Delayed feedback control of uncertain systems with time-varying input delay

Yue, Dong; Han, Qing‐Long

doi:10.1016/j.automatica.2004.09.006

Cited by 249 publications

(173 citation statements)

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“…The reduction transformation method for the input delay system (1) was suggested by Kwon and Pearson [9]. An extension to time-varying systems can be found in [10]. Consider a linear transformation from ( ) x t and u(α),…”

Section: An Overview Of Reduction Transformationmentioning

confidence: 99%

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Stabilization of linear systems with distributed input delay using reduction transformation

Choon

2011

Chin. Sci. Bull.

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We propose a new stabilization method for linear systems with distributed input delay via reduction transformation and Riccati equation approach. In the presented stabilization scheme, the gain matrix of controller is constructed by the well-known linear control technique for delay-free systems. The transformation kernel matrix can be determined by solving the non-symmetric matrix Riccati equation backward with the boundary condition. When point delay systems are considered, it will be shown that the proposed control law degenerates to the standard one for input delay systems.delay systems, delay-free systems, distributed delay, reduction transformation, riccati equation Citation:Choon K A. Stabilization of linear systems with distributed input delay using reduction transformation. Chinese Sci Bull, 2011Bull, , 56: 1413Bull, −1416Bull, , doi: 10.1007 In industrial processes, time delays often occur in the transmission of information or material between different parts of a system. The presence of time delays causes serious deterioration on the stability and performance of the system and considerable researches have been done on the control problems of time delay systems [1,2]. Time delay systems are a special case of infinite dimensional systems which have an infinite number of poles. This feature makes the control of time delay systems a difficult task to handle. The easiest way is to reduce time delay systems to delayfree systems and then apply the well developed control techniques for the finite dimensional systems. The Smith predictor may be one of the most well known delay compensation methods utilizing this concept. Although a number of improved versions of the Smith predictor have been proposed by many researchers, the Smith predictor methods suffer from some inherent shortcomings. First, the Smith predictor cannot be applied to unstable systems [3]. The second drawback is that the initial state of the system is ignored in the Smith predictor method. The degradation of the performance is an inevitable result, when it is applied to the systems with nonzero initial conditions. The third shortcoming is the lack of robustness. The performance of the Smith predictor method is sensitive to the accuracy of the model of the system and time delay. It also suffers from sluggish responses to disturbances. To overcome the above mentioned difficulties, a number of improved versions of the Smith predictor have been proposed by many researchers [4]. The reduction transformation method is a different approach from the state-space setting to overcome these problems. The explicit reduction transformation method of input delay systems was suggested by Kwon and Pearson [5]. In [5], Kwon and Pearson employed the receding horizon method to input delay systems, where an unexpected good stabilization method (reduction transformation) was founded. The reduction transformation method was extended to the output-feedback case in [6], where a delay-free observer was introduced. This observer can directly estimate the linear funct...

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Section: An Overview Of Reduction Transformationmentioning

confidence: 99%

“…Also, the reduction transformation technique was used to design a robust controller for multiple input delayed systems with parametric uncertainties in [9]. The authors in [10] extended the reduction transformation method to linear systems with time-varying input delay. Most results on the reduction transformation were restricted to systems with point delay.…”

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confidence: 99%

Stabilization of linear systems with distributed input delay using reduction transformation

Choon

2011

Chin. Sci. Bull.

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“…En caso de existir discrepancia entre el modelo original y aproximado, el sistema en bucle cerrado no elimina los retardos de la ecuación característica. En esteúltimo trabajo, y en [134], se estudia la aplicación de la ley de control FSA sobre sistemas con incertidumbres.…”

Section: El Retardo Considerado En La Ley De Control Fsa Coincide Conunclassified

“…Esquemas de compensación de tiempo muerto (DTC), cuyo objetivo es eliminar el retardo de la ecuación característica en bucle cerrado incorporando de algún modo la predicción futura del estado en base al modelo del proceso. Cabe distinguir al respecto dos soluciones bien conocidas en la literatura: El Predictor de Smith y sus modificaciones [114,97,93] (para retardos constantes) y la técnica de Asignación de Espectro Finito (FSA), [83,122,134,141]. En [49,93] se puede encontrar numerosas aplicaciones experimentales del esquema de control basado en las técnicas DTC.…”

Section: Introductionunclassified

“…Un análisis detallado de estos métodos y sus modificaciones revelan que todos ellos utilizan, de un modo implícito o explícito, la predicción del estado, con el fin de contrarrestar el efecto del retardo y por ende obtener la respuesta deseada. La característica más destacada del controlador basado en predictor es que, en ausencia de incertidumbres en el modelo y para retardo constante y conocido, el comportamiento en bucle cerrado es similar al sistema equivalente libre de retardo [134], [94], [48].…”

Section: Introductionunclassified

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