comprehensive procedure for the derivation of an optimal control strategy based on the calculus of variation. This work is an application of Lewis’ formulation to the control of a structure for earthquake resistance. We developed a computer software which can be used to generate a dynamic model to simulate a planar structure and to construct the control law. This model also includes the tendon driven actuators, sensors and true history of earthquake excitation. The control law has two parts: (I) the feedback control which depends on the estimate state variables (Kalman filter) and (II) the record of the realistic earthquake excitation. The optimal control problem eventually leads to a two-point boundary value problem whose solution hinges on the knowledge of the entire history of the earthquake excitation. We employ true records of earthquake excitation as input. This approach enables one to solve the Riccati equations rigorously. Then, from the simulation results, one may study the relations between the control algorithm design and the characteristics (frequency, amplitude and duration) of earthquake excitation.
Deployment of the meta heuristic Colonial Competitive Algorithm in synthesis of unequally spaced linear antenna array