Membership function modification of fuzzy logic controllers with histogramequalization

In most fuzzy logic controllers (FLCs), initial membership functions (MFs) are normally laid evenly all across the universes of discourse (UD) that re present fuzzy control inputs. However, for evenly distributed MFs, there ex ists a potential problem that may adversely affect the control performance; that is, if the actual inputs are not equally distributed, but instead con centrate within a certain interval that is only part of the entire input ar ea, this will result in two negative effects, On one hand, the MFs staying in the dense-input area will not be sufficient to react precisely to the in puts, because these inputs are too close to each other compared to the MFs in this area. The same fuzzy control output could he triggered for several different inputs. On the other hand, some of the MFs assigned for the spars e-input area are "wasted." In this paper we argue that, if we arrange the placement of these MFs accor ding to a statistical study of feedback errors in a closed-loop system, we ran expect a better control performance. To this end, we introduce a new me chanism to modify the evenly distributed MFs with the help of a technique t ermed histogram equalization. The histogram of the errors is actually the s patial distribution of real-time errors of the control system. To illustrate the proposed MF modification approach, a computer simulation of a simple system that has a known mathematical model is first analyzed, l eading to our understanding of how this histogram-based modification mechan ism functions. We then apply this method to an experimental laser tracking system to demonstrate that in real-world applications, a better control per formance can be obtained by using this proposed technique.