Modified disturbance rejection problem

In this study, vibration control of earthquake-excited structures is treated as a modified disturbance rejection problem with a parameter ξ_s first introduced in Pincer procedure and the optimal control policy is derived by using well known Hamilton-Jacobi optimality equation. The parameter ξ_s has effects both in feed back and feed forward control components. Main focus is on the physical meaning of the parameter ξ_s and investigation of its feedback effect on the controlled system response. For high values of ξ_s, feedback effect results in a significant decrease in displacements while the corresponding control forces have no significant increase. It is also shown that the significant decrease in displacements is closely related to ξ_s and the natural logarithm of ξ_s can be considered as a measure of the asymptotic stability of the system since all the eigenvalues of the closed loop system have real parts less than negative natural logarithm of ξ_s.