Algebraic forms of solutions of linear state equations for determined control vectors

• Autorzy: Porada Ryszard , Mielczarek Norbert

Identyfikatory

DOI

10.21008/j.1897-0737.2020.104.0007

• Języki publikacji: EN

Abstrakty

EN

Despite intensive development of numerical methods of resolution of ordinary differential equations, we still seek analytical solutions of these equations in the algebraic form. The analytical solution in an algebraic form, is very convenient in case of investigation of the course of solution in a large interval of changes of parameters, it also gives more qualitative informations. This concerns first of all linear equations which are the most often met models of physical objects. Important advantage of these solutions is also their open form regarding established state of the system. The paper proves existence of algebraic forms of solutions of control vectors with components: exponential, sinusoidal with different circular frequencies and sinusoidal multiple. Also solutions for other kind of control vectors which are mentioned in the literature are presented.

Słowa kluczowe

EN

state equation; solutions of state equations; algebraic forms

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2020
• Tom: No. 104
• Strony: 75--86
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Porada Ryszard

• Poznan University of Technology

autor

Mielczarek Norbert

• Poznan University of Technology

Bibliografia

• [1] Chua L.O., Pen-Min Lin, Computer-Aided Analysis of Electronic Circuits. Prentice-Hall, Inc. Englewood Cliffs, New Jersey, USA, 1975.
• [2] Isidori A., Nonlinear Control Systems. Springer, Berlin, 1995.
• [3] Kaczorek T., Control Theory and systems. PWN, Warszawa 1996 (in Polish).
• [4] Kaczorek T., Dzieliński A., Dąbrowski W., Łopatka R., Basics of the Control theory. WNT, Warszawa 2005 (in Polish).
• [5] Kaczorek T., Vectors and Matrices in the Automatic and Electrical Engineering. WNT, Warszawa 1998 (in Polish).
• [6] Krajewski W., Mathematical model of the induction machine in the state space method for the control vector with variable structure. Doctor’s Thesis, Poznań 1983 (in Polish).
• [7] Nijmeijer H., van der Schaft A.J., Nonlinear Dynamical Control Systems, Springer-Verlag, New York, 1991.
• [8] Ogata K., State Space Analysis of Control Systems. Prentice-Hall, Inc. Englewood Cliffs, New Jersey, USA, 1967.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).