Modified disturbance rejection problem

In this study, vibration control of earthquake-excited structures is treated as a modified disturbance rejection problem with a parameter ξs first introduced in Pincer procedure and the optimal control policy is derived by using well known Hamilton–Jacobi optimality equation. The parameter ξs has effects both in feed back and feed forward control components. Main focus is on the physical meaning of the parameter ξs and investigation of its feedback effect on the controlled system response. For high values of ξs, 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 ξs and the natural logarithm of ξs 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 ξs.