Anti-windup design with guaranteed regions of stability: an LMI-based approach

Abstract

Abstract-This note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs. Considering that a linear dynamic output feedback has been designed to stabilize the linear system (without saturation), a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed-loop system. It is shown that the closed-loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity. A modified sector condition is then used to obtain stability conditions based on quadratic Lyapunov functions. Differently from previous works these conditions are directly in linear matrix inequality form. Some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones.

Stability Analysis and Stabilization of Systems Presenting Nested Saturations

“…Remark 1: Particular formulations of Lemma 1 can be found in [7] (concerning the case of systems with a single saturation function, i.e., p = 1) and in [16] (concerning systems presenting both amplitude and dynamics restricted actuators).…”

“…In contrast, in [4], the recursive algorithms have been developed for solving the CARE of the weakly coupled systems. Recently, an algorithm that is based on the Lyapunov iterations for solving the CARE has been introduced [6], [7]. Although such algorithms can be computed by using the dimension of each subsystem, the convergence rate is given by the linear convergence.…”

“…This note also proposes a new decoupling algorithm for computing Newton's iterations as another important feature. As a result, a reduction in the computation is attained by using the existing fixed-point algorithm [6], [7].…”

Dynamic Output Feedback for Discrete-Time Systems Under Amplitude and Rate Actuator Constraints

“…We propose the synthesis of a nonlinear dynamic controller which is composed of a classical linear dynamic controller in cascade with input saturating integrators and two static anti-windup loops. It should be pointed out that, contrary to the anti-windup approaches (see for instance [15], [16], [17], [18], [19], [20], and references therein), where the controller is considered to be given, the idea here consists of computing the controller and the anti-windup gains simultaneously. The anti-windup gains appear, therefore, as extra degrees of freedom in the synthesis problem.…”

“…In particular, they are also useful to obtain conditions in LMI form. The theoretical conditions for solving the synthesis problem are based on the application of a generalized sector condition proposed in [20], which is applicable for deadzone nonlinearities. This condition encompasses the classical sector condition used, for instance, in [10], [13], [21], [14] and allows (contrary to the classical one) the formulation of regional stabilization conditions directly in LMI form.…”