scholarly journals Fast Stability Analysis for Proportional-Integral Controller in Interval Systems

2018 ◽  
Vol 2 (2) ◽  
pp. 111
Author(s):  
Hau Huu Vo
Keyword(s):  
Stability Analysis ◽  
Continuous Time ◽  
Polynomial Equation ◽  
Pi Controller ◽  
Time Interval ◽  
Stability Range ◽  
Proportional Integral ◽  
Polynomial Inequalities ◽  
Direct Technique ◽  
Computing Speed

The paper describes a technique for stability analysis of proportional-integral (PI) controller in linear continuous-time interval control systems. The stability conditions of Kharitonov's theorem together with related criterions, such as Routh-Hurwitz criterion for continuous-time systems, bring out sets of polynomial inequalities. The sets are very difficult to solve directly, especially in case of high-order systems. Direct technique was used for stability analysis without solving polynomial inequalities. Solving polynomial equation directly makes its computing speed low. In the paper, a set theory-based technique is proposed for finding robust stability range of PI controller without solving any Kharitonov polynomials directly Computation results confirm expected computing speed of the proposed technique.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

scholarly journals Time to Intervene: A Continuous-Time Approach to Network Analysis and Centrality

Psychometrika ◽  
2021 ◽  
Author(s):  
Oisín Ryan ◽  
Ellen L. Hamaker
Keyword(s):  
Network Analysis ◽  
Discrete Time ◽  
Continuous Time ◽  
Centrality Measures ◽  
Time Interval ◽  
Direct Effects ◽  
Network Approach ◽  
Var Models ◽  
Auto Regressive ◽  
Conceptual Shift

AbstractNetwork analysis of ESM data has become popular in clinical psychology. In this approach, discrete-time (DT) vector auto-regressive (VAR) models define the network structure with centrality measures used to identify intervention targets. However, VAR models suffer from time-interval dependency. Continuous-time (CT) models have been suggested as an alternative but require a conceptual shift, implying that DT-VAR parameters reflect total rather than direct effects. In this paper, we propose and illustrate a CT network approach using CT-VAR models. We define a new network representation and develop centrality measures which inform intervention targeting. This methodology is illustrated with an ESM dataset.

scholarly journals Period-Life of a Branching Process with Migration and Continuous Time

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 868
Author(s):  
Khrystyna Prysyazhnyk ◽  
Iryna Bazylevych ◽  
Ludmila Mitkova ◽  
Iryna Ivanochko
Keyword(s):  
Random Process ◽  
Generating Function ◽  
Continuous Time ◽  
Branching Process ◽  
Probability Generating Function ◽  
Time Interval ◽  
The Moment ◽  
First Time ◽  
Critical Branching Process ◽  
Number Of Particles

The homogeneous branching process with migration and continuous time is considered. We investigated the distribution of the period-life τ, i.e., the length of the time interval between the moment when the process is initiated by a positive number of particles and the moment when there are no individuals in the population for the first time. The probability generating function of the random process, which describes the behavior of the process within the period-life, was obtained. The boundary theorem for the period-life of the subcritical or critical branching process with migration was found.

scholarly journals Fuzzy Controller Applied to a Remote Energy Harvesting Emulation Platform

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5874 ◽  
Author(s):  
Marcelo Miranda Camboim ◽  
Juan Moises Maurício Villanueva ◽  
Cleonilson Protasio de Souza
Keyword(s):  
Renewable Energy ◽  
Energy Harvesting ◽  
Renewable Energy Sources ◽  
Setting Time ◽  
Pi Controller ◽  
Step Response ◽  
Energy Sources ◽  
Thermal Source ◽  
Proportional Integral ◽  
Thermal Pattern

In the last decades, a lot of effort has been made in order to improve the use of environmentally friendly and renewable energy sources. In a context of small energy usage, energy harvesting takes place and thermal energy sources are one of its main energy sources because there are several unused heat sources available in the environment that may be used as renewable energy sources. To rapidly evaluate the energy potential of such thermal sources is a hard task, therefore, a way to perform this is welcome. In this work, a thermal pattern emulation system to evaluate potential thermal source in a easy way is proposed. The main characteristics of the proposed system is that it is online and remote, that is, while the thermal-source-under-test is being measured, the system is emulating it and evaluating the generated energy remotely. The main contribution of this work was to replace the conventional Proportional Integral Derivative (PID) controller to a Fuzzy-Proportional Integral (PI) controller. In order to compare both controllers, three tests were carried out, namely: (a) step response, (b) perturbation test, (c) thermal emulation of the thermal pattern obtained from a potential thermal source: tree trucks. Experimental results show that the Fuzzy-PI controller was faster than the PID, achieving a setting time 41.26% faster, and also was more efficient with a maximum error 53% smaller than the PID.

scholarly journals Exponential Stability of Periodic Solution to Wilson-Cowan Networks with Time-Varying Delays on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jinxiang Cai ◽  
Zhenkun Huang ◽  
Honghua Bin
Keyword(s):  
Periodic Solution ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Time Scales ◽  
Continuous Time ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Time Varying

We present stability analysis of delayed Wilson-Cowan networks on time scales. By applying the theory of calculus on time scales, the contraction mapping principle, and Lyapunov functional, new sufficient conditions are obtained to ensure the existence and exponential stability of periodic solution to the considered system. The obtained results are general and can be applied to discrete-time or continuous-time Wilson-Cowan networks.

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