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[nazev] => Řešení diferenciálních a diferenčních rovnic metodou Z - transformace
[nazev_orig] => Řešení diferenciálních a diferenčních rovnic metodou Z - transformace
[duvernost_udaju_id] => S
[popis] => První část příspěvku se zabývá diskretizací diferenciálních rovnic přibližnými metodami, které využívající různých aproximací jako je náhrada derivací diferencemi. V diferenciální rovnici se nahradí derivace proměnných jejich diferencemi a tím se převedou diferenciální rovnice na diferenční. Druhá část pak pojednává o jedné z méně používaných metod pro řešení diferenčních rovnic a to použitím z-transformace. Tato část obsahuje i převáděcí vztahy z Laplaceových přenosů na z- přenosy a vhodný slovník pro zpětnou z-transformaci.
[popis_orig] => První část příspěvku se zabývá diskretizací diferenciálních rovnic přibližnými metodami, které využívající různých aproximací jako je náhrada derivací diferencemi. V diferenciální rovnici se nahradí derivace proměnných jejich diferencemi a tím se převedou diferenciální rovnice na diferenční. Druhá část pak pojednává o jedné z méně používaných metod pro řešení diferenčních rovnic a to použitím z-transformace. Tato část obsahuje i převáděcí vztahy z Laplaceových přenosů na z- přenosy a vhodný slovník pro zpětnou z-transformaci.
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[identifikator] => ISBN 80-227-1995-1
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[citace_text] => ŠVARC, I. Řešení diferenciálních a diferenčních rovnic metodou Z - transformace. In 3rd International Conference Aplimat. Bratislava: Slovak University of Technology in Bratislava, 2004. 9 s. ISBN: 80-227-1995-1.
[citace_html] => ŠVARC, I. Řešení diferenciálních a diferenčních rovnic metodou Z - transformace. In 3rd International Conference Aplimat. Bratislava: Slovak University of Technology in Bratislava, 2004. 9 s. ISBN: 80-227-1995-1.
[citace_rtf] =>
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author="Ivan {Švarc}",
title="Řešení diferenciálních a diferenčních rovnic metodou Z - transformace",
booktitle="3rd International Conference Aplimat",
year="2004",
pages="9",
publisher="Slovak University of Technology in Bratislava",
address="Bratislava",
isbn="80-227-1995-1"
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[nazev_en] => Solution of Differential and Difference Equations by Z - Transform
[popis_en] => The first part of contribution contains discretizing the differential equations. Difference equations can also be obtained by discretizing differential equations Here a first order differential is approximated by a first order difference, a second order differential by a second order difference, etc. The second part of contribution offers solution of difference equations by z-transform. It solves the link between s and z. It contains the special z-transform table for inverse z-transform.
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[popis] => Discretization is necessary for the analysis and design of discrete-time systems. It is also useful for simulating continuous-time control systems on the digital computer. One of the simplest ways of discretizing or approximating a continuous-time plant is numerical approximation of differential equations. Difference equations can be obtained by discretizing differential equations – it is the first part of this contribution. The other way of discretization is discretization by z transformation of transfer function G(s). In this contribution is shown Euler’s method and bilinear method of this transformation.
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[ins_ts] => 2025-09-22
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[identifikator] => ISBN 9958-617-21-8
[identifikator_popis] => ISBN - Trends in the Development of Machinery and Associated Technology
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[citace_text] => ŠVARC, I. Solutions of Continuous-Time Systems by the Discrete Methods. In Trends in the Development of Machinery and Associated Technology. Zenica: DOM STAMPE Zenica, 2004. 5 p. ISBN: 9958-617-21-8.
[citace_html] => ŠVARC, I. Solutions of Continuous-Time Systems by the Discrete Methods. In Trends in the Development of Machinery and Associated Technology. Zenica: DOM STAMPE Zenica, 2004. 5 p. ISBN: 9958-617-21-8.
