## 4 Self-Tuning Fuzzy Control Strategy
### Self-Tuning Hierarchic Fuzzy Logic Control (SHFLC) Strategy
If the factors are too small, the input value of the sub-level FLC will be converted to a small value in the universe of discourse, and the output voltage will be too low. Thus, the performance of the PFD cannot be fully utilized. On the other hand, if the factors are too large, the input value will be converted to a larger value in the universe of discourse. This will lead to a large \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Isolation Velocity**} & \multicolumn{8}{c}{**Isolation Displacement**} \\ \cline{2-9}  & **NL** & **NM** & **NS** & **ZE** & **PS** & **PM** & **PL** \\ \hline NL & VL & VL & L & L & M & S & ZE \\ NM & VL & L & L & M & S & ZE & S \\ NS & L & L & M & S & ZE & S & M \\ ZE & L & M & S & ZE & S & M & L \\ PS & M & S & ZE & S & M & L & L \\ PM & S & ZE & S & M & L & L & VL \\ PL & ZE & S & M & L & L & VL & VL \\ \hline \hline \end{tabular} Note: NL: negative large, NM: negative medium, NS: negative small, ZE: zero, PS: positive small, PM: positive medium, and PL: positive large.  
\end{table} 
Table 3: Fuzzy rule base for sub-level FLC. Figure 6: Fuzzy control surface for sub-level FLC. damping force and limit the effectiveness of the controller. The supervisory FLC can automatically adjust the value of the normalization factors to different types and intensities of earthquakes. To also ensure that the PFD will operate in an effective manner during a non-pulse-type near-fault earthquake or a far-field earthquake, a lower command voltage would be necessary for the damper otherwise, the damping force will be too large. If that were the case, the damper would not dissipate much energy since it would not slide as expected. On the other hand, to ensure that the damping force is not reduced too much, therefore not providing enough energy dissipation under strong earthquakes, such as pulse-type near-fault earthquakes, the output scaling factor with a range from 0 to 1.3 was used to scale the command voltage of the piezoelectric friction damper. In the preliminary simulations, the universe of discourse for each normalization factor was selected according to the maximum structural response of the base-isolated building subjected to different types and intensity of earthquakes. Gaussian-type membership functions were selected for both input and output variables, as shown in Figure 7. The membership functions of the input variables are defined as S: small, M: medium, and L: large, and the output membership functions are defined as low: LOW, medium: MED and high: HIG. The control principles for the supervisory FLC are described as follows. If the input values are large (L), which indicate the earthquake intensity is strong and the structural response is large, then the values of normalization factors should be set to low. This will prevent the structural response from over exceeding the input universe of discourse of the sub-level FLC, and avoid the damper to be set in a full power condition for a long time. At the same time, to make the friction damper output a large damping force, the scaling factor \(S_{\text{roll}}\) should be increased to enhance the output voltage of the sub-level fuzzy controller. On the contrary, if the input value is small (S) or medium (M), which indicates the earthquake intensity is low and structure response is small, then the normalization factors of the  
Figure 7: Input and output membership functions for supervisory FLC: (**a**) input seismic acceleration; (**b**) input seismic velocity; (**c**) output displacement normalization factor; (**d**) output velocity normalization factor; and (**e**) output voltage scaling factor. sub-level FLC should be appropriately increased. To make the damper output an appropriate damping force, the scaling factor \(S_{\text{v}ollt}\) should be decreased to reduce the output voltage of the sub-level FLC. Furthermore, the smaller damping force can be output by the friction damper. The control rules of the supervisory fuzzy controller are shown in Tables 4 and 5, respectively.