Stability of zeros of discrete-time multivariable systems with GSHF

Int. J. Control Autom. Syst.

2015

Self Cite

It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems. When the usual digital control with zero-order hold (ZOH) or fractionalorder hold (FROH) input is used, unstable zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than two is of minimum phase. This paper investigates the zero dynamics, as the sampling period tends to zero, of sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time nonlinear plant and a sampler in cascade. More precisely, we show how an approximate sampled-data model can be obtained for nonlinear systems with two special GSHF cases such that sampled zero dynamics of the resulting model can be arbitrarily placed. Further, two GSHFs with appropriate parameters provide nonlinear zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. It is also shown that the intersample behavior arising from the multirate input can be localised by appropriately selecting the design parameters based on the stability condition of the zero dynamics. The results presented here generalize well-known ideas from the linear to nonlinear cases.

Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Comparative study of discretization zero dynamics behaviors in two multirate cases

Int. J. Control Autom. Syst.

2015

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“…Perhaps the first attempt to study discrete system zero dynamics was given byÅström and coworkers [1], who described the asymptotic behavior of the discrete-time zero dynamics for fast sampling rate when the original continuous-time plant is discretized with ZOH. More research for discrete zero dynamics has been shown in the past decade, and these known results present the asymptotic characterization of zero dynamics for the discretized systems without time delay [8][9][10][11][12][13][14][15]. However, time delay of controlled systems inherently exists in many mechanical engineering applications and therefore must be integrated into system models.…”

Section: Introductionmentioning

confidence: 99%

Improvement of the Asymptotic Properties of Zero Dynamics for Sampled-Data Systems in the Case of a Time Delay

Abstract and Applied Analysis

Zhong

et al. 2014

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It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems, and deeply limits the achievable control performance. When a continuous-time system with relative degree greater than or equal to three is discretized using a zero-order hold (ZOH), at least one of the zero dynamics of the resulting sampled-data model is obviously unstable for sufficiently small sampling periods, irrespective of whether they involve time delay or not. Thus, attention is here focused on continuous-time systems with time delay and relative degree two. This paper analyzes the asymptotic behavior of zero dynamics for the sampled-data models corresponding to the continuous-time systems mentioned above, and further gives an approximate expression of the zero dynamics in the form of a power series expansion up to the third order term of sampling period. Meanwhile, the stability of the zero dynamics is discussed for sufficiently small sampling periods and a new stability condition is also derived. The ideas presented here generalize well-known results from the delay-free control system to time-delay case.

“…These facts sparked interest in other holds such as multirate sampling control and digital control with the generalized sampled-data hold function (GSHF) (Kabamba, 1987;Chan, 1998;Liang and Ishitobi, 2004a;Yuz et al, 2004;Liang et al, 2010;Ugalde et al, 2012). Though some deficiencies such as poor intersample behavior in the case of a GSHF cannot be avoided, the GSHF can be used to solve many more ambitious control problems for linear systems as long as it is formulated exclusively in intersample terms.…”

Section: Introductionmentioning

confidence: 99%

Improving the stability of discretization zeros with the Taylor method using a generalization of the fractional-order hold

International Journal of Applied Mathematics and Computer Science

Zhang

et al. 2014

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Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.