A convex framework for the design of dynamic anti-windup for state-delayed systems

Bender, Fernando Augusto; Silva, J.M. Gomes da; Tarbouriech, Sophie

doi:10.1109/acc.2010.5531620

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…By considering the case where n a = n p +n c , these conditions can be simplified. In particular, different frameworks can be adapted in order to obtain quasi-convex or convex conditions in the case n a = n p +n c : one can, for example, cite the framework used in [2,23], based on the projection lemma, or that one based on some change of variables [24,25]. For the ease of the presentation, we choose the above-mentioned second framework.…”

Section: Propositionmentioning

confidence: 99%

Anti‐windup strategy for reset control systems

Tarbouriech

Loquen

Prieur

2011

Intl J Robust & Nonlinear

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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.

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Section: Propositionmentioning

confidence: 99%

Anti‐windup strategy for reset control systems

Tarbouriech

Loquen

Prieur

2011

Intl J Robust & Nonlinear

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“…Throughout the paper, it is assumed that ω i and α i are known. Then, the synthesis conditions in Theorems and are in LMI forms, and hence, well‐developed convex optimization algorithms can be applied to solve the problem of the maximization of ROA , the disturbance tolerance problem, and the disturbance attenuation problem (i.e., the

{scriptL}_{2}

gains from disturbance or reference signals to performance outputs) . For instance, in order to maximize the ROA by Theorem , the following optimization problem can be considered :

\begin{matrix} \begin{matrix} \min & Trace (R) \end{matrix} \\ \begin{matrix} subject & to \end{matrix} \\ [\begin{matrix} R & I \\ I & bold-italicW \end{matrix}] > 0 \\ and (35) - (38) \end{matrix}

When estimating the ROA by the aforementioned algorithm, rows and columns, which correspond to w ( t ) and z ( t ) in , need to be removed.…”

Section: Resultsmentioning

confidence: 99%

“…As a result, the anti-windup framework can be applied to the case that '.q/ regionally satisfies the inequality (7). Considering the aforementioned setup, we aim at determining the anti-windup gains E 1 , E 2 , and E 3 and variable matrices B c' and D c' to address the following problems [24,25]:…”

Section: Remarkmentioning

confidence: 99%

“…As a result, the anti‐windup framework can be applied to the case that φ ( q ) regionally satisfies the inequality . Considering the aforementioned setup, we aim at determining the anti‐windup gains E 1 , E 2 , and E 3 and variable matrices B c φ and D c φ to address the following problems : Estimate the region of attraction: in the absence of disturbances w ( t ), we would like to determine an ellipsoid

scriptE (P)

as large as possible such that the trajectories of the closed‐loop system asymptotically converge to the origin with any initial point in it. Determine the

{scriptL}_{2}

gain: with a disturbance w ( t ) satisfying , we would like to design anti‐windup controller to ensure the trajectories of the closed‐loop system composed of and remain bounded. Moreover, the

{scriptL}_{2}

gain from the disturbance w ( t ) to the performance output z ( t ) should be minimized. Estimate the tolerable

{scriptL}_{2}

norm of w ( t ) : considering the null initial conditions, the objective is to maximize the

{scriptL}_{2}

norm bound of the disturbance w ( t ) such that the trajectories of the closed‐loop system remain bounded. …”

Section: Problem Statementmentioning

confidence: 99%

See 1 more Smart Citation

Modified static anti-windup for saturated systems with sector-bounded and slope-restricted nonlinearities

Wang

Pei

Tang

2016

Int. J. Robust. Nonlinear Control

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SUMMARYThis paper proposes modified static anti-windup techniques for saturated systems with sector-bounded and slope-restricted nonlinearities by augmenting the pre-designed controller with the so-called differential compensator to process the slope restriction. By using a purely quadratic Lyapunov function and with a modified sector condition dealing with actuator saturation, LMI-based synthesis conditions are presented to address the problems of the estimates of the region of attraction and L 2 performance analysis of the closed-loop system. Numerical examples illustrate the effectiveness of the proposed approaches.

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“…In the context of systems with state delay, the estimate of the region of attraction is even more challenging because a sequence of state vectors is required as the initial conditions. The actuator saturation problem for systems with time-delay has been studied, as can be seen in Bender et al [2011], Dey et al [2012], Gomes da Silva Jr. et al [2009], Ting and Liu [2011], and Wang et al [2013], where all theses papers deal with continuous-time systems with state delay. Moreover, the estimated region of attraction is characterized as one ball set, which may lead to conservative results.…”

Section: Introductionmentioning

confidence: 99%