## 1 Introduction
The goal of utilizing a semi-active device in a base-isolated structure is to mitigate the displacement response of the isolation system according to the current stage of excitation without an obvious increase in the superstructure response. In order to utilize the full capabilities of the semi-active devices employed in a semi-active isolation system, an effective control algorithm is essential. Due to the uncertainties in the nature of earthquakes and the characteristics of base-isolated systems, the task of developing an optimal controller is a challenging task. For instance, a controller designed for near-fault earthquakes that cause significant deformations in the isolation system might develop large damper forces during a far field earthquake of generally moderate excitation. As a result, the isolation system may not perform as expected, and a significant increase in the acceleration response of the superstructure may be observed. Alternatively, if the controller is designed for an earthquake with far-field characteristics, the damper force may not be large enough to effectively reduce the structural responses during the pulse-type ground motion. Thus, semi-active dampers need an adaptive control strategy for both far-field and near-field earthquakes. Recently, fuzzy logic control has been shown to be a promising control algorithm and has been widely used by many researchers for the control of semi-active devices due to its superiority and effectiveness in dealing with complex, uncertain, and nonlinear systems [16]. [PERSON] et al. [17] studied the fuzzy control for seismic protection of civil structures using MR dampers. [PERSON] and [PERSON] [18] adopted the supervisory fuzzy control technique in a similar manner to MR dampers in order to reduce seismic response of a base-isolated benchmark building. [PERSON] and [PERSON] [19] developed a supervisory fuzzy logic controller and a GA-based self-organizing fuzzy logic controller for piezoelectric friction dampers that are employed as semi-active devices in the base-isolated structure. An adaptive fuzzy neural control strategy was also developed by [PERSON] et al. [20] to adjust the contact force of the variable friction dampers (VFDs) that are used in a smart isolation system. In addition, [PERSON] and [PERSON] [21] proposed a new fuzzy logic controller that is designed for seismic protection of base-isolated structures utilizing piezoelectric friction damper against near-fault earthquakes for different ground sites. In this study, an improved self-tuning fuzzy logic control strategy is proposed in order to adjust the contact force of the piezoelectric friction damper (PFD) that is used in a smart isolation system. The control strategy employs an intelligent upper-level supervisory controller and a sub-level knowledge-based fuzzy controller. In this control strategy, the supervisory controller provides a mechanism to identify the nature of the earthquake, while the sub-level fuzzy controller specifies the command voltage for the damper by using isolation displacement and velocity as the two input variables. In particular, the supervisory controller tunes normalization factors of the sub-level controller inputs and the scaling factor of the sub-level controller outputs in order to improve the performance of the controller under different types of earthquakes. Taking into account that the pulse-type near-fault earthquake contains great acceleration and velocity pulses, seismic acceleration and seismic velocity are selected as two inputs of the supervisory controller. In order to verify the adaptability of the proposed control strategy under earthquakes with different intensities, and pulse-type near-fault earthquakes, non-pulse-type near-fault earthquakes and far-field earthquakes are employed as external excitations in the numerical simulations. For comparison purposes, maximum passive operation of the PFD and uncontrolled case are also considered in the simulations.