TY - JOUR
T1 - Preservation of robustness, non-fragility and passivity for controllers using linear fractional transformations
AU - Fernández-Anaya, Guillermo
AU - Flores-Godoy, José Job
AU - Álvarez-Ramírez, José
AU - Del Muro, Basilio
PY - 2006/5
Y1 - 2006/5
N2 - In this work, using algebraic methods, we characterize the parameters of a linear fractional transformation such that the composition of a class of rational function with the linear fractional transformation preserves stability, in the case that the rational function is stable, or stabilizes the original rational function, in the case that the rational function is unstable. As a consequence, we obtain a dual result about the robust stabilization of a plant-represented as a rational function-compensated with a controller when there is a nonlinear disturbance induce by function composition on the parameters of the controller. This implies the non-fragility of the controller and also the plant robust stabilization for the same class of disturbances. Also, for a particular choice of one of the parameters in the linear fractional transformation, the composition of functions preserves the structure of Proportional, Proportional-Derivative and Proportional-Derivative-IntegraI type of controllers. Finally, results about stabilization based in passivity using the linear fractional transformation are given.
AB - In this work, using algebraic methods, we characterize the parameters of a linear fractional transformation such that the composition of a class of rational function with the linear fractional transformation preserves stability, in the case that the rational function is stable, or stabilizes the original rational function, in the case that the rational function is unstable. As a consequence, we obtain a dual result about the robust stabilization of a plant-represented as a rational function-compensated with a controller when there is a nonlinear disturbance induce by function composition on the parameters of the controller. This implies the non-fragility of the controller and also the plant robust stabilization for the same class of disturbances. Also, for a particular choice of one of the parameters in the linear fractional transformation, the composition of functions preserves the structure of Proportional, Proportional-Derivative and Proportional-Derivative-IntegraI type of controllers. Finally, results about stabilization based in passivity using the linear fractional transformation are given.
KW - Composition
KW - Linear fractional transformation
KW - PD/PI/PID controllers
KW - Robust stabilization
UR - http://www.scopus.com/inward/record.url?scp=33744741987&partnerID=8YFLogxK
M3 - Artículo
AN - SCOPUS:33744741987
SN - 1109-2734
VL - 5
SP - 603
EP - 610
JO - WSEAS Transactions on Circuits and Systems
JF - WSEAS Transactions on Circuits and Systems
IS - 5
ER -