Quasi-sliding mode control with compensator for ATMD-buildings

Active tuned mass damper (ATMD) control systems for building structures have attracted considerable attention in recent years. This paper emphasizes on the combined application of the quasi-sliding mode control theory and the compensators theory to design and optimize the different parameters of the ATMD control scheme for getting the best results in the reduction of the building response under earthquake excitations. According to the linear quadratic optimal control theory, this paper designs a fixed-order compensator to make trade-offs between control efforts and specific response quantities of the structure. Existing sliding mode control method via exponential reaching law suffers, in our opinion, has the shortcoming that it is almost very difficult to avoid excessive flutter effect. Therefore the quasi-sliding mode control law involving saturation function is proposed. Considering the actuators are always of limited capacity in practice, this paper designs the saturated control law to be used when the needed control force exceeds the maximum control force of an actuator. Finally numerical simulations are given for SDOF (Single-Degree-of-Freedom) shear building model with ATMD. The simulation results obtained from the proposed control scheme are compared with those obtained from ATMD system excluding the compensator, active mass damper (AMD) system and the tuned mass damper (TMD) system. From the simulation results, it is demonstrated that the performance of quasi-sliding mode controller is remarkable, and the robustness of the control approach is also approved. Therefore, the new control method is quite promising for practical implementations of active control systems on seismically excited linear structures.