Design of low-order observers for linear feedback control laws

Fortmann, T.; Williamson, D.

doi:10.1109/tac.1972.1100006

Cited by 177 publications

(46 citation statements)

References 8 publications

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“…By using steps [1][2][3][4][5][6][7] above, a linear functional reduced order observer (6) and feedback controller (2) are obtained.…”

Section: Obtain Matrix G From Equ (14)mentioning

confidence: 99%

“…Design procedures are suggested for observing a scalar linear function of a state of a multiple output system in Moore [4] Murdoc [5] and Roman [6]. Fortmann and Williamson [7] are the first to reconstruct vector linear functionals of the state for multiple output systems. Another method based on the reduction of a state observer for a system in form, where the state functional are treated as additional outputs, was proposed by Fairmann and Gupta.…”

Section: Introductionmentioning

confidence: 99%

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Design of Linear Functional Observer for MIMO LTI systems

Nakade¹,

Galgate²

2010

IJCA

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This paper presents an efficient technique to design reduce order linear functional observer for linear time invariant systems. Assuming the existence of linear state feedback controller to achieve stability or some control performance criteria of the linear system, a design procedure is proposed for reconstruction of the state feedback control action. The attractive features of the proposed design procedure are that the resulted linear state functional state observer is of a very low order and it requires information of a small number of outputs. The proposed observer asymptotically converges to any number of linear functions. Numerical examples are considered to illustrate the properties of the observer.

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“…By using steps [1][2][3][4][5][6][7] above, a linear functional reduced order observer (6) and feedback controller (2) are obtained.…”

Section: Obtain Matrix G From Equ (14)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of Linear Functional Observer for MIMO LTI systems

Nakade¹,

Galgate²

2010

IJCA

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“…Since initial works of [10,17,18] two kinds of design techniques of such observers can be distinguished. On the one hand, we find those who start with the solution of the Sylvester equation which appears in the existence conditions of such an observer.…”

Section: Introductionmentioning

confidence: 99%

Some new standpoints in the design of asymptotic functional linear observers

Rotella

Zambettakis

2015

ESAIM: Proc.

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Abstract. The owl of Minerva spreads its wing only with the falling of the dusk. The aim of this work is to provide some new trends in the observation for linear systems. In the general framework of designing linear functional observers for linear systems the necessary and sufficient existence conditions are well known. Whether in the O'Reilly textbook or in the recently published ones on this topic, and, roughly speaking, the design methods can be categorized in two kinds. The first one is based on the solution of a Sylvester equation and a projection of the observed linear functional. The second one, based on the recent notion of functional observability, starts from the Darouach criterion which is an Popov-Belevitch-Hautus type one. Nevertheless, the main drawback of the deduced methods is that they cannot be used for linear time-varying systems. These models are of primary importance, for instance with linearization about a trajectory. Consequently, we cope with this problem by considering a new point of view for the design of linear functional observers. We see also that Darouach observers or Cumming-Gopinath observers are particular cases of the proposed methodology. For simplicity sake we suppose the system has no unknown inputs and is not described by a distributed parameters model as well. Nevertheless, these cases can be thought as possible extensions of the presented standpoints.Résumé. La chouette de la connaissance ne vole qu'à la nuit tombée. L'objet de cet article est de proposer des pistes pour l'observation dans le cadre des systèmes linéaires. De façon plus générale, en considérant l'observation de fonctions linéaires de l'état d'un modèle linéaire, les conditions nécessaires et suffisantes d'existence de ces observateurs sont connues depuis longtemps. Que ce soit dans l'ouvrage de base de O'Reilly ou dans les ouvrages plus récents qui traitent de ce sujet, les différentes méthodes de conception d'un observateur de fonctionnelle linéaire peuvent, schématiquement,être rassemblées en deux groupes. Celles qui demandent la résolution d'uneéquation de Sylvester et d'uneéquation de projection et celles basées sur l'extension du critère d'existence de Darouach, ces dernières utilisant un critère de type Popov-Belevitch-Hautus. Ainsi les méthodes déduites de ces critères peuventêtre difficilementétendues aux systèmes linéaires non stationnaires. De façonà contourner cet inconvénient majeur lorsque l'on songeà la linéarisation autour d'une trajectoire, nous proposons une technique pratique et systématique de conception d'un observateur. On montre par exemple que les observateurs de Darouach ou de Cumming-Gopinath n'en sont que des cas particuliers. Bien sûr, pour ne pas compliquer inutilement la présentation nous n'envisagerons que des modèles linéaires stationnaires de dimension finieà entrées toutes connues, les autre situations pouvantêtre envisagéesà titre d'extension.

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“…Therefore, efforts are made to have a simplified low-order model which retains the dominant characteristics of the original system. During the last four decades, a significant attention has been paid to construct the reduced order model by retaining only a few modes of linear difference system [1][2][3][4] . The appropriate definition and determination as to which state variables significantly participate in the selected modes become very important.…”

Section: Introductionmentioning

confidence: 99%

“…Balanced approach reduced order model: Consider a linear discrete time system described by the following equation ( 1) ( )…”

Section: Introductionmentioning

confidence: 99%

Designing of PID Controller for Discrete Time Linear System Using Balanced Approach Reduced Order Model

Ravichandran¹,

Rani²,

Manikandan³

2007

American J. of Applied Sciences

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Abstract:Modeling physical systems usually results in complex high-order dynamic models. It is often desirable to approximate these models by simpler models with reduced order. This study deals with the design of discrete time linear system using a balanced approach reduced order model. The reduced order model retains the desired state variable which contains a significant contribution. A PID controller is designed for the reduced second order model to meet the desired performance specifications by using pole-zero cancellation method. The stabilization of linear discrete time system is achieved by selection of parameters of the PID controller. A numerical example is given to illustrate the design method.

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Design of low-order observers for linear feedback control laws

Cited by 177 publications

References 8 publications

Design of Linear Functional Observer for MIMO LTI systems

Design of Linear Functional Observer for MIMO LTI systems

Some new standpoints in the design of asymptotic functional linear observers

Designing of PID Controller for Discrete Time Linear System Using Balanced Approach Reduced Order Model

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