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.
Highlights
In order to use and control various dynamic processes, more and more complex control systems are being created
Simulation becomes a main part of hybrid dynamic system (HDS) analysis
The investigated systems are presented as the set of interacting piecewise linear aggregates (PLA), which include processes described with di erential equations
Summary
In order to use and control various dynamic processes, more and more complex control systems are being created. Janilionis simulation systems in which the models of HDS components can be created, interconnected and changed as the system evolves Such components can have hybrid behavior, consisting of continuous-time phases separated by discreteevent transitions. It needs the tools which could ensure the solution of general m-th order di erential equations and general systems of rst-order di erential equations For this purpose there is used and developed automatic di erentiation method 3 5], which provides an elegant and conceptually simple solution of an ordinary non-linear di erent equation. The large and expandable library of operators and functions and the language orientation to the operation with vectors imitate mathematical symbolism in APL2 These mentioned features t in automatic di erentiation very well 6]
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