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.

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 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.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Cheng Zeng ◽  
Shan Liang ◽  
Jiaqi Zhong ◽  
Yingying Su
Keyword(s):  
Time Delay ◽  
Continuous Time ◽  
Order Term ◽  
Power Series Expansion ◽  
Relative Degree ◽  
Zero Dynamics ◽  
Sampled Data ◽  
Major Barrier ◽  
Continuous Time Systems ◽  
Time Systems

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.

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.

Sign in / Sign up

Export Citation Format

Share Document