[1]ZHANG Xiang-yan,ZHANG Nai-yao.Analytical structure of a classic fuzzy controller with π membership functions[J].CAAI Transactions on Intelligent Systems,2008,3(1):31-37.
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Analytical structure of a classic fuzzy controller with π membership functions

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 3 Number of periods: 2008 1 Page number: 31-37 Column: 学术论文—智能系统 Public date: 2008-02-25
Title:
Analytical structure of a classic fuzzy controller with π membership functions
Author(s):
ZHANG Xiang-yan;  ZHANG Nai-yao
Department of Automation, Tsinghua University, Beijing 100084, China
Keywords:
classic fuzzy controller;  π membership function ;  analyt ical structure
CLC:
TP273
DOI:
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Abstract:
A new classic fuzzy controller with π membership functions is proposed. The π function, a spline function with twoorder approximation, has been widely u sed in approximation theory. Since fuzzy controllers with triangular membership functions are only universal approximators with only firstorder approximation accuracy, it is very valuable to study the property of fuzzy controllers with me mbership functions. In this paper, we define the new fuzzy controller, deduce it s output expression and prove that the controller is equivalent to an integratio n of a twodimensional multilevel relay and a local nonlinear PD controller. On th is basis, we finally analyze the limiting and nonlinear properties of the contro ller.
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