Asymptotic Properties of Zeros of Sampled-Data Systems for Continuous-Time Plants With Nondecouplability

2013 ◽  
Author(s):  
Mitsuaki Ishitobi ◽  
Sadaaki Kunimatsu
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Asymptotic Properties ◽  
Sampling Period ◽  
Approximate Expression ◽  
Zero Order ◽  
Data Systems ◽  
Sampled Data ◽  
Static State ◽  
Power Series Expansions

When a continuous-time linear system is discretized using a hold, stability of poles are preserved. However, the transformations of zeros are much more complicated and the number of the zeros increases in some cases in the discretization process. This paper is concerned with the zeros of a sampled-data model resulting from a continuous-time multivariable system which is not decouplable by static state feedback and has all of the relative degrees one. Two cases of a zero-order hold and a fractional-order hold are treated. An approximate expression of the zeros is given as power series expansions with respect to a sampling period in the zero-order hold case. Further, the limiting zeros are analyzed in the fractional-order hold case. Then, the advantage of the fractional-order hold to the zero-order hold is discussed from the viewpoint of stability of the zeros.

scholarly journals Improving the Asymptotic Properties of Discrete System Zeros in Fractional-Order Hold Case

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Cheng Zeng ◽  
Shan Liang ◽  
Yingying Su
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Discrete System ◽  
Order Term ◽  
Asymptotic Properties ◽  
Sampling Period ◽  
Approximate Expression ◽  
Sampled Data ◽  
Form Representation ◽  
Time Systems

Remarkable improvements in the asymptotic properties of discrete system zeros may be achieved by properly adjusted fractional-order hold (FROH) circuit. This paper analyzes asymptotic properties of the limiting zeros, as the sampling periodTtends to zero, of the sampled-data models on the basis of the normal form representation of the continuous-time systems with FROH. Moreover, when the relative degree of the continuous-time system is equal to one or two, an approximate expression of the limiting zeros for the sampled-data system with FROH is also given as power series with respect to a sampling period up to the third-order term. And, further, the corresponding stability conditions of the sampling zeros are discussed for fast sampling rates. The ideas of the paper here provide a more accurate approximation for asymptotic zeros, and certain known achievements on asymptotic behavior of limiting zeros are shown to be particular cases of the results presented.

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

2014 ◽  
Vol 24 (4) ◽  
pp. 745-757 ◽  
Author(s):  
Cheng Zeng ◽  
Shan Liang ◽  
Yuzhe Zhang ◽  
Jiaqi Zhong ◽  
Yingying Su
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Order Term ◽  
Sampling Period ◽  
Approximate Expression ◽  
Relative Degree ◽  
Sampled Data ◽  
Time System ◽  
The Stability ◽  
Continuous Time System

Abstract 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.

Continuous-time deadbeat control for sampled-data systems

1996 ◽  
Vol 41 (10) ◽  
pp. 1478-1481 ◽  
Author(s):  
H. Katoh ◽  
Y. Funahashi
Keyword(s):  
Continuous Time ◽  
Data Systems ◽  
Sampled Data ◽  
Deadbeat Control

Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 101-109 ◽  
Author(s):  
E. Polak
Keyword(s):  
Pulse Width ◽  
Phase Plane ◽  
Sampling Period ◽  
Second Order ◽  
Data Systems ◽  
Sampled Data ◽  
Relay System ◽  
Pulse Width Modulated ◽  
Minimal Time ◽  
Time Control

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.

scholarly journals Event-Based Sampled-Data Average Consensus

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Hang Gong ◽  
Fangke Wu ◽  
Runzhi Liu ◽  
Xin Jin ◽  
Wei Zhou ◽  
...  
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Sampling Period ◽  
Graph Laplacian ◽  
Systematic Investigation ◽  
Lyapunov Theory ◽  
Matrix Analysis ◽  
Sampled Data ◽  
Average Consensus ◽  
Event Triggered

This study addresses one of the most essential distributed control problems in multiagent systems, called the average consensus issue, using a new event-triggered sampling control perspective. Although the continuous-time sampling for average consensus has provided good results currently, a systematic investigation into the continuous-time agent dynamics with sampled-data control inputs under an event-triggered mechanism is critically lacking. The problem considered in this paper can be formulated into an average consensus problem of hybrid systems. The method considers three types of control schemes, among which periodic sampling is integrant. The first scheme is a classical sampling controller reinvestigated through a lemma. The second scheme realizes aperiodic control update as well as periodic communication, while the third scheme achieves both aspects aperiodically. Corresponding sufficient conditions of the aforementioned three schemes are derived such that the asymptotic stability of systems is ensured by using algebraic graph theory, matrix analysis, and Lyapunov theory. The constraints for the allowed sampling period, event parameter, and maximum eigenvalue of graph Laplacian are explicitly derived. Moreover, the potential Zeno behavior of agents due to the sampling control theory is avoided. Thus, a digitally implementable technique is provided. Finally, some numerical examples are provided to verify the effectiveness of the proposed theoretical analysis.

Sampled-Data Systems, Revisited: Reflections, Recollections, and Reassessments

1980 ◽  
Vol 102 (4) ◽  
pp. 208-217 ◽  
Author(s):  
E. I. Jury
Keyword(s):  
Digital Signal ◽  
Sampling Period ◽  
Data Systems ◽  
Sampled Data ◽  
Recent Emergence ◽  
New Development ◽  
Technological Developments ◽  
Discrete Interval ◽  
Discrete Theory ◽  
The Impact

A review of the progress made in sampled-data systems during the last thirty years is presented in this paper. In particular the impact of the discrete theory on the continuous counterpart is mentioned. Additionally, the limiting process of discrete system theory when the discrete interval (or the sampling period) goes to zero, is discussed. Recent emergence of digital signal processing and digital filters as an aftermath of sampled-data systems is brought into focus as well as the technological developments which aided in this new development. The paper concludes with a critical view of the past achievements in this field as well as indications of possible future developments.

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