## 4 Conclusions  
In this study, active-controlled structures with different combinations and feedbacks of the active control were investigated under seismic excitations using HA and FPA to evaluate the performances of various feedback strategies. The conclusions about the performances of the feedback strategies in the active-controlled structure are as follows:  
1. The structural responses such as maximum displacement (from 97.53 to 60.39 cm), maximum velocity (from 8.14 to 4.85 m/s), and maximum total acceleration (from 64.72 to 37.02 m/s\({}^{2}\)) on the first (ground) floor are reduced under seismic excitations using the active control system, respectively.
2. The properties of the structure and the ground motions play an important role in the performances of the feedback strategies. Acceleration feedback (more successful in reducing structural reactions of at least 30 out of 56 ground motions) is generally the most appropriate type of feedback for numerical examples and earthquake records.
3. HS and FPA are an important solution method to determine the optimum PID parameters for different feedback strategies.
4. The position of the control system on each floor is more advantageous to keep the control force limit (3050 for Case 1 and 338 KN for Case 2) at the appropriate value in terms of applicability.  
As the main advantage of the method compared to other studies, the proposed method using PID controllers tuned via metaheuristic methods provides a realized control approach.  
Figure 5: The earthquake ground motions of Chi-Chi, Taiwan, TCU084 component.  
The control system is optimized by directly considering the time-domain response of the structure and utilizing a powerful search of design variables taken as control parameters in metaheuristic-based optimization. This method also considers limitations related to the physical application of the method, such as the time delay and control force limitations.  
[PERSON], [PERSON], and [PERSON] generated the analysis code. [PERSON] and [PERSON] developed the theory background and formulations of the active control system. The modification of HS was done by [PERSON] and [PERSON]. The text of the paper was written by [PERSON], [PERSON], and [PERSON] The figures were drawn by [PERSON], [PERSON], and [PERSON] [PERSON] and [PERSON] edited the paper and supervised the research direction. All authors have read and approved the final manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01011131). This research was also supported by the Energy Cloud R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (2019 MGF2A1073164).  
Not applicable.  
The data can be provided via e-mail by authors.  
The authors declare no conflict of interest.
Figure 17: The maximum structural responses of different feedback control under near-fault ground motions with a pulse and the time history of critical excitation for Case \(1\) according to the harmony search algorithm.  
Figure 18: Cont.  
Figure 16: The maximum structural responses of different feedback control under near-fault ground motions without a pulse and the time history of critical excitation for Case 1 according to the harmony search algorithm.  
Figure A3: The maximum structural responses of different feedback control under near-fault ground motions with a pulse and the time history of critical excitation for Case 2 according to the harmony search algorithm.