Arief Syaichu, Rohman, Anti-Windup Controller Parameterizations 80 ANTI-WINDUP CONTROLLER PARAMETERIZATIONS Arief Syaichu-Rohman School of Electrical Engineering & Informatics Institut Teknologi Bandung, Jl. Ganesa 10, Bandung 40132, Indonesia arief@stei.ee.itb.ac.id ABSTRACT Following a linear controller design, an anti-windup compensation is a popular approach that may be taken to deal with input saturation. There have been many anti-windup techniques proposed. Based on a transfer function parameterization of the resulting anti-windup controller, these anti- windup techniques may be classified into two categories, which may be called 1-degree of freedom (1-DOF) and 2-degree of freedom (2-DOF) parameterizations. Using newly known equivalence between a multivariable nonlinear algebraic loop and a constrained quadratic programming, two kind parameterizations of some existing anti-windup compensations are explained. INTRODUCTION Actuator saturation is a ubiquitous constraint that may induce adverse effects in any control systems. For linear systems, there have been many approaches proposed to overcome the effects of control input saturation. Anti-windup approaches (including conditioning techniques) are widely popular in which an anti-windup compensator is only active in the nonlinear region or a linear controller take control otherwise, see Fig.1. ζ P ˆ u u + + - - e r y v K Fig.1 An anti-windup scheme The anti-windup compensator may be a static gain matrix (e.g. (Mulder et.al., 2001)) or a dynamic transfer matrix (e.g. (Grimm et.al., 2003). Some of anti-windup schemes may include a nonlinear algebraic loop. It is illustrated in (Mulder et.al., 2001) that a nonlinear algebraic loop in an anti-windup scheme may improve the performance of its closed loop system under input saturation. The resulting anti-windup controller is a combination of the nominal controller and anti-windup compensator. Based on a transfer function parameterization, these anti-windup approaches may be classified into two categories, which may be called 1-degree of freedom (1-DOF) and 2-degree of freedom (2-DOF) parameterizations. In fact, a unified view of some anti-windup approaches that has been presented in (Kothare et.al., 1994) may be presented in a 2-DOF parameterization. Meanwhile, the 1-DOF parameterization may be found in