Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slo...Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which sire-plifies the time-delay system the relation is discussed for into a delay-free one. Firstly, two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.展开更多
Optimal ReplacementVariables(ORV)is amethod for approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.An earlier...Optimal ReplacementVariables(ORV)is amethod for approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.An earlier version of ORV[1]had some issues,including limited accuracy and in some rare cases,instability.Here we present a newversion of ORV,inspired by the linear quadratic regulator problemof control theory,which provides better accuracy,a guarantee of stability and is in some ways easier to use.展开更多
基金supported by the National Natural Science Foundation of China ( 10532050, 10702024 and 10702025) the Doctoral Fund of MOE of China (20070287029)
文摘Time delays in the feedback control often dete- riorate the control performance or even cause the instability of a dynamic system. This paper presents a control strategy for the dynamic system with a constant or a slowly time-varying input delay based on a transformation, which sire-plifies the time-delay system the relation is discussed for into a delay-free one. Firstly, two existing reduction-based linear quadratic controls. One is continuous and the other is discrete. By extending the relation, a new reduction-based control is then developed with a numerical algorithm presented for practical control implementation. The controller suggested by the proposed method has such a promising property that it can be used for the cases of different values of an input time delay without redesign of controller. This property provides the potential for stabilizing the dynamic system with a time-varying input delay. Consequently, the application of the proposed method to the dynamic system with a slowly time-varying delay is discussed. Finally, numerical simulations are given to show the efficacy and the applicability of the method.
基金the support of this work under RGC grant HKBU 200910。
文摘Optimal ReplacementVariables(ORV)is amethod for approximating a large system of ODEs by one with fewer equations,while attempting to preserve the essential dynamics of a reduced set of variables of interest.An earlier version of ORV[1]had some issues,including limited accuracy and in some rare cases,instability.Here we present a newversion of ORV,inspired by the linear quadratic regulator problemof control theory,which provides better accuracy,a guarantee of stability and is in some ways easier to use.