[citace_rtf] =>
[citace_bibtex] => @inproceedings{BUT12527,
author="Ivan {Švarc}",
title="Solutions of Continuous-Time Systems by the Discrete Methods",
booktitle="Trends in the Development of Machinery and Associated Technology",
year="2004",
pages="5",
publisher="DOM STAMPE Zenica",
address="Zenica",
isbn="9958-617-21-8"
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[popis_en] => Discretization is necessary for the analysis and design of discrete-time systems. It is also useful for simulating continuous-time control systems on the digital computer. One of the simplest ways of discretizing or approximating a continuous-time plant is numerical approximation of differential equations. Difference equations can be obtained by discretizing differential equations – it is the first part of this contribution. The other way of discretization is discretization by z transformation of transfer function G(s). In this contribution is shown Euler’s method and bilinear method of this transformation.
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[nazev] => STABILITA NELINEÁRNÍCH SYSTÉMŮ
[nazev_orig] => STABILITA NELINEÁRNÍCH SYSTÉMŮ
[duvernost_udaju_id] => S
[popis] => Řídicí systémy v energetických zařízeních obvykle obsahují nelineární prvky. Proto není možno pro jejich vyšetřování použít lineárních metod, jmenovitě metod pro vyšetřování stability lineárních spojitých systémů. Metody pro vyšetřování nelineárních systémů patří k obtížným úkolům inženýrské praxe. Cílem tohoto příspěvku je jejich zjednodušení do té míry, aby se staly snadno dostupné a použitelné pro technickou praxi. Jsou zde uvedeny tři nejpoužívanější metody a všechny tři jsou dovedeny do přehledných tabulek, z kterých se dá zjistit, zda je či není vyšetřovaný systém stabilní a to bez speciálních znalostí ze řízení systémů.
[popis_orig] => Řídicí systémy v energetických zařízeních obvykle obsahují nelineární prvky. Proto není možno pro jejich vyšetřování použít lineárních metod, jmenovitě metod pro vyšetřování stability lineárních spojitých systémů. Metody pro vyšetřování nelineárních systémů patří k obtížným úkolům inženýrské praxe. Cílem tohoto příspěvku je jejich zjednodušení do té míry, aby se staly snadno dostupné a použitelné pro technickou praxi. Jsou zde uvedeny tři nejpoužívanější metody a všechny tři jsou dovedeny do přehledných tabulek, z kterých se dá zjistit, zda je či není vyšetřovaný systém stabilní a to bez speciálních znalostí ze řízení systémů.
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[identifikator_popis] => ISBN - Control of Power Systems'04
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[citace_text] => ŠVARC, I. STABILITA NELINEÁRNÍCH SYSTÉMŮ. In Control of Power Systems'04. Štrbské Pleso, High Tatras: Slovak Universitz of Technologz in Bratislava, 2004. 8 s. ISBN: 80-227-2059-3.
[citace_html] => ŠVARC, I. STABILITA NELINEÁRNÍCH SYSTÉMŮ. In Control of Power Systems'04. Štrbské Pleso, High Tatras: Slovak Universitz of Technologz in Bratislava, 2004. 8 s. ISBN: 80-227-2059-3.
[citace_rtf] =>
[citace_bibtex] => @inproceedings{BUT12534,
author="Ivan {Švarc}",
title="STABILITA NELINEÁRNÍCH SYSTÉMŮ",
booktitle="Control of Power Systems'04",
year="2004",
pages="8",
publisher="Slovak Universitz of Technologz in Bratislava",
address="Štrbské Pleso, High Tatras",
isbn="80-227-2059-3"
}
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[poznamka_metriky] =>
[nazev_en] => Stability of Nonlinear Systems
[popis_en] => 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, this 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.
Then it is easy to find out the nonlinear system is or is not stable.
[klicova_slova_en] => Nonlinear control system, equilibrium points, phase-plane trajectory, Lyapunov method, Popov criterion; modified frequency response; linearization, global asymptotic stability (GAS).
[vysledek_datum] => 2004-01-01T00:00:00+01:00
)
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(
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[nazev] => Stability Analysis of Nonlinear Control Systems
[nazev_orig] => Stability Analysis of Nonlinear Control Systems
[duvernost_udaju_id] => S
[popis] => The most powerful methods of systems analysis have been developed for linear control systems. For a linear control system, all the relationships between the variables are linear differential equations, usually with constant coefficients. But actual control systems usually contain some nonlinear elements.
