Anti‐windup strategy for reset control systems

Abstract

This paper proposes an anti-windup strategy to deal with stability and performance requirements for a class of hybrid systems, such as those including a reset controller and subject to input saturation. The computation of the anti-windup compensator aiming at ensuring both L 2 input-to-state stability and internal stability of the closed-loop system is carried out from the solution of matrix inequalities. Depending on the way chosen to describe reset rules, the conditions for designing the anti-windup compensator are expressed through nonlinear matrix inequalities or linear matrix inequalities. Some optimization criteria in both cases are considered for the synthesis purpose: maximization of the L 2 -norm upper bound on the admissible disturbances for which the trajectories are assured to be bounded; minimization of the L 2 -gain of the disturbance to the system to-be-controlled output; and the maximization of an estimate of the domain of attraction of the origin.

Stabilization of linear impulsive systems through a nearly-periodic reset

“…The first one may be the generalization of this work to nonlinear systems. Also the performance issues may be considered either for linear impulsive systems or for nonlinear ones [28]. One criterion to be optimized may be the rejection of perturbations and the gain perturbations/output to be made as low as possible.…”

Static anti-windup scheme for a class of homogeneous dwell-time hybrid controllers

“…Although the results here cover a wider class of hybrid systems, we stress that the strategies adopted to describe the hybrid loops are different in the two papers, yielding to different conditions whenever the results in here are applied to a SISO plant controlled by a FORE controller. In this sight, this paper completes [22], with alternative conditions. Notice that both this paper and [22] present in some cases BMIs, due to the complexity of the problem.…”

“…In this sight, this paper completes [22], with alternative conditions. Notice that both this paper and [22] present in some cases BMIs, due to the complexity of the problem.…”

“…On the other hand, for local (regional) exponential stability, the conditions are BMIs. Within the literature, we mention [22], where anti-windup strategies were proposed for SISO systems with a FORE controller. Although the results here cover a wider class of hybrid systems, we stress that the strategies adopted to describe the hybrid loops are different in the two papers, yielding to different conditions whenever the results in here are applied to a SISO plant controlled by a FORE controller.…”

Using Luenberger observers and dwell‐time logic for feedback hybrid loops in continuous‐time control systems

“…In the quest of providing more flexible stabilizing controllers and more efficient design techniques, research efforts have focused on developing control algorithms using controllers that involve switching or online adaptation, leading to dynamic controllers whose states can experience jumps (namely, hybrid controllers). Such a flexibility may overcome some fundamental limitations of linear control (see [1] for an example, and see [2][3][4][5] for nonlinear controls) and improve the performance of linear closed-loop systems [6][7][8][9]. A particular class of hybrid controllers of interest for this paper is the so-called reset controller class where a part of the state is reset when it satisfies some algebraic conditions.…”