This article proposes an experimental investigation of a four-story structure that is connected to a shaking table. Also, the whale optimization algorithm (WOA) is used for the identification of the experimental structure parameters such as mass, stiffness and damp- ing. Moreover, this article addresses a numerical study which is a productive approach based on a combination of two well-known and practical controllers, namely optimal-based robust control method and proportional–integral–derivative (PID) controller. The sug- gested hybrid optimal-based robust and PID (HORPID) controller is used for vibration attenuation of a four-degree-of-freedom smart structure equipped with an active tuned mass damper. By using an optimization process based on the WOA, the HORPID is designed. By taking into consideration four real data of earthquake ground motion. the performance of the HORPID is evaluated. After that, the results obtained from the simulations are compared with results achieved by robust control. The simulation results show that the proposed HORPID is more effective than the earlier method in decreasing the amplitude of displacement and acceleration of each floor level.

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