TY - JOUR
T1 - On the impossibility of building a thau observer for a nonlinear model of an induction motor
AU - Perez, Jose Humberto
AU - Santiago, Eric
AU - Figueroa, Maricela
AU - Pacheco, Jaime
AU - Avila, David
AU - Tamayo, Pedro Alejandro
AU - Mancilla, Juana Eloina
AU - Flores, Luis Armando
N1 - Publisher Copyright:
© 2003-2012 IEEE.
PY - 2018/7
Y1 - 2018/7
N2 - Given the simplicity of Thau observer, it could be attractive to try to build this kind of observer for an induction motor. However, in this paper, (metaheuristic) arguments are provided to explain why such purpose cannot be accomplished. In order to establish the impossibility of developing a Thau observer for the nonlinear model of an induction motor, first, it must be established that Thau inequality cannot be satisfied. Therefore, Lipschitz constant for nonlinear model of the motor was determined. Next, given the absence of a systematic procedure of design and due to the great diversity of possible values for observer parameters, Thau relation should be maximized. Nevertheless, as this last task is difficult and in order to avoid the drawbacks of classical methods, in this work, differential evolution algorithm was used. In spite of having maximized successfully Thau relation, Thau inequality could not be satisfied. As a last attempt, the motor model was scaled. Lipschitz constant for this model was minimized and Thau relation was again maximized. Notwithstanding, Thau inequality could not be satisfied for scaled model. Based on exhaustive bibliographic searches, it can be assured that this is the first time that this kind of problem is considered in the technical literature.
AB - Given the simplicity of Thau observer, it could be attractive to try to build this kind of observer for an induction motor. However, in this paper, (metaheuristic) arguments are provided to explain why such purpose cannot be accomplished. In order to establish the impossibility of developing a Thau observer for the nonlinear model of an induction motor, first, it must be established that Thau inequality cannot be satisfied. Therefore, Lipschitz constant for nonlinear model of the motor was determined. Next, given the absence of a systematic procedure of design and due to the great diversity of possible values for observer parameters, Thau relation should be maximized. Nevertheless, as this last task is difficult and in order to avoid the drawbacks of classical methods, in this work, differential evolution algorithm was used. In spite of having maximized successfully Thau relation, Thau inequality could not be satisfied. As a last attempt, the motor model was scaled. Lipschitz constant for this model was minimized and Thau relation was again maximized. Notwithstanding, Thau inequality could not be satisfied for scaled model. Based on exhaustive bibliographic searches, it can be assured that this is the first time that this kind of problem is considered in the technical literature.
KW - Differential evolution algorithm
KW - Induction motor
KW - Lipschitz constant
KW - Nonlinear observer
KW - Thau inequality
UR - http://www.scopus.com/inward/record.url?scp=85052738319&partnerID=8YFLogxK
U2 - 10.1109/TLA.2018.8447351
DO - 10.1109/TLA.2018.8447351
M3 - Artículo
SN - 1548-0992
VL - 16
SP - 1870
EP - 1877
JO - IEEE Latin America Transactions
JF - IEEE Latin America Transactions
IS - 7
M1 - 8447351
ER -