Seismic control of structure with phase control active tuned mass damper

In this paper, the innovative phase control active tuned mass damper (PC-ATMD) is developed so that the PC-ATMD can achieve a 90° phase lag of structure to induce maximum power flow. The equation of motion and proposed phase control algorithms are derived in detail. By utilizing the ATMD velocity relative to structure and different structural measurement feedback, two phase control algorithms are, thus, proposed individually. The PC-ATMD, which uses structural displacement feedback, is denoted as the phase control displacement feedback active tuned mass damper (PCD-ATMD), whereas the use of structural absolute acceleration feedback is the phase control acceleration feedback active tuned mass damper (PCA-ATMD). The control of PC-ATMD is smooth, proportional, and neither full-state system measurement nor estimation required. This paper also describes the optimal control gains of the PCD-ATMD or PCA-ATMD which can be determined by direct output feedback optimization method. The shear building structures that apply PC-ATMDs are subjected to earthquakes. The results indicate that, after applying the PCD-ATMD or PCA-ATMD, the peak displacement and absolute acceleration of the primary structure are both well suppressed. Moreover, the PCD-ATMD has comparable effectiveness than the traditional linear quadratic designed ATMD which uses full-state feedback, while the PCA-ATMD is only slightly less performance than the PCD-ATMD but more feasible for the application related to tall building structures. Finally, the stability of the proposed algorithms is also verified. It concludes that the PCD-ATMD and PCA-ATMD are both quite stable systems in a certain range of control gains.