Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems
Name
TeoMITTR10.pdf
Description
PDF file
Size
825.18 KB
Format
Adobe PDF
Checksum (MD5)
c15489e6f215cea26d55139bb0f7eb10
Author(s)
Teo, Justin
How, Jonathan P.
Date Issued
March 15, 2010
Series/Report no.
;ACL10-01
Abstract
The gradient projection anti-windup (GPAW) scheme was recently proposed as an anti-windup method for nonlinear multi-input-multi-output systems/controllers, the solution of which was recognized as a largely open problem in a recent survey paper. This report analyzes the properties of the GPAW scheme applied to an input constrained first order linear time invariant (LTI) system driven by a first order LTI controller, where the objective is to regulate the system state about the origin. We show that the GPAW compensated system is in fact a projected dynamical system (PDS), and use results in the PDS literature to assert existence and uniqueness of its solutions. The main result is that the GPAW scheme can only maintain/enlarge the exact region of attraction of the uncompensated system. We illustrate the qualitative weaknesses of some results in establishing true advantages of anti-windup methods, and propose a new paradigm to address the anti-windup problem, where results relative to the uncompensated system are sought.
Subjects
gradient projection anti-windup
constrained planar LTI systems
projected dynamical systems
equilibria
region of attraction
Persistent DSpace Link
