Channel-by-channel anti-windup design for a class of multivariable systems

Abstract

This paper considers the design of anti-windup compensators with simple, transparent structures for multivariable constrained input systems. The main results in the paper show how, for multivariable plants with a particular structure, a multivariable anti-windup compensator can be constructed from several "single-loop" anti-windup compensators. Simple conditions, which can be interpreted as a linear program, are then derived which ensure that this concatenated compensator indeed guarantees stability of the multivariable system. The advantages of the resulting compensator is that it is easier to tune, and more transparent for implementation, than an unstructured multivariable compensator. Results from a nonlinear quadrotor simulation show the effectiveness of the proposed method.

Anti-windup design for input-coupled double integrator systems with application to quadrotor UAV’s

“…A similar problem was considered in [20,21], but in that paper, it was assumed that the plant was strictly stable, G i (s) ∈ RH ∞ for all i ∈ {1, . .…”

“…This section introduces a specially structured anti-windup compensator which exploits the structure of the plant (2) and controller (9). The approach used is based on that introduced in [20,21].…”

“…It is of course possible to use quite standard anti-windup techniques to tackle input saturation in such classes of system and the reader is referred to [7,8,9,10,11,12,13,14,15,16,17,18,19] and references therein for details of these. Furthermore, some specific anti-windup techniques for a class of system 20 which includes that considered here have also been recently proposed by the authors [20,21].…”

Alternative approach to anti-windup synthesis for double integrator systems

“…Consider the quadrotor system taken from [26], [13] and depicted in Figure 4. This is a multivariable system, but one …”

“…In recent years, the study of anti-windup techniques has grown steadily and this has led to major developments in approaches that provide favourable stability and performance results for systems with input saturation. Examples of relevant papers are [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13] and recent books on the topic include [14], [15], [16], [17] Many modern approaches to anti-windup design are formulated and solved using linear matrix inequalities (LMIs) to ensure that the anti-windup compensator bestows some sort of stability and performance guarantees on the system under consideration [18]. However, the use of LMIs may seem excessive in some situations, especially in the design of compensators for relatively simple systems.…”