Fuzzy Velocity and Fuzzy Acceleration in Fractional Order Motion

Abstract

Fractional calculus presents a new perspective for solution of scientific and engineering problems. There are still many fields where fractional calculus promise fresh understanding of real world problems. In this study, we present an investigation on fractional order motion, where we extend our comprehension from velocity and acceleration concepts to a fuzzy velocity and acceleration domains. Here, fundamentally, we suggest a debate on interpretation of fractional-order derivative system on the bases of integer-order derivative knowledge. We observed that the continuous fractional-order motion equation set can be considered to cover the discrete integer-order motion equation set and physical meaning of fractional-order motion systems can be better understood by using a fuzzy conceptualization of integer-order derivative systems according to the dissimilarity metric.

High Performance Control of Grid Connected Cascaded H-Bridge Active Rectifier Based on Type II-Fuzzy Logic Controller with Low Frequency Modulation Technique

“…The controller which is employed in the Figure 4 is similar to the controller that has been introduced in [ The complete block diagram of Type II Fuzzy Logic Control (Type II-FLC) system is shown in Figure 5. Based on the Figure 5, four sections have been defined as the main components of the Type II Fuzzy Logic Controller [18][19][20];  First, the Knowledge Base (KB) which is encompassing knowledge regards of all the input and output fuzzy parts. Also, it contains the term set and the membership functions of the controller about the input variables to the fuzzy 'Rule-Base' (RB) system and the output or decision variables to the plant.…”

“…5] and[16][17][18]. The main difference is using Type II fuzzy logic controller instead of PI controllers to improve the performance of the Optimal SHE-PWM technique.…”

High Performance Control of Grid Connected Cascaded H-Bridge Active Rectifier Based on Type II-Fuzzy Logic Controller with Low Frequency Modulation Technique

“…Figure 4 presents the bock diagram of the Fuzzy controller which is used in the proposed controller. The controller which is employed in the Figure 4 is similar to the controller that has been introduced in [5] and [16][17][18]. The main difference is using The complete block diagram of Type II Fuzzy Logic Control (Type II-FLC) system is shown in Figure 5.…”

“…The main difference is using The complete block diagram of Type II Fuzzy Logic Control (Type II-FLC) system is shown in Figure 5. Based on the Figure 5, four sections have been defined as the main components of the Type II Fuzzy Logic Controller [18][19][20];  First, the Knowledge Base (KB) which is encompassing knowledge regards of all the input and output fuzzy parts. Also, it contains the term set and the membership functions of the controller about the input variables to the fuzzy 'Rule-Base' (RB) system and the output or decision variables to the plant.…”

“…There are two types of Fuzzy Controller which are used in applications: Type I Fuzzy Logic Controller (Type I-FLC) and Type II Fuzzy Logic Controller (Type II-FLC) [18][19][20][21][22]. The big difference between them is in dealing with uncertainty issues.…”