A note on a relationship between a fractional-order continuous-time system pole configuration and its dynamics

2008 ◽  
Vol 42 (6-8) ◽  
pp. 789-806
Author(s):  
Piotr Ostalczyk
Keyword(s):  
Fractional Order ◽  
Continuous Time ◽  
Time System ◽  
Pole Configuration ◽  
Order Continuous ◽  
Continuous Time System

An Exact Discrete Analog to a Closed Linear First-Order Continuous-Time System with Mixed Sample

1987 ◽  
Vol 3 (1) ◽  
pp. 143-149 ◽  
Author(s):  
Terence D. Agbeyegbe
Keyword(s):  
Continuous Time ◽  
Discrete Model ◽  
Moving Average ◽  
Discrete Analog ◽  
Time System ◽  
First Order ◽  
Exact Discrete Model ◽  
Asymptotically Efficient ◽  
Order Continuous ◽  
Continuous Time System

This article deals with the derivation of the exact discrete model that corresponds to a closed linear first-order continuous-time system with mixed stock and flow data. This exact discrete model is (under appropriate additional conditions) a stationary autoregressive moving average time series model and may allow one to obtain asymptotically efficient estimators of the parameters describing the continuous-time system.

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.

Stability of real-time hybrid simulation involving time-varying delay and direct integration algorithms

2021 ◽  
pp. 107754632110016
Author(s):  
Liang Huang ◽  
Cheng Chen ◽  
Shenjiang Huang ◽  
Jingfeng Wang
Keyword(s):  
Real Time ◽  
Discrete Time ◽  
Continuous Time ◽  
Hybrid Simulation ◽  
Time Varying ◽  
Discrete Time System ◽  
Time System ◽  
Integration Algorithms ◽  
The Stability ◽  
Continuous Time System

Stability presents a critical issue for real-time hybrid simulation. Actuator delay might destabilize the real-time test without proper compensation. Previous research often assumed real-time hybrid simulation as a continuous-time system; however, it is more appropriately treated as a discrete-time system because of application of digital devices and integration algorithms. By using the Lyapunov–Krasovskii theory, this study explores the convoluted effect of integration algorithms and actuator delay on the stability of real-time hybrid simulation. Both theoretical and numerical analysis results demonstrate that (1) the direct integration algorithm is preferably used for real-time hybrid simulation because of its computational efficiency; (2) the stability analysis of real-time hybrid simulation highly depends on actuator delay models, and the actuator model that accounts for time-varying characteristic will lead to more conservative stability; and (3) the integration step is constrained by the algorithm and structural frequencies. Moreover, when the step is small, the stability of the discrete-time system will approach that of the corresponding continuous-time system. The study establishes a bridge between continuous- and discrete-time systems for stability analysis of real-time hybrid simulation.

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