Characteristic polynomials of positive and minimal-phase electrical circuits

• Autorzy: Kaczorek T.

Identyfikatory

DOI

niezależność wielomianu charakterystycznego

Warianty tytułu

PL

Wielomiany charakterystyczne dodatnich i minimalnofazowych obwodów elektrycznych

• Języki publikacji: EN

Abstrakty

EN

Characteristic polynomials of positive and minimal-phase electrical circuits are addressed. It is shown that the characteristic polynomials of the electrical circuits are independent of the choice of their reference mesh and of their reference node. Conditions are established under which the positive electrical circuits have real eigenvalues and are minimal-phase linear systems. Sufficient conditions for cancelation of zeros and poles of minimal-phase electrical circuits are given.

PL

W pracy wykazano, że wielomiany charakterystyczne obwodów elektrycznych są niezależne od wyboru oczka odniesienia w metodzie oczkowej i węzła odniesienia w metodzie węzłowej analizy tych obwodów. Podano warunki przy spełnieniu których dodatnie obwody elektryczne mają rzeczywiste wartości własne i są minimalnofazowymi obwodami elektrycznymi. Podano również warunki wystarczające skracania zer i biegunów w minimalnofazowych obwodach elektrycznych. Rozważania zostały zilustrowane przykładami dodatnich i minimalnofazowych obwodów elektrycznych.

Słowa kluczowe

EN

minimal phase; electrical circuit; cancellation; pole; independence of characteristic polynomial

PL

minimalnofazowość; dodatniość; obwód elektryczny; biegun; niezależność wielomianu charakterystycznego

• Wydawca: Wydawnictwo SIGMA-NOT
• Czasopismo: Przegląd Elektrotechniczny
• Rocznik: 2016
• Tom: R. 92, nr 6
• Strony: 79--85
• Opis fizyczny: Bibliogr. 36 poz., rys.

Twórcy

autor

Kaczorek T.

• Politechnika Białostocka, Wydział Elektryczny, ul. Wiejska 45D, 15-351 Białystok

Bibliografia

• [1] Benvenuti L., Farina L., A tutorial on the positive realization problem. IEEE Trans. on Automatic Control, 49 (2004), no. 5, 651-664.
• [2] Cholewicki T., Matrix Analysis of Electrical Circuits. PWN, Warszawa-Wrocław, 1958.
• [3] Farina L., Rinaldi S., Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
• [4] Kaczorek T., A class of positive and stable time-varying electrical circuits. Electrical Review, 91 (2015), no. 5, 121-124.
• [5] Kaczorek T., A modified state variables diagram method for determination of positive realizations of linear continuoustime systems with delays. Int. J. Appl. Math. Comput. Sci., 22 (2012), no. 4, 897-905.
• [6] Kaczorek T., A realization problem for positive continuoustime linear systems with reduced numbers of delays. Int. J. Appl. Math. Comput. Sci., 16 (2006), no. 3, 325-331.
• [7] Kaczorek T., Computation of positive stable realizations for discrete-time linear systems. Computational Problems of Electrical Engineering, 2 (2012), no. 1, 41-48.
• [8] Kaczorek T., Computation of positive stable realizations for linear continuous-time systems. Bull. Pol. Acad. Techn. Sci., 59 (2011), no. 3, 273-281.
• [9] Kaczorek T., Computation of realizations of discrete-time cone systems. Bull. Pol. Acad. Sci. Techn., 54 (2006), no. 3, 347-350.
• [10] Kaczorek T., Constructability and observability of standard and positive electrical circuits. Electrical Review, 89 (2013), no. 7, 132-136.
• [11] Kaczorek T., Decoupling zeros of positive continuous-time linear systems and electrical circuits. Advances in Systems Science. Advances in Intelligent Systems and Computing, 240 (2014), Springer, 1-15.
• [12] Kaczorek T., Determination of positive realizations with reduced numbers of delays or without delays for discrete-time linear systems. Archives of Control Sciences, 22 (2012), no. 4, 371-384.
• [13] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, 13, 2015.
• [14] Kaczorek T., Linear Control Systems, vol. 1. Research Studies Press, J. Wiley, New York, 1992.
• [15] Kaczorek T., Minimal-phase positive electrical circuits, Submitted to Electrical Review, 2015.
• [16] Kaczorek T., Minimal-phase realizations for positive linear systems, Proc. of Conf. TransComp, Zakopane, 2015.
• [17] Kaczorek T., Minimum energy control of positive electrical circuits. Proc. of Conf. MMAR, Miedzyzdroje, Aug. 2-5, 2014, 2-9.
• [18] Kaczorek T., Normal positive electrical circuits. IET Circuits Theory and Applications, 9 (2015), no. 5, 691-699.
• [19] Kaczorek T., Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
• [20] Kaczorek T., Positive and asymptotically stable realizations for descriptor discrete-time linear systems. Bull. Pol. Acad. Sci. Techn., 61 (2013), no. 1, 229-237.
• [21] Kaczorek T., Positive electrical circuits and their reachability. Archives of Electrical Engineering, 60 (2011), no. 3, 283-301.
• [22] Kaczorek T., Positive fractional linear electrical circuits. Proceedings of SPIE, 8903, Bellingham WA, USA, Art. No 3903-35.
• [23] Kaczorek T., Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Techn., 53 (2005), no. 3, 293-298.
• [24] Kaczorek T., Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Techn., 58 (2010), no. 3, 453-458.
• [25] Kaczorek T., Positive realizations with reduced numbers of delays for 2-D continuous-discrete linear systems. Bull. Pol. Acad. Sci. Techn., 60 (2012), no. 4, 835-840.
• [26] Kaczorek T., Positive stable realizations for fractional descriptor continuous-time linear systems. Archives of Control Sciences, 22 (2012), no. 3, 255-265.
• [27] Kaczorek T., Positive stable realizations of discrete-time linear systems. Bull. Pol. Acad. Sci. Techn., 60 (2012), no. 3, 605-616.
• [28] Kaczorek T., Positive stable realizations of fractional continuous-time linear systems. Int. J. Appl. Math. Comput. Sci., 21 (2011), no. 4, 697-702.
• [29] Kaczorek T., Positive stable realizations with system Metzler matrices. Archives of Control Sciences, 21 (2011), no. 2, 167-188.
• [30] Kaczorek T., Positive systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems – regular paper, 58 (2011), no. 6, 1203-1210.
• [31] Kaczorek T., Positive unstable electrical circuits. Electrical Review, 88 (2012), no. 5a, 187-192.
• [32] Kaczorek T., Realization problem for fractional continuoustime systems. Archives of Control Sciences, 18 (2008), no. 1, 43-58.
• [33] Kaczorek T., Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comput. Sci., 16 (2006), no. 2, 101-106.
• [34] Kaczorek T., Sajewski Ł., Realization Problem for Positive and Fractional Systems, Springer, 2014.
• [35] Kaczorek T., Zeroing of state variables in descriptor electrical circuits by state-feedbacks. Electrical Review, 89 (2013), no. 10, 200-203.
• [36] Shaked U., Di xon M., Generalized minimal realization of transfer-function matrices. Int. J. Contr., 25 (1977), no. 5, 785-803.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.