The simulation of dynamic systems using combined modelling

Abstract

The new approach to the problems of dynamic systems simulation is proposed. The analytical and imitation modelling of non‐linear complex dynamic systems which comprise simulation of continuous and discrete processes with constant and variable parameters, are investigated. The aggregate mathematical modelling scheme [1] and the method of control sequences for discrete systems specification and simulation are used as well as the dynamic mathematical modelling scheme for continuous process formalization and modelling. According to them the investigated systems are presented as the set of interacting piecewise linear aggregates, which can include processes described with differential equations. The above mentioned approach is used in developing software for the construction and research of the models. The modelling of the dynamic systems’ control is also analyzed and developed software for the dynamic systems’ simulation is presented. It is related to the proposed combined modelling methodology. The developed dynamical simulation system ADPRO (Automatic Differentiation PROgram) extends applicability of the system SIMAS (SIMulation of the Aggregate Systems) [2] with dynamical simulation means realized with APL2 (A Programming Language 2) and based on automatic differentiation [3]. The created model of service process and its control can be used as a base for other models of wide class complex dynamics’ systems [4], the parts of which are described with differential equations.

Dinaminių sistemų kombinuotas modeliavimas

Santrauka. Darbe nagrinėjamas naujas dinaminių sistemų modeliavimo metodas. Ištirti analitiniai ir imitaciniai sudėtingų dinaminių sistemų modeliavimo būdai, tirti tolydieji ir diskretieji procesai. Pateikta nauja dinaminio matematinio modeliavimo schema, skirta tolydžių procesų formalizavimui ir modeliavimui. Sukurta programinę įrangą, leidžianti sudaryti ir tirti tokio tipo matematinius modelius. Taip pat tirtas dinaminių sistemų valdymo modeliavimas bei sukurta atitinkama programinė įranga.

First Published Online: 14 Oct 2010