Design and Implementation of Takagi-Sugeno Fuzzy Tracking Control for a DC-DC Buck Converter

This paper presents the design and implementation of a Takagi-Sugeno (T-S) fuzzy controller for a DC-DC buck converter using Arduino board. The proposed fuzzy controller is able to pilot the states of the buck converter to track a reference model. The T-S fuzzy model is employed, firstly, to represent exactly the dynamics of the nonlinear buck converter system, and then the considered controller is designed on the basis of a concept called Virtual Desired Variables (VDVs). In this case, a two-stage design procedure is developed: i) determine the reference model according to the desired output voltage, ii) determine the fuzzy controller gains by solving a set of Linear Matrix Inequalities (LMIs). A digital implementation of the proposed T-S fuzzy controller is carried out using the ATmega328P-based Microcontroller of the Arduino Uno board. Simulations and experimental results demonstrate the validity and effectiveness of the proposed control scheme

Pious Critique: Abū Isḥāq al-Shīrāzī and the 11th Century Practice of Juristic Disputation (Munāẓara)

The 5th/11th century Shāfi‘ī jurist Abū Isḥāq al-Shīrāzī (d. 476/1083) rose to scholarly fame in the context of a Baghdad culture of pious critical debate. The emergence of the practice of disputation (munāẓara) within the 10th century Muslim lands of Iraq and Persia had shaped a class of jurists dedicated to open and continual face-to-face debate in their search for God’s law (ijtihād). Jurists debated each other on contentious legal issues (al-khilāf): one jurist would adopt a thesis and try to defend it in the face of his opponent’s objections. They structured their practice around the boundaries of school affiliation and hierarchies. They debated those of equal rank and defended their doctrines from outside-school detractors. Their intended audience was fellow-jurists who could benefit and learn from exposure to critical debate. The ideal setting for the disputation was a space like the mosque because it was removed from the court of rulers and their potential influence on the debate. The pedagogical ethics of the disputation demanded that all present treat the practice with the seriousness and sincerity characteristic of acts of religious devotion. The jurists’ exclusion of lay Muslims from their debates entrenched their role as religious guides of the community and re-inforced the gender-hierarchy that marginalized women’s voices in the shaping of the law. Transcripts of Shīrāzī’s disputations reflect the impact of the disputation on the development of Shāfi‘ī legal doctrine. The jurists’ acknowledgement of the epistemic uncertainty of legal proofs led them to posit the need and sometimes even the obligation to have their ideas subjected to rigorous objections. Moreover, legal uncertainty justified that this process of debate continue even on issues that had already been examined over generations. The disputation did not typically resolve differences of opinion and did not spell the end of the debate. Records of Shīrāzī’s disputations show how this process of critical engagement with opponents inside and outside of the Shāfi‘ī school allowed the jurist to continue to test, develop, and refine his arguments for the law. Shīrāzī’s freedom to explore his legal tradition free from the demands of the courts and the petitions of lay Muslims permitted him to turn to building his own rendering of the Shāfi‘ī tradition with the greatest rigour possible. The impact of this process on the eventual formation of school doctrine was less certain. The canonization of Shāfi‘ī doctrine in the 13th century in the works of Yaḥyā b. Sharaf al-Nawawī (d. 676/1278) show that the eventual authoritative position of a school was not necessarily dependent on the force of argument but rather on the fame of the person who subscribed to it.Ph.D