Three methods for stability analysis of nonlinear control systems will be introduced in this lecture: 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.
In the lecture we will show how the equations for nonlinear elements may be linearized. But the result is applicable only in a small enough region. When all the roots of the characteristic equation are located in the left half-plane, the system is stable.
We can construct the table includes the nonlinear equations and their the linear approximation. Then it is easy to find out if the nonlinear system is or is not stable.
Lyapunov direct method: Lyapunovs method is a very powerful tool for studying the stability of equilibrium points. However, there is drawback of the method that we should be aware of. There is no systematic method for finding a Lyapunov function for a given system. We would like to eliminate the first drawback of Lyapunovs method. This is the table of Lyapunovs functions .
Popov criterion: The Popov criterion is considered as one of the most appropriate criteria for nonlinear systems and it can be compared with the Nyquist criterion for linear systems. The sufficient condition for stability of nonlinear circuit is that the plot of G(s) should lie entirely to the right of the Popov line which crosses the real axis at -1 divided k at a slope 1 divided q (q is an arbitrary real number) . We can construct the table that 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.
[popis_orig] => The most powerful methods of systems analysis have been developed for linear control systems. For a linear control system, all the relationships between the variables are linear differential equations, usually with constant coefficients. But actual control systems usually contain some nonlinear elements.
Three methods for stability analysis of nonlinear control systems will be introduced in this lecture: 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.
In the lecture we will show how the equations for nonlinear elements may be linearized. But the result is applicable only in a small enough region. When all the roots of the characteristic equation are located in the left half-plane, the system is stable.
We can construct the table includes the nonlinear equations and their the linear approximation. Then it is easy to find out if the nonlinear system is or is not stable.
Lyapunov direct method: Lyapunovs method is a very powerful tool for studying the stability of equilibrium points. However, there is drawback of the method that we should be aware of. There is no systematic method for finding a Lyapunov function for a given system. We would like to eliminate the first drawback of Lyapunovs method. This is the table of Lyapunovs functions .
Popov criterion: The Popov criterion is considered as one of the most appropriate criteria for nonlinear systems and it can be compared with the Nyquist criterion for linear systems. The sufficient condition for stability of nonlinear circuit is that the plot of G(s) should lie entirely to the right of the Popov line which crosses the real axis at -1 divided k at a slope 1 divided q (q is an arbitrary real number) . We can construct the table that 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.
[klicova_slova] => Popov criterion; Lyapunov criterion; linearization; transfer function.
[klicova_slova_orig] => Popov criterion; Lyapunov criterion; linearization; transfer function.
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[citace_text] => ŠVARC, I. Stability Analysis of Nonlinear Control Systems. In Summer School on Control Theory and Applications. Graz: Graz University of Technology, 2004. p. 29-29.
[citace_html] => ŠVARC, I. Stability Analysis of Nonlinear Control Systems. In Summer School on Control Theory and Applications. Graz: Graz University of Technology, 2004. p. 29-29.
[citace_rtf] =>
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author="Ivan {Švarc}",
title="Stability Analysis of Nonlinear Control Systems",
booktitle="Summer School on Control Theory and Applications",
year="2004",
pages="29--29",
publisher="Graz University of Technology",
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[nazev_en] => Stability Analysis of Nonlinear Control Systems
[popis_en] => The most powerful methods of systems analysis have been developed for linear control systems. For a linear control system, all the relationships between the variables are linear differential equations, usually with constant coefficients. But actual control systems usually contain some nonlinear elements.
Three methods for stability analysis of nonlinear control systems will be introduced in this lecture: 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.
In the lecture we will show how the equations for nonlinear elements may be linearized. But the result is applicable only in a small enough region. When all the roots of the characteristic equation are located in the left half-plane, the system is stable.
We can construct the table includes the nonlinear equations and their the linear approximation. Then it is easy to find out if the nonlinear system is or is not stable.
