title: Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.
abstract: This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.
authors.affiliation: Department of Electrical Engineering, Indian Institute of Technology, Kharagpur-721302, India. mohan@ee.iitkgp.ernet.in
authors.forename: B M
authors.initials: BM
authors.lastname: Mohan
authors.forename: Arpita
authors.initials: A
authors.lastname: Sinha
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D017143:Fuzzy Logic; D016014:Linear Models