Convex Design of a Robust Antiwindup Controller for an LFT Model

Ferreres, G.; Biannic, Jean‐Marc

doi:10.1109/tac.2007.908357

Cited by 19 publications

(29 citation statements)

References 13 publications

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“…Based on a small gain argument, following [11] or [12], a standard approach to preserve stability despite saturations effects consists in minimizing the H ∞ -norm of the transfer function from w δ to z δ . Including nominal and robust performance leads to a multi-objective H ∞ control design problem:…”

Section: B a Design-oriented Representationmentioning

confidence: 99%

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Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization

Biannic¹,

Apkarian²

2011

Proceedings of the 2011 American Control Conference

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This paper investigates constrained control design problems involving mixed magnitude and rate saturations. We show that simultaneous design of structured feedback and antiwindup gains can be recast as minimizing two H ∞ -norm objectives. One is associated with nominal system operation while the other also captures the saturations effects. Because of the two-block structure of the controller, the problem is inherently difficult. We use recently available tools in nonsmooth optimization to compute controller components in a single run thereby alleviating the conservatism of more conventional schemes. The proposed methodology is applied to an aircraft control problem for which a PID feedback controller and a second-order antiwindup compensator are optimized simultaneously. keywords: Anti-windup, magnitude and rate saturations, structured controllers, hinfstruct, nonsmooth programming.

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Section: B a Design-oriented Representationmentioning

confidence: 99%

“…It is important to notice that constraints in (10) will be met as soon as a value less than one is achieved for program (12). In general, it is neither necessary nor advisable to run the code to completion and a quick exit is triggered when the unit target value is reached.…”

Section: Resolution Via Nonsmooth Optimizationmentioning

confidence: 99%

Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization

Biannic¹,

Apkarian²

2011

Proceedings of the 2011 American Control Conference

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“…If the plant is a high dimensional system and the unconstrained controller inherits this complexity, the optimization problem may become large and computationally demanding. On the other hand, the DLAW concept has a significant advantage over the other approach: as it is based on the robust control machinery, the modeling errors and uncertainties can be easily integrated into the design procedure [2]. This paper focuses on the other class, the model-recovery (MRAW) solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The direct method considers the unconstrained feedback loop as a special plant and the compensator as a special controller. The compensator construction is then reformulated as a control design problem for which the existing synthesis algorithms -LTI [12] or LPV [2] -can be easily adapted. Since the plant in the compensator design consists of the original plant and the controller, the LMIs are formulated in the extended (plant+controller dimensional) space.…”

Section: Introductionmentioning

confidence: 99%

“…Since the LPV structure is a powerful extensions of the LTI class, it makes sense to investigate the possibilities of extending the LTI anti-windup solutions to parameter varying models. In case of DLAW design the extension is a bit easier because the parameter-dependence can be easily integrated in the general control design framework ( [19], [13], [2], [20]). Although the problem is more delicate in the MRAW framework, some approaches have already been extended to parameter-varying plants.…”

Section: Introductionmentioning

confidence: 99%

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Model recovery anti-windup compensator design for magnitude and rate saturated LPV systems

Péni

Szabó

Vanek

et al. 2013

52nd IEEE Conference on Decision and Control

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Abstract-This paper extends the LTI anti-windup compensator scheme proposed in [6] to linear parameter-varying (LPV) systems. Following the MRAW concept, the dynamical part of the compensator is formed by the exact copy of the plant. The design procedure is thus simplified to the construction of a parameter-dependent state feedback, which stabilizes the plant's copy and determines the performance and the domain of applicability of the compensator. To decrease the conservatism, the presented method applies parameter-dependent Lyapunov function and embeds the saturation (dead-zone) in a parameterdependent sector. The design is formulated as an LMI-based convex optimization problem.The paper also investigates the possibility of eliminating certain free variables in order to reduce the complexity of the synthesis procedure. It is shown that an elimination procedure similar to that in [6] can be carried out, but with LPV systems the reconstruction of the compensator gain is not so straightforward. To overcome the difficulty a novel method is proposed, which is based on a closed formula parameterizing all solutions of the synthesis LMIs. Both of the fully parameterized and the reduced complexity syntheses are presented and their properties are analyzed. The applicability of the methods is demonstrated on a simple LPV plant. I. INTRODUCTIONControl input limitations are always present in real physical systems. If the controller is designed irrespective of these limitations, the later appearance of a saturation may cause undesired behavior in the closed loop: it leads to performance degradation or even instability. This effect is called controller windup.One possible way to minimize the undesired effects of controller windup is using an anti-windup compensator. The concept is simple ([17], [21]): the controller is designed irrespective of the saturation and then a a static or dynamic compensator is designed so that the following three criteria are fulfilled: (1) the closed loop is (locally) stable; (2) if there is no saturation, the nominal performance is guaranteed; (3) in case of saturation the system is driven by the compensator so that the signals leave the saturating domain and the nominal performance is recovered as quickly as possible.There are two large groups of model-based anti-windup solutions ([21], [8]): Direct Linear Anti-Windup (DLAW) and Model Recovery Anti-Windup (MRAW) methods. The direct method considers the unconstrained feedback loop as a special plant and the compensator as a special controller. The compensator construction is then reformulated as a control design problem for which the existing synthesis algorithms -LTI [12] or LPV [2] -can be easily adapted. Since the plant in the compensator design consists of the original plant and the controller, the LMIs are formulated in the extended (plant+controller dimensional) space. If the plant is a high dimensional system and the unconstrained controller inherits this complexity, the optimization problem may become large and computationally demanding. O...

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Robust and nonlinear control literature survey (No. 5)

2008

Intl J Robust & Nonlinear

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In order to keep readers up to date, the journal will contain a list of recently published journal articles relevant to the fields of robust and nonlinear control six times a year. This list is compiled from a wide range of journals. Please note that even though the list has been broadly categorized, these classifications are by no means strict and are there to assist the reader. Please also note that inclusion in the list is not an endorsement of a paper's quality. If you have any suggestions or comments, please email Jonas Balderud at j.balderud@eee.strath.ac.uk or Leonardo Giovanini at leonardo.giovanini@eee.strath.ac.uk. THEORETICAL DEVELOPMENTS IN ROBUST CONTROL

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Convex Design of a Robust Antiwindup Controller for an LFT Model

Cited by 19 publications

References 13 publications

Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization

Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization

Model recovery anti-windup compensator design for magnitude and rate saturated LPV systems

Robust and nonlinear control literature survey (No. 5)

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Convex Design of a Robust Antiwindup Controller for an LFT Model

Cited by 19 publications

References 13 publications

Anti-windup design via nonsmooth multi-objective H<inf>&#x221E;</inf> optimization

Anti-windup design via nonsmooth multi-objective H<inf>&#x221E;</inf> optimization

Model recovery anti-windup compensator design for magnitude and rate saturated LPV systems

Robust and nonlinear control literature survey (No. 5)

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Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization

Anti-windup design via nonsmooth multi-objective H<inf>∞</inf> optimization