TY - JOUR
T1 - An Algebraic Fuzzy Pole Placement Approach to Stabilize Nonlinear Mechanical Systems
AU - Meda-Campana, Jesus Alberto
AU - Rodriguez-Manzanarez, Roman A.
AU - Ontiveros-Paredes, S. Denisse
AU - Rubio, Jose de Jesus
AU - Tapia-Herrera, Ricardo
AU - Hernandez-Cortes, Tonatiuh
AU - Obregon-Pulido, Guillermo
AU - Aguilar-Ibanez, Carlos
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - Based on the general structure of mechanical systems described by their state-space representation, the Takagi-Sugeno fuzzy modeling, and the controllability property of fuzzy systems, an algebraic and practical approach to computing the fuzzy gain capable of ensuring the stability property of the Takagi-Sugeno fuzzy model is proposed in this article. The main idea consists of finding a continuous fuzzy gain such that any linear behavior, defined by the adequate selection of eigenvalues, is induced in the closed-loop fuzzy system. Therefore, by continuity, if the fuzzy model is an approximation sufficiently close to the mechanical system, then such a nonlinear system is also stabilized by the fuzzy controller. A notable advantage of the proposed method, when compared with similar approaches, is the simplicity of the resulting gain. The validity of the approach is illustrated through the numerical simulation of a sufficiently complex nonlinear system.
AB - Based on the general structure of mechanical systems described by their state-space representation, the Takagi-Sugeno fuzzy modeling, and the controllability property of fuzzy systems, an algebraic and practical approach to computing the fuzzy gain capable of ensuring the stability property of the Takagi-Sugeno fuzzy model is proposed in this article. The main idea consists of finding a continuous fuzzy gain such that any linear behavior, defined by the adequate selection of eigenvalues, is induced in the closed-loop fuzzy system. Therefore, by continuity, if the fuzzy model is an approximation sufficiently close to the mechanical system, then such a nonlinear system is also stabilized by the fuzzy controller. A notable advantage of the proposed method, when compared with similar approaches, is the simplicity of the resulting gain. The validity of the approach is illustrated through the numerical simulation of a sufficiently complex nonlinear system.
KW - Fuzzy controllability
KW - Takagia-Sugeno (Ta-S) fuzzy modeling
KW - fuzzy pole placement
KW - mechanical systems
KW - state-space representation
UR - http://www.scopus.com/inward/record.url?scp=85115691248&partnerID=8YFLogxK
U2 - 10.1109/TFUZZ.2021.3113560
DO - 10.1109/TFUZZ.2021.3113560
M3 - Artículo
AN - SCOPUS:85115691248
SN - 1063-6706
VL - 30
SP - 3322
EP - 3332
JO - IEEE Transactions on Fuzzy Systems
JF - IEEE Transactions on Fuzzy Systems
IS - 8
ER -