Directionality compensation for linear multivariable anti-windup synthesis

Abstract

We develop new synthesis procedures for optimizing anti-windup control applicable to open-loop exponentially stable multivariable plants subject to hard bounds on the inputs. The optimizing antiwindup control falls into a class of compensator commonly termed directionality compensation. The computation of the control involves the on-line solution of a low-order quadratic program in place of simple saturation. We exploit the structure of the quadratic program to incorporate directionality information into the off-line anti-windup synthesis using a decoupled architecture similar to that proposed in the literature for anti-windup schemes with simple saturation. We demonstrate the effectiveness of the design compared to several schemes using a simulated example.

A framework for multivariable algebraic loops in linear anti-windup implementations

“…To test the feasibility of (6), we might seek vectorsû ∈ R m (free) and λ ∈ R 2m (restricted) for a given input vector v ∈ R m , and fixed parameters L, b and H. Note that v andû are respectively the input and the output vectors of the algebraic loop subsystem (2). The algebraic loop description (6) comprises linear equations, linear inequalities and complementarity conditions and is generally termed a mixed LCP (mLCP) [32,6].…”

“…4 where the linear controller K has been factored into K 1 and K 2 and with K 2 wrapped around the quadratic program [2]. Depending on the factorization scheme adopted, different directionality compensation techniques can be realized.…”

“…This separation between H 1 and H 2 suggests that the anti-windup design can be carried out in two stages: first, choose H 1 such that the overall closed-loop system is stable and then choose H 2 such that the algebraic loop is well-posed and to enhance closed-loop performance (see [2] for detailed discussion on this subject).…”

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

“…However, when saturation is present i.e χ(v) = v, the saturation element causes some nonlinear coupling between the system's m control loops and, unless X is diagonal, the decoupling offered by the nominal 70 controller (10) is lost. This coupling is a well known trigger for performance deterioration and instability [25].…”

Alternative approach to anti-windup synthesis for double integrator systems

“…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.…”