Mohan, B M and Ghosh, Arpita (2006) *The simplest fuzzy PID controllers: mathematical models and stability analysis.* Soft Computing - A Fusion of Foundations, Methodologies and Applications, 10 . pp. 961-975.

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## Abstract

This paper reveals mathematical models for the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical models are derived via left and right trapezoidal membership functions for each in- put, singleton or triangular membership functions for output, algebraic product triangular norm, different combinations of triangular co-norms and inference methods, and center of sums (COS) defuzziﬁcation method. Properties of these structures are studied to examine their suitability for control application. For the structure which is suitable for control,bounded-input bounded-output (BIBO) stability proof is presented. An approach to design fuzzy PID controllers is given.Finally, some numerical examples along with their simulation results are included to demonstrate the effectiveness of the simplest fuzzy PID controllers.

Item Type: | Article |
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Official URL/DOI: | http://10.1007/s00500-005-0023-9 |

Uncontrolled Keywords: | Fuzzy PID controllers · Mathematical models · Algebraic product triangular norm · BIBO stability |

Divisions: | Material Science and Technology |

ID Code: | 5623 |

Deposited By: | DR ARPITA GHOSH SINHA |

Deposited On: | 28 Jun 2012 10:28 |

Last Modified: | 03 Sep 2012 17:13 |

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