## 3 Fuzzy Logic Controller
### Rule Base Tuning  
Every rule in the rule base presents one possible reasoning. The effectiveness and rationality of every rule determines the overall performance of the FLC. The traces shown in Figure 3 present a simple reasoning logic: if the previous perturbation can result in an increase in PV power, the next perturbation in PV voltage will follow the previous direction with the same offset, and vice versa. However, it is not sufficiently effective. As discussed at the beginning of this section, the perturbation offset should be adaptive in order to accelerate tracking process and to suppress the power oscillation around the MPP. Therefore, several reasoning rules can be added, i.e.,:  
IF dP/dV is \"PB\" and dV is \"PB\", then PT is \"PB\" IF dP/dV is \"PB\" and dV is \"PS\", then PT is \"PB\" IF dP/dV is \"NB\" and dV is \"NS\", then PT is \"NB\" IF dP/dV is \"NB\" and dV is \"NB\", then PT is \"NB\"  
The above rules can efficiently push the operation point towards the MPP within a few steps, when the operation point is far from the MPP. However, they are not efficient when the operation point approaches the transition areas where the slope of the P-V curve rapidly increases or decreases. Additionally, considering that the operation point may not move along a single P-V curve due to the environmental changes, the incremental changes in PV power may not be meaningful, in real environmental conditions. Figure 6 illustrates several conditions which may lead the FLC to make wrong decisions. As seen in Figure 9a, the first perturbation pushes the operation point from \(P_{1}\) to \(P_{2}\) when the large incremental change in PV power is detected, while at this moment, if the FLC cannot detect the fact that the operation point being located at \(P_{2}\) is near MPP, the FLC will probably keep perturbing the operation point to the right with a large perturbation offset. If so, the operation point could be shifted to \(P_{3}\). Given the hill shape of P-V curves, the incremental change between \(P_{2}\) and \(P_{3}\) may be still positive so that the operation point could be further perturbed to \(P_{4}\). Then, wrong decisions will be made. Moreover, wrong decisions generated by the FLC may not be easily found because the process shown in Figure 9 is invisible. Other conditions that can result in wrong decisions are presented by Figure 9c,d. Assuming that the FLC changes the perturbation offset in a timely manner, the operation point moves slowly towards the MPP. However, if the environmental conditions, such as irradiation and temperature, change the P-V characteristics of photovoltaics will vary immediately. As seen in Figure 9c, irradiation increasing makes the operation point move to another P-V curve so that the incremental change in PV power between \(P_{2}\) and \(P_{3}\) is enlarged. The FLC may consider that the operation point is far from the MPP, whereas \(P_{3}\) is actually close to the new MPP. Therefore, the operation point could be perturbed from \(P_{3}\) to \(P_{4}\). Given the Figure 9d, an irradiation drop or temperature increase could also lead the FLC to make wrong decisions again. The problems shown in Figure 9 can be solved by adding a slope-detection mechanism into the rule base of FLC. A minimum perturbation is mandatorily fulfilled after the FLC implements its previous reasoning decision. The minimum perturbation can help the FLC to detect the changes of the P-V curve with the minimum trade-off. If a rapidly incremental change in PV power can be detected by fulfilling the minimum perturbation in PV voltage, environmental changes can be inferred. If so, the FLC will abandon previous reasoning, and reconsider the status of the operation point and updated P-V curve. Including the self-calibration mechanism, the rule-base of the proposed FLC is shown in Table 1.