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1
Content available Algebraic forms of solutions of linear state equations for determined control vectors
Porada Ryszard, Mielczarek Norbert
Poznan University of Technology Academic Journals. Electrical Engineering
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2020
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No. 104
75--86
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.
2
Content available A computer algorithm for the solution of the Astate equation for time-varying fractional discrete-time linear systems
Kaczorek T., Borawski K.
Measurement Automation Monitoring
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2015
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Vol. 61, No. 1
2--4
EN
Method for finding of the solution of the state equation for time-varying fractional discrete-time linear systems is proposed and computer algorithm is presented. The effectiveness of the proposed algorithm is demonstrated on numerical examples.
3
Content available Solution of the state equations of descriptor fractional discrete-time linear systems with regular pencils
Kaczorek T.
TTS Technika Transportu Szynowego
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2013
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R. 20, nr 10
415--422, CD
EN
A method for finding of the solutions of the state equations of descriptor fractional discrete-time linear systems with regular pencils is proposed. The derivation of the solution formula is based on the application of the Z transform and the convolution theorem. A procedure for computation of the transition matrix is proposed. The effectiveness of the proposed method is demonstrated on a simple numerical example.
PL
Podano metodę wyznaczania rozwiązań równań stanu deskryptowych układów dyskretnych rzędów niecałkowitych o pękach regularnych. Rozwiązanie to zostało wyprowadzone korzystając z przekształcenia zet i twierdzenia o transformacie splotu. Zaproponowano procedurę wyznaczania macierzy tranzycji tych układów. Proponowaną metodę zilustrowano przykładem numerycznym.
4
Content available remote Algebraical Characterisation of Interval-Timed Petri Nets with Discrete Delays
Popova-Zeugmann L., Pelz E.
Fundamenta Informaticae
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2012
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Vol. 120, nr 3/4
341-357
EN
In this paper we consider Interval-Timed Petri nets (ITPN) which are an extension of Timed Petri nets. They are considered to behave with discrete delays. The class of ITPNs is Turing complete and therefore the reachability of an arbitrary marking in such a net is not decidable. We introduce a time dependent state equation for a firing sequence of ITPNs, which is analogous to the state equation for a firing sequence in standard Petri nets and we prove its correctness using linear algebra. Our result is original and delivers both a necessary condition for reachability and a sufficient condition for non-reachability of an arbitrary marking in an ITPN.
5
Content available remote Względna punktowa zupełność i względna osiągalność określonej klasy singularnych dodatnich układów dyskretnych z opóźnieniem
Busłowicz M.
Pomiary Automatyka Robotyka
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2007
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R. 11, nr 2
PL
W pracy rozpatrzono określoną klasę liniowych dodatnich singularnych układów dyskretnych z jednym opóźnieniem zmiennych stanu o kanonicznych postaciach macierzy stanu. Podano analityczną postać rozwiązania równania stanu oraz rozpatrzono problemy punktowej zupełności i osiągalności. Sformułowano definicje oraz podano warunki konieczne i wystarczające względnej punktowej zupełności oraz względnej osiągalności. Rozważania zilustrowano przykładem.
EN
The paper considers a class of linear singular positive discrete-time systems with unit delay with canonical forms of state matrices. An analytical form of the solution of the state-equation is derived and the problems of pointwise completeness and reachability are considered. The definitions of relative pointwise completeness and relative reachability are introduced and necessary and sufficient conditions are given. The considerations are illustrated by example.
6
Content available remote A Method to Prove Non-Reachability in Priority Duration Petri Nets
Werner M., Popova-Zeugmann L., Richling J.
Fundamenta Informaticae
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2004
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Vol. 61, nr 3,4
351--368
EN
Times and priorities are important concepts that are frequently used to model real-world systems. Thus, there exist extensions for Petri nets which allow to model times and priorities. In contrast, many proof techniques are based on classical (time-less and priority-less) Petri nets. However, this approach fails frequently for timed and prioritized Petri nets. In this paper, we present an approach to prove non-reachability in a Priority Duration Petri net. We use for this proving technique a state equation as well as conditions for firing that include a priority rule and a maximal step rule. Our approach leads to a system of equations and inequalities, which provide us with a sufficient condition of non-reachability. We demonstrate the application of our approach with an example
7
Content available remote Using State Equation to Prove Non-Reachability in Timed Petrinets
Popova-Zeugmann L., Werner M., Richling J.
Fundamenta Informaticae
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2003
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Vol. 55, nr 2
187-202
EN
Non-reachability proofs in Timed Petrinets were usually done by proving the non-reachability within the underlying timeless net. However, in many cases this approach fails. In this paper, we present an approach to prove non-reachability within the actual Timed Petrinet. For this purpose, we introduce a state equation for Timed Petrinets in analogy to timeless nets. Using this state equation, we can express reachability as a system of equations and inequations, which is solvable in polynomial time.
8
Content available remote 3D multistage computations of turbine flows using different state equations
Rusanov A. V., Yershov S., Lampart P., Świrdyczuk J., Gardzielewicz A.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2002
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Vol. 6, No 4
591-600
EN
The paper describes the implementation of a modified state equation for perfect gas and Tammann equation into a 3D RANS solver FlowER. In the modification the specific heats are assumed as linear functions of temperature. A 5-stage LP steam turbine stage is calculated, and the comparison of results for constant and variable specific heats is illustrated. The modification significantly improves the correctness of determination of thermodynamic parameters in the entire flow region, especially in the exit stage.
9
Content available remote Narrowing Petri Net State Spaces Using the State Equation
Schmidt K.
Fundamenta Informaticae
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2001
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Vol. 47, nr 3,4
325-335
EN
Given a (possibly partially defined) state, all count vectors of transition sequences reaching that state are solutions to a corresponding Petri net state equation. We propose a search strategy where sequences corresponding to a minimal solution of the state equation are explored first. Then step by step the search space is relaxed to arbitrary count vectors. This heuristics relies on the observation that in many (though provably not in all) cases, minimal solutions of the state equation can be realized as a firing sequence. If no target state is reachable, either the state equation does not have solutions, or our search method would yield the full state space. We study the impact of the state equation on reachability, present an algorithm that exploits information from the state equation and discuss its application in stateless search as well as its combination with stubborn set reduction.
10
Content available Model for evaluation of the maneuvering object's trajectory using Kalman filters
Breznev B., Muha V.
Control and Cybernetics
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2001
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Vol. 30, no 1
63-70
EN
A new approach for construction of an object maneuvering model for evaluation of movement trajectory using Kalman filter is proposed. The approach proposed is based on application of the object's dynamic equations. Such approach is better for obtaining adequate models of object maneuvering in comparison with the known ones. The state equations of Kahnan filter are derived for describing the movement of a ship maneuvering by the heading.
11
Content available remote Influence of electrostriction on state and continuity equations
Sawicki J. M.
Archives of Hydro-Engineering and Environmental Mechanics
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1999
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Vol. 46, nr 1-4
91-103
EN
The electrostriction consists in the change of the solvent density, due to the presence of dissolved substance. This phenomenon has very important consequences for the state equation. The paper is devoted to the analysis of these consequences and to the formulation of the full equation of state and its simplified versions, after the neglect of electrostriction. In the next order the equations of continuity of the solution and its components were considered. As a result the simplified versions of these equations were derived, rejecting the electrostriction and correcting the definition of the solution advection velocity.
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