Modified disturbance rejection problem

Abstract

Abstract 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 .