A Generalization of Optimal Control Theory: Linear and Nonlinear Structures
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A systematic generalization of the theory of optimal control for seismic-excited linear, nonlinear and hysteretic structures is presented. The generalized theory includes the effect of actuator dynamics and a penalty on the acceleration response of the structure. The proposed generalized performance index includes the acceleration response so that either a simultaneous reduction of the deformation and acceleration or a trade-off between them can be achieved. Experimental results indicate that a significant contribution to the system time delay comes from the actuator response. In this report, the actuator dynamics is explicitly accounted for in the optimization process so that the gain matrix involves actuator characteristics leading to a better control performance. In Part I, optimal control theory for linear structures is presented. Numerical simulation results are obtained to demonstrate the advantages of the generalized optimal control theory. In Part II, an optimal nonlinear control method is proposed for applications to nonlinear and hysteretic structures. The proposed nonlinear control method is based on a generalized performance index. Both the absolute acceleration vector of the structural response and the actuator dynamics are taken into account in the optimization process. The control method using acceleration and velocity feedbacks are also derived. Simulations indicate that the proposed nonlinear control method is effective for hybrid control of seismic-excited building structures.