TY - JOUR
T1 - A Robust PI Control Design for a Class of Nonlinear Systems with Uncertainty Using Sum of Squares Decomposition
TT - روش طراحی کنترلگر PI برای دستهای از سیستمهای غیرخطی دارای عدم قطعیت به کمک تجزیه مجموع مربعات
JF - joc-isice
JO - joc-isice
VL - 6
IS - 3
UR - http://joc.kntu.ac.ir/article-1-51-en.html
Y1 - 2012
SP - 27
EP - 35
KW - Robust PI Control
KW - Sum of Squares Decomposition
KW - Density Function
KW - Nonlinear Control Synthesis
KW - Parametric Uncertainty.
N2 - This paper presents a new algorithmic method to design PI controller for a class of nonlinear systems whose state space description is in the form of polynomial functions. Design procedure is taken place based on certain or uncertain nonlinear model of system and sum of squares optimization. A so called density function is employed to formulate the design problem into a convex optimization program of sum of squares optimization form. Robustness of the design is guaranteed by taking parametric uncertainty into account with an approach similar to that of generalized S-Procedure. Validity and applicability of the proposed method is certified with numerical simulation. This paper, besides presenting an innovated PI control design which is not based on local linearization and works globally, announces a new approach in formulating parametric uncertainty in nonlinear systems. Derived stability conditions do not suffer from any drawbacks seen in previous results, such as depending on a linearized model or a stable model and it can overcome most control difficulties. Furthermore, employing sum of squares techniques makes it possible to drive stability conditions with least conservatism and directly derive stability of nonlinear system.
M3
ER -