Publication detail

A New Approach to Stability Analysis of Nonlinear Control Systems

ŠVARC, I.

Czech title

Nový přístup k vyšetřování stability nelineárních řídicích systémů

English title

A New Approach to Stability Analysis of Nonlinear Control Systems

Type

conference paper

Language

en

Original abstract

Three methods for stability analysis of nonlinear control systems are introduced in this contribution: method of linearization, Lyapunov direct method and Popov criterion. Since stability analysis of nonlinear control systems is difficult task in engineering practice, these methods are made easier and tabulated. Method of linearization: The table includes the nonlinear equations and their linear approximation. Lyapunov direct method: The table contains Lyapunov functions for usually used equations second order. Popov criterion: The table will allow us to directly determine the stability of the nonlinear circuit with the transfer function G(s) and the nonlinearity that satisfies the slope k.

Czech abstract

V tomto příspěvku jsou uvedeny tři metody vyšetřování nelineárních systémů řízení: metoda linearizace, Ljapunovova přímá metoda a Popovovo kritérium. Protože vyšetřování stability nelineárních řídicích systémů je obtížná úloha pro inženýrskou praxi,tyto metody jsou vyjasněny a ztabelovány. Metoda linearizace: tabulka zahrnuje nelineární rovnice a jejich lineární aproximace. Ljapunovova přímá metoda: tabulka obsahuje Ljapunovovy funkce pro běžně užívané rovnice druhého řádu. Popovovo kritérium: tabulka nám umožní přímo určovat stabilitu nelineárního obvodu z přenosu G(s) a nelinearity, která má směrnici k.

English abstract

Three methods for stability analysis of nonlinear control systems are introduced in this contribution: method of linearization, Lyapunov direct method and Popov criterion. Since stability analysis of nonlinear control systems is difficult task in engineering practice, these methods are made easier and tabulated. Method of linearization: The table includes the nonlinear equations and their linear approximation. Lyapunov direct method: The table contains Lyapunov functions for usually used equations second order. Popov criterion: The table will allow us to directly determine the stability of the nonlinear circuit with the transfer function G(s) and the nonlinearity that satisfies the slope k.

Keywords in Czech

Rovnovážné stavy; stavová trajektorie; Ljapunovova metoda; Popovovo kritérium; linearizace; globální asymptotická stabilita.

Keywords in English

Equilibrium points; phase-plane trajectory; Lyapunov method; Popov criterion; linearization; GAS (global asymptotic stability).

RIV year

2005

Released

07.09.2005

Publisher

VŠB-Technical University of Ostrava, Faculty of Mechanical Engineering

Location

Ostrava

ISBN

80-248-0773-4

Book

Principia Cybernetica 2005

Edition number

1

Pages count

2

BIBTEX


@inproceedings{BUT18239,
  author="Ivan {Švarc},
  title="A New Approach to Stability Analysis of Nonlinear Control Systems",
  booktitle="Principia Cybernetica 2005",
  year="2005",
  month="September",
  publisher="VŠB-Technical University of Ostrava, Faculty of Mechanical Engineering",
  address="Ostrava",
  isbn="80-248-0773-4"
}