On application of the describing function method for optimization of feedback control systems

Lozowicki, Adam

doi:10.1002/(sici)1099-1239(199710)7:10<911::aid-rnc250>3.0.co;2-3

Cited by 5 publications

(4 citation statements)

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“…Thus, C contains 3 combinations with 2 rows. Combinations for the specified output frequency component (ω out = ω 1 ) can be obtained according to (20) with the condition r 1 + r 2 + r 3 …”

Section: Example Applicationmentioning

confidence: 99%

“…In order to compare computation times required to identify the values of unknowns of equations accord- ing to the number of frequency components in the analysis using single nonlinear function only the term is left in (22) to be y(t) 3 . If the truncation values are selected respectively as R x 1 = R x 2 = R x = 1, 2, .…”

Section: Example Applicationmentioning

confidence: 99%

“…Though it is a generalization of linear transfer functions to nonlinear case, mathematical computations and graphical interpretations are not as easy as in the linear case. Another frequency response approach, which is one dimensional in frequency but less general, is the describing function method based on harmonic balance [2][3][4][5]. Because of its practical applications in engineering, the harmonic balance has been a widespread method for the investigation of nonlinear frequency response characteristics.…”

Section: Introductionmentioning

confidence: 99%

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A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

2008

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A symbolic algorithm is developed for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the wellknown Duffing-Van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. The computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity are also investigated.

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Section: Example Applicationmentioning

confidence: 99%

Section: Example Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

2008

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“…The second method of analysing the non-linear systems is the harmonically linearization method. This method base on the idea of the describing function (compare (Łozowicki, 1997;Peyton Jones and Billings, 1991;Taylor, 1999)). The describing function of the non-linear element P i will be denoted by _ P i .…”

Section: High-precision State Feedback Control Systemsmentioning

confidence: 99%

High‐precision state feedback control systems for linear and non‐linear plants

2008

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Purpose -The purpose of this paper is to provide the high-precision robust control method for plants given by a high order of differential equations. This method is useful for linear and non-linear plants. Considering the problem of minimization of energy consumed in the world is very important and very actual. Design/methodology/approach -For theoretical solving of the problem, the functional analysis and methods of the Banach spaces H 2 and H 1 are used. Next the conditions for controllability with 1-accuracy are given. For the non-linear plants additionally two methods are used -method based on van der Schaft inequality and harmonically linearization. Findings -Provides state feedback control systems with sufficiently large gain (called Tytus feedback). Such systems can perform a high-degree accuracy (called there 1-accuracy). Practical implications -The considerations have many practical applications. For example, solving the problem of a high-precision robust control for a ship track-keeping and designing of a robust controller for a non-linear two-benchmark problem. Originality/value -This is an original theoretical method of obtaining a high-precision performance for feedback control systems. System presented in the paper enables controlling with 1-accuracy the stable or unstable plants P described by high-degree differential equations. Paper regards a robust control of stable as well as unstable plants with uncertainty.

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Robust Controller Design for a Non-linear Benchmark Problem

Lozowicki

1999

European Journal of Control

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On application of the describing function method for optimization of feedback control systems

Cited by 5 publications

References 0 publications

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

High‐precision state feedback control systems for linear and non‐linear plants

Robust Controller Design for a Non-linear Benchmark Problem

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