Lyapunov direct method: Lyapunovs method is a very powerful tool for studying the stability of equilibrium points. However, there is drawback of the method that we should be aware of. There is no systematic method for finding a Lyapunov function for a given system. We would like to eliminate the first drawback of Lyapunovs method. This is the table of Lyapunovs functions .
Popov criterion: The Popov criterion is considered as one of the most appropriate criteria for nonlinear systems and it can be compared with the Nyquist criterion for linear systems. The sufficient condition for stability of nonlinear circuit is that the plot of G(s) should lie entirely to the right of the Popov line which crosses the real axis at -1 divided k at a slope 1 divided q (q is an arbitrary real number) . We can construct the table that 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.
[klicova_slova_en] => Popov criterion; Lyapunov criterion; linearization; transfer function.
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[popis] => Velmi významnou roli v technické diagnostice hraje frekvenční analýza, která se opírá především o rychlou Fourierovu transformaci. Z výsledků frekvenční analýzy je možno určit nejen okamžitý technický stav sledovaného objektu, ale také příčiny případných problémů a zdroje blížící se poruchy. Tento článek se pokouší ukázat některé možnosti a výsledky přiblížení této problematiky ve výuce s využitím vhodných modelů, čímž volně navazuje na podobný článek, přednesený na této konferenci před dvěma lety.
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[klicova_slova_orig] => Analyzátor, frekvenční analýza, frekvenční spektrum, technická diagnostika, vibrace
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[popis] => Příspěvek se zamýšlí nad požadavky na měřicí techniku a její úlohu v diagnostice, která se v dnešní době stále výrazněji uplatňuje ve všech technických oborech. V řadě případů se uplatní technická diagnostika v podobě trvalého sledování stavu strojů, v jiných se využívá metod tzv. proaktivní údržby apod. Ve všech aplikacích je ale základem posouzení skutečného stavu sledovaného zařízení především kvalitní měřicí technika.
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[popis_en] => The paper deals with requirements on measurement equipment and his part in diagnostics, which is invariable bolder asserted on all technical branches in the time. Technical diagnostics is asserted in series cases as condition monitoring of machines, in other cases it is utilizing of methods so-called active maintenance etc. In all applications base is of real condition review of monitoring equipment quality measurement technique above all.
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[citace_text] => VDOLEČEK, F. Nejistoty akustických měření v širších souvislostech. In Akustika 2004. České Budějovice: Studio D Akustika s.r.o. České Budějovice, 2004. 8 s. ISBN: 80-239-2311-0.
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author="František {Vdoleček}",
title="Nejistoty akustických měření v širších souvislostech",
booktitle="Akustika 2004",
year="2004",
number="1.",
pages="8",
publisher="Studio D Akustika s.r.o. České Budějovice",
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[nazev_en] => Acoustic Measurement Uncertainties in Wider Relations
[popis_en] => This paper is intended beyond problems expression uncertainties in acoustic measurements. The uncertainties are monitoring in two angle of vision. Primary view is composed applicable accessing and methods for uncertainty analysis in acoustics, secondary it is cause exercise of uncertainties, as these are resulting out of new harmonized metrology legislative, which was accepted in last year.
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[popis] => The automation and technical diagnostics are inherent parts of our everyday live. The automation is most specifying position in diagnostics branch just as automation cannot perform less of diagnostics in the time. Close relations and interference are between diagnostics and control systems in both directions and both branches have very many common attributes. The paper is required present in following articles some this basic realities.
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[vlozil] => Informační systém Automat
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[citace_text] => VDOLEČEK, F. Automation and Diagnostics. In Mechanical Engineering 2004. Bratislava: SjF STU v Bratislavě, 2004. 4 p. ISBN: 80-227-2105-0.
[citace_html] => VDOLEČEK, F. Automation and Diagnostics. In Mechanical Engineering 2004. Bratislava: SjF STU v Bratislavě, 2004. 4 p. ISBN: 80-227-2105-0.
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[title] => Řešení diferenciálních a diferenčních rovnic metodou Z - transformace
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[year] => 2004
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Publication results Year: 2004
ŠVARC, I.
Publication results Year: 2004
ŠVARC, I.
Showed 376–390 from 2086 results