Application of practical fuzzy arithmetic to fuzzy internal model control |
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Authors: | Laurent Vermeiren Thierry Marie Guerra Hakim Lamara |
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Affiliation: | a Univ Lille Nord de France, F-59000 Lille, France b UVHC, LAMIH, F-59313 Valenciennes, France c CNRS, FRE 3304, F-59313 Valenciennes, France |
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Abstract: | This paper applies a new fuzzy arithmetic of interval calculus and fuzzy quantities to automatic control. Practical results are obtained which overcome those based on the extension principle or α-cuts. The proposed approach is based on a different representation of fuzzy numbers, though most common arithmetic operators cannot be directly applied for designing a fuzzy controller due to the unjustified overestimation effect. To avoid this phenomenon, a procedure based on an “exact” resolution calculus is proposed, whose solutions allow creating a fuzzy internal model control scheme. The validity of the new method is illustrated by a real-time educational engineering application on classical control design: a coupled tanks system. |
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Keywords: | Fuzzy arithmetic Fuzzy number Fuzzy model inversion Internal model control Weighted fuzzy fusion φ-calculus arithmetic |
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