TELKOMNIKA Telecommunication, Computing, Electronics and Control
A novel two-polynomial criteria for higher-order systems stability boundaries detection and control
Dublin Core
Title
TELKOMNIKA Telecommunication, Computing, Electronics and Control
A novel two-polynomial criteria for higher-order systems stability boundaries detection and control
A novel two-polynomial criteria for higher-order systems stability boundaries detection and control
Subject
Absolute, Characteristic polynomial, Higher-order dynamics, Marginal stability, Stability boundaries
Description
There are many methods for identifying the stability of complex dynamic
systems. Routh and Hurwitz’s criterion is one of the earliest and commonly used analytical tools analysing the stability of dynamic systems. However, it requires tedious and lengthy derivations of all components of the Routh array to solve the stability problem. Therefore, it is not a simple method to define analytically, stability boundaries for the coefficients of the system characteristic equation. The proposed brand-new criterion is an effective alternative technique in identifying stability higher-order linear time-invariant dynamic system that binds the coefficients of the system characteristic polynomial at the stability boundaries by means of an additional single constant k. It defines the necessary and sufficient conditions for the absolute stability of higher-order dynamic systems. It also allows the analysing of the system’s precise marginal stability or marginal instability condition when the
roots are relocated on imaginary jω-axis of s-plane. The criterion proposed by the authors, in contrast to Routh criteria, simplifies the identification of maximum and minimum stability limits for any coefficient of the higher-order characteristic equation significantly. The derived in the paper stability boundary formulas for the polynomial coefficients are successfully used for the proportional integral derivative (PID) controller with single or multiple gains selections in closed-loop control systems.
systems. Routh and Hurwitz’s criterion is one of the earliest and commonly used analytical tools analysing the stability of dynamic systems. However, it requires tedious and lengthy derivations of all components of the Routh array to solve the stability problem. Therefore, it is not a simple method to define analytically, stability boundaries for the coefficients of the system characteristic equation. The proposed brand-new criterion is an effective alternative technique in identifying stability higher-order linear time-invariant dynamic system that binds the coefficients of the system characteristic polynomial at the stability boundaries by means of an additional single constant k. It defines the necessary and sufficient conditions for the absolute stability of higher-order dynamic systems. It also allows the analysing of the system’s precise marginal stability or marginal instability condition when the
roots are relocated on imaginary jω-axis of s-plane. The criterion proposed by the authors, in contrast to Routh criteria, simplifies the identification of maximum and minimum stability limits for any coefficient of the higher-order characteristic equation significantly. The derived in the paper stability boundary formulas for the polynomial coefficients are successfully used for the proportional integral derivative (PID) controller with single or multiple gains selections in closed-loop control systems.
Creator
N. Mir-Nasiri, Md. Hazrat Ali
Source
DOI: 10.12928/TELKOMNIKA.v18i6.16256
Publisher
Universitas Ahmad Dahlan
Date
October 2020
Contributor
Sri Wahyuni
Rights
ISSN: 1693-6930
Relation
http://journal.uad.ac.id/index.php/TELKOMNIKA
Format
PDF
Language
English
Type
Text
Coverage
TELKOMNIKA Telecommunication, Computing, Electronics and Control
Files
Collection
Citation
N. Mir-Nasiri, Md. Hazrat Ali, “TELKOMNIKA Telecommunication, Computing, Electronics and Control
A novel two-polynomial criteria for higher-order systems stability boundaries detection and control,” Repository Horizon University Indonesia, accessed April 11, 2025, https://repository.horizon.ac.id/items/show/4193.
A novel two-polynomial criteria for higher-order systems stability boundaries detection and control,” Repository Horizon University Indonesia, accessed April 11, 2025, https://repository.horizon.ac.id/items/show/4193.