E.V. Klimanova - Post-graduate Student, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: e.v.klimanova@yandex.ru A.V. Maksimov - Ph. D. (Eng.), Associate Professor, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: av_maximov@bk.ru E.A. Maksimova - Assistant, Department «Computer systems and networks», Kaluga branch of the Bauman MSTU E-mail: eam@mail333.com

The paper discusses modeling features for complex valued and quaternion based transfer functions of control systems typical parts. The entire body of work is divided into three parts. The first part is substantiated the mathematical apparatus for the two-dimensional control systems modeling in the basis of input-output complex functions. Particular attention is paid to the complex functions form of representation. It is shown that the use of the algebraic notation for functions and complex numbers does not yield new information on the control system structure. The most effective form of notation for the two-dimensional systems modeling purpose is a matrix form. Block diagram of the two-dimensional control systems using the matrix form provides the two-dimensional full mesh system, whereas the algebraic form results in a system with two separate unrelated control channels. The important point to note there is a justification for complex unit matrix choice is given. Despite the fact that developer has a large variety of imaginary unit matrices to use, the effectiveness of latter is either poorly understood or little use to achieve the goals. There are the best matrices for standard units modeling purposes is proved in the paper. It is concluded that the given mathematical apparatus allows successfully develop and explore the transfer functions of two-dimensional control systems typical parts. The results of these studies will be presented in the second part of the work. The third part will be devoted to the study of multidimensional control systems typical parts with the involvement of quaternions.

 

1. Branec V.N., SHmyglevskijj I.P. Primenenie kvaternionov v zadachakh orientacii tverdogo tela. M.: Nauka. 1973. 320 s.
2. CHelnokov JU.M. Kvaternionnye modeli i metody dinamiki, navigacii i upravlenija dvizheniem. M.: FIZMATLIT. 2011. 560 s.
3. Efremov A.P. Issledovanie kvaternionnykh prostranstv i ikh vzaimosvjazi s sistemami otscheta i fizicheskimi poljami. M.: RUDN. 2008. 208 s.
4. Maksimov A.V, Maksimova E.A. Informativnost zakona Oma v kvaternionnojj forme // EHlektromagnitnye volny i ehlektronnye sistemy. № 10. 2013. S. 7−9.
5. Kurosh A.G. Kurs vysshejj algebra. M.: Nauka. 1968. 433 s.
6. Furmanov JA.A., Kreveckijj A.V., Rozhencev A.A. i dr. Komplesnoznachnye i giperkompleksnye sistemy v zadachakh obrabotki cifrovykh signalov / Pod red. Furmana JA.A. M.: FIZMATLIT. 2004. 456 s.
7. Karataev E.A. Preobrazovanija giperkompleksnykh chisel. M.: SOLON-PRESS. 2016. 300 s.
8. Besekerskijj V.A., Popov E.P. Teorija sistem avtomaticheskogo regulirovanija. Izd. 3-e, ispr. M.: Nauka. 1970. 768 s.
9. Metody klassicheskojj i sovremennojj teorii avtomaticheskogo upravlenija. T. 1: Matematicheskie modeli, dinamicheskie kharakteristiki i analiz sistem avtomaticheskogo upravlenija / Pod red. K.A. Pupkova, N.D. Egupova. M.: Izd-vo MGTU im. N.EH. Baumana. 2004. 656 s.
10. Matrichnye metody rascheta i proektirovanija slozhnykh sistem avtomaticheskogo upravlenija dlja inzhenerov / Pod red. K.A. Pupkova i N.D. Egupova. M.: Izd-vo MGTU im. N.EH. Baumana. 2007. 664 s.