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Design of the oscillatory systems with the extremal dynamic properties

Górecki H., Zaczyk M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2014

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Vol. 62, nr 2

241--253

EN

In this article the problem of determination of such coefficients a1, a2, ..., an and eigenvalues s1, s2, ..., sn of the characteristic equation which yield required extremal values of the solution x(t) at the extremal value τ of time is solved. The extremal values of x(τ ) and τ are treated as functions of the roots s1, s2, ..., sn. The analytical formulae enable us to design the systems with prescribed dynamic properties. For solution of the problem the properties of symmetrical equations are used. The method is illustrated by an example of the equation of 4-th degree. The regions of the different kinds of the roots: real, with one pair of complex and two pairs of complex roots are illustrated. A practical problem is shown.

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Extension of first order predictive functional controllers to handle higher order internal models

Khadir M. T., Ringwood J. V.

International Journal of Applied Mathematics and Computer Science

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2008

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Vol. 18, no 2

229-239

EN

Predictive Functional Control (PFC), belonging to the family of predictive control techniques, has been demonstrated as a powerful algorithm for controlling process plants. The input/output PFC formulation has been a particularly attractive paradigm for industrial processes, with a combination of simplicity and effectiveness. Though its use of a lag plus delay ARX/ARMAX model is justified in many applications, there exists a range of process types which may present difficulties, leading to chattering and/or instability. In this paper, instability of first order PFC is addressed, and solutions to handle higher order and difficult systems are proposed. The input/output PFC formulation is extended to cover the cases of internal models with zero and/or higher order pole dynamics in an ARX/ARMAX form, via a parallel and cascaded model decomposition. Finally, a generic form of PFC, based on elementary outputs, is proposed to handle a wider range of higher order oscillatory and non-minimum phase systems. The range of solutions presented are supported by appropriate examples.

3

Przegląd metod wyznaczania parametrów dynamiki obiektów oscylacyjnych w oparciu o poimar odpowiedzi skokowej

Żuchowski A.

Pomiary Automatyka Kontrola

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2007

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R. 53, nr 9 bis

181--182

PL

Omówiono kilka prostych metod wyznaczania parametrów obiektów oscylacyjnych, wykorzystujących pomiar charakterystyki skokowej z uwzględnieniem zakresu ich stosowalności, zalet i wad. Stwarza ono pewną alternatywę i ułatwia wybór właściwej metody.

EN

The several methods for estimation of oscillatory system parameters have been presented. All considered methods use the result of measurement of system step response. The disadvantages and advantages as well as scope of application of methods under consideration have been deeply discussed. These comparative discussion seems to be helpful in decision process aimed at choice of best method for given circumstances.