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EN
Functionally graded materials are used in aircrafts, space vehicles and defence industries because of their good thermal resistance. Geometrically nonlinear free vibration of a functionally graded beam with clamped ends (FGCB) is modeled here by an N-dof discrete system presenting an equivalent isotropic beam, with effective bending and axial stiffness parameters obtained via a homogenization procedure. The discrete model is made of N masses placed at the ends of solid bars connected by rotational springs, presenting the flexural rigidity. Transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modeled by longitudinal springs. The nonlinear semi-analytical model previously developed is used to reduce the vibration problem, via application of Hamilton’s principle and spectral analysis, to a nonlinear algebraic system involving the mass and rigidity tensors mij and kij and the nonlinearity tensor bijkl. The material properties of the (FGCB) examined is assumed to be graded according to a power rule of mixture in the thickness direction. The fundamental nonlinear frequency parameters found for the (FGCB) are in a good agreement with previously published results showing the validity of the present equivalent discrete model and its availability for further applications to non-uniform beam.
PL
W pracy przedstawiono propozycję rozwiązania problemu automatycznego sterowania wielkością zamówień dokonywanych w systemach magazynowych z dużymi opóźnieniami. Zaproponowano zastosowanie struktury regulatora niecałkowitego rzędu ze sprzężeniem w przód i w tył oraz ze zmodyfikowanym predyktorem Smitha. Uzyskane wyniki porównane zostały z dwoma alternatywnymi układami sterowania: rzędu całkowitego oraz rzędu ułamkowego o mniejszym stopniu swobody. Do wyznaczenia nastaw układu regulacji został wykorzystany algorytm optymalizacji wielokryterialnej SPEA2. Wyniki uzyskane dla poszczególnych regulatorów zostały zobrazowane w postaci frontów Pareto-optymalnych oraz wybranych odpowiedzi czasowych układu.
EN
The paper presents a new fractional order structure for making orders in the automatic control warehouse system with variable time delay. Considered control system uses a discrete feedback-feedforward fractional order PDμ, PDν controller with Smith predictor. Results are compared with two alternative controllers: integer order controller and fractional order controller with reduced complexity. In order to obtain controller parameters the multi-objective optimization algorithm SPEA2 is employed. Results are shown and compared on Pareto plot as well as the selected time responses of the system.
EN
In this paper three simplified forms of the fractional-order (FO) backward difference (BD) are proposed and analysed. Due to time and frequency characteristics criteria parameters of simplified forms of the FOBDs are chosen. Applications of the simplified forms of the FOBDs diminish a number of multiplications and additions needed to evaluate the FOBD. This is very important in real-time microprocessor calculations. It is proved that in a discrete state-space description of a fractional-order system one should correct the input matrix with simplified forms of the FOBD. Investigations are supported by two numerical examples.
EN
The European leader for satellite systems and at the forefront of orbital infrastructures, Thales Alenia Space, is a joint venture between Thales (67%) and Finmeccanica (33%) and forms with Telespazio a Space Alliance. Thales Alenia Space is a worldwide reference in telecoms, radar and optical Earth observation, defence and security, navigation and science. It has 11 industrial sites in 4 European countries (France, Italy, Spain and Belgium) with over 7200 employees worldwide. Satellite evolution and the wish to design more autonomous missions imply the enhancement of the satellite architecture and special attention paid to fault management (i.e., Fault Detection, Isolation and Recovery, or FDIR, in space). Nevertheless, the constraints on FDIR techniques and strategies remain the same as for standard missions: robustness, reactive detection, quick isolation/identification and validation. This paper gives an introduction to Fault Tolerance (FT) in the space domain and some principles for the coming FT architectures. The current context of FDIR is presented by describing the approach implemented on telecommunication satellites and, more precisely, on one of the most FDIR sensible subsystems: the AOCS (Attitude and Orbit Control System). Following the current state of FDIR in the space domain, some perspectives are given such as a centralized distributed FDIR strategy for the next generation of autonomous satellites as well as some research tracks and hybrid diagnosis.
PL
W artykule zaprezentowane zostały nowe metody wspomagające proces analizy systemów dyskretnych opisanych sieciami Petriego. Relacje w prototypowanym systemie dyskretnym są odwzorowane hiper-grafem. Dzięki temu projektowany, wbudowany, rekonfigurowany sterownik logiczny może zostać poddany efektywniejszemu procesowi analizy z wykorzystaniem nowych algorytmów, związanych z traktowanymi łącznie teoriami hipergrafów i sieci Petriego. Wykorzystano między innymi takie procedury jak dopełnienie, dualizm, transwersale, transwersale dokładne oraz kolorowanie hipergrafu. W artykule w sposób nieformalny wykorzystano autorskie twierdzenia, wspomagające cały proces projektowania sterowników. Szczególną uwagę zwrócono na nowe sposoby analizy systemów dyskretnych, opisanych sieciami Petriego, takie jak częściowa weryfikacja poprawności specyfikacji sterownika na podstawie struktury hipergrafu współbieżności oraz zastosowanie transwersal do-kładnych w procesie wyodrębniania powiązanych ze sobą procesów sekwencyjnych.
EN
In the paper application of the hypergraph theory to analysis of discrete-systems described by means of Petri Nets is proposed. The relations between local states are represented by hypergraph vertices whose edges correspond to the global states. Therefore, the analysis of a prototype system can be performed by more effective operations supported by the hypergraph theory as well as the Petri net theory (such as dualism, hypergraph complement, transversals, exact transversals, hypergraph colouring). In the paper the authors propose application of the concurrency hypergraph to the analysis of a discrete-system. Such a structure refers to the traditional concurrency graph, however it keeps information about global states of the analysed system. Moreover, the concurrency hypergraph has some unique properties, which can lead to reduction in the computational complexity of some algorithms of the analysis. All minimal transversals in the concurrency hypergraph are also exact transversals. Therefore, such a hypergraph can be applied also to the decomposition process of a discrete-system, which is described by a Petri Net. After the analysis, a controller described by a Petri Net can be decomposed into concurrent sub-nets (concurrent automata). Each exact transversal of the concurrency hypergraph refers to the concurrent automata. The proposed solution allows significantly reducing the computational complexity to a polynomial. The traditional methods, based on the coloring of a concurrency graph are exponential time algorithms, thus they are defined to be NP-complete.
EN
This paper presents a constrained decomposition methodology with output injection to obtain decoupled partial models. Measured process outputs and decoupled partial model outputs are used to generate structured residuals for Fault Detection and Isolation (FDI). An algebraic framework is chosen to describe the decomposition method. The constraints of the decomposition ensure that the resulting partial model is decoupled from a given subset of inputs. Set theoretical notions are used to describe the decomposition methodology in the general case. The methodology is then detailed for discrete-event model decomposition using pair algebra concepts, and an extension of the output injection technique is used to relax the conservatism of the decomposition.
7
Content available remote Stanowa synteza systemów bezstratnych o skończonej odpowiedzi impulsowej
PL
W artykule przedstawiono nowy algorytm syntezy ortogonalnych równań stanu systemów o skończonej odpowiedzi impulsowej. W odróżnieniu od istniejących algorytmów opartych na przekształceniach wielomianowych, prezentowana technika wykorzystuje rozwinięcie równań stanu w szereg potęgowy. Takie podejście pozwala prowadzić obliczenia z wykorzystaniem rachunku macierzowego liczb rzeczywistych. Dzięki temu algorytm ten może być bezpośrednio zaimplementowany przy użyciu typowych programów matematycznych operujących na macierzach.
EN
In this paper, a novel state-space synthesis algorithm for orthogonal finite impulse response systems is presented. In contrast to known algorithms based on polynomial transformations, this technique utilizes the power series expansion. Such an approach allows performing calculations by means of real matrix calculations. Thanks to it, this algorithm can be directly implemented using standard mathematical software based on matrix representation.
8
Content available remote The visualization of discrete sequential systems
EN
Purpose: The paper is focused on the assumptions of the method of discretizing the states of sequential systems for an exemplary robotized metallurgical semi- finished products treatment department. The control of digital equipment is described on the bases of the patterns of control bites sequence configuration. The need for the development of a discretization method stems from difficulties encountered in representing the state of a process of an analogue nature. The crucial barrier is the method of treating the input signal to the visualization system. Design/methodology/approach: The proposed method is based on determining the variables that control the course of visualization in a manner enabling the treatment of all signals as boolean variables. Such approach requires a proper formulation of the input information flux to secure an explicit identification of the states of the served process. Findings: On the grounds of the assumptions a system of visualization is created to attempt the service of a robotized treatment centre. The main emphasis is put on devising an unambiguous way of identifying the states of an industrial robot and its cooperating sensors. Research limitations/implications: The result is the presentation of the combination of control elements in a bite vector used for defining the state of failure or for detecting operational irregularities. Originality/value: The originality of the paper is the approach towards the problem of processes visualization which may be categorized to a group of discrete processes with elements of analogue control data processing.
PL
Przedstawiono zagadnienie pomiaru sygnałów okresowych, w systemie pomiarowym, w którym warunki pomiaru determinują dynamikę czujników. Czujniki mają zmienne w czasie i okresowe właściwości. Badany system pomiarowy ma strukturę równoległą. Dwa równolegle pracujące tory pomiarowe posiadają, każdy, własne czujniki pomiarowe, przetworniki A/C oraz układy korekcyjne. Układy korekcyjne systemu określono jako systemy dynamiczne dyskretne i niestacjonarne. Zmienne w czasie współczynniki dynamiki korektorów przedstawiono w postaci dyskretnych szeregów czasowych, o zadanej liczbie składowych harmonicznych, których amplitudy i fazy są dostrajane za pomocą metod optymalizacji parametrycznej. Skuteczność korekcji w systemie pomiarowym zbadano za pomocą metod symulacyjnych. Analiza wyników optymalizacji łącznie z wynikami pomiaru w symulowanym systemie pomiarowym daje podstawę do wnioskowania o ograniczonej możliwości stosowania tych metod w niestacjonarnym systemie pomiarowym.
EN
The question of the measurements of periodical signals is presented, in the measurement system in which the conditions of the measurement environment determine the dynamics of sensors. The sensors become time-varying and periodical objects. The studied measurement system has the parallel structure. Two simultaneously working measurement channels possess, every one, its own sensors, analog-to-digital A/D converters and serial correctors in algorithmic form. The correctors were defined as nonstationary discrete-time systems. The coefficients of theirs dynamics models are represented as discrete-time series, with the set number of harmonic components. The amplitudes and phases of the coefficients are tuned up by means of the parametric optimization methods. The effectiveness of the correction algorithm in the measurement system was examined by computer simulation methods. The analysis of the results of the optimization together with the results of the measurements in the simulated measurement system gives the basis to the inference about the constrict possibility of the use of these methods in nonstationary measurement system.
PL
W artykule zaproponowana zostanie metoda podziału systemu dyskretnego z wykorzystaniem teorii hipergrafów. System dyskretny reprezentowany jest poprzez hipergraf. Poszczególne moduły odzwierciedlane są poprzez wierzchołki, natomiast połączenia pomiędzy modułami - poprzez hiperkrawędzie. Tak określony system dyskretny może zostać poddany procesowi dekompozycji z wykorzystaniem teorii hipergrafów. Metoda podziału systemów dyskretnych z wykorzystaniem hipergrafów zostanie zilustrowana przykładem. Szczegółowo przedstawione zostaną wszystkie kroki, jakie są niezbędne do wykonania procesu dekompozycji hipergrafów.
EN
A new method of the discrete-system decomposition is proposed in the paper. The method is based on the hypergraph reduction and partition. A discrete-system is represented by a hypergraph; where module corresponds to the vertex and connection (net) corresponds to the hyperedge. The proposed method allows hierarchical reduction of the hypergraph and finally - partition of the discrete-system. All steps that are required in order to perform the decomposition of the discreete -system will be shown. The method of the hierarchical reduction and partition of hypergraphs will be illustrated by an example.
11
Content available remote Time-scaling of SISO and MIMO discrete-time systems
EN
The idea for time-scaling of output signals of linear and nonlinear SISO and MIMO discreet-time systems has been presented. It is shown, that algorithms for SISO discrete-time systems can be useful for scaling of MIMO ones, if so-called V-model of MIMO system can be determined and its SISO components can be scaled separately by equipping them with correctors processing the associated state variables. Applying the presented idea one can speed up or slow down the responses of technical systems conserving their reference forms.
PL
Przedstawiono koncepcję skalowania czasowego systemów dyskretnych SISO i MIMO, tak liniowych, jak i nieliniowych. Pokazano, że algorytmy skalowania dla układów SISO mogą być przydatne do skalowania tych układów MIMO, dla których potrafimy wyznaczyć model typu „V”, jednak pod warunkiem, że elementy SISO modelu „V” mogą być skalowane oddzielnie, poprzez wprowadzenie korektora wejściowego i korektora sprzężenia zwrotnego. W oparciu o proponowane algorytmy skalowania można formować takie sygnały wejściowe, które przyspieszają bądź spowalniają odpowiedzi systemów technicznych, zachowując przy tym pożądany kształt tych odpowiedzi.
PL
W referacie zaprezentowana zostanie metoda dekompozycji systemów dyskretnych z wykorzystaniem hipergrafów. Podział uzyskano poprzez zastosowanie hierarchicznej redukcji wierzchołków hipergrafu. W procesie partycjonowania bloki systemu dyskretnego reprezentowane są poprzez wierzchołki hipergrafu, natomiast połączenia pomiędzy blokami - poprzez hiperkrawędzie. Przedstawiona metoda umożliwia sekwencyjną redukcję wierzchołków hipergrafu, w których projektant sam może zadecydować, na którym poziomie hierarchii chce zakończyć partycjonowanie. Dzięki temu dany system może zostać podzielony na dowolną liczbę mniejszych układów.
EN
In the paper a method of discrete-system decomposition is proposed. The method is based on the hypergraph reduction and partition. A discrete-system is represented by a hypergraph; where module corresponds to the vertice and connection (net) corresponds to the hyperedge. The proposed method allows hierarchical reduction of the hypergraph and finally - partition of the discrete-system.
13
Content available remote FFT-based spectral dynamic analysis for linear discrete dynamic systems
EN
Purpose: An FFT-based spectral dynamic analysis method is developed for the viscously damped, linear discrete dynamic systems subjected to nonzero initial conditions. Design/methodology/approach: The discrete Fourier transform (DFT) theory is used to develop a spectral dynamic analysis method. The dynamic response of a linear system is assumed as the sum of the forced and free vibration response parts. The forced vibration response part is obtained by convolving the dynamic stiffness matrix and Fourier components of excitation force through the Duhamel's integral, and the free vibration response part is obtained by determining its integral constants so as to satisfy initial conditions in frequency-domain. Findings: It is shown through some numeral examples that the proposed FFT-based spectral dynamic analysis method provides the solutions which accurately satisfy all initial conditions. Practical implications: This analysis method is applicable to viscously damped, linear discrete dynamic systems subjected to nonzero arbitrary initial conditions. In this study, two types of viscous damping are considered: proportional damping and non-proportional damping. Originality/value: The FFT-based spectral dynamic analysis method proposed in this paper is unique because the pseudo-force concept or the superposition of corrective free vibration solution used by other researchers is not used to take into account non-zero initial conditions.
14
Content available remote Analysis of some dual properties in discrete dynamic systems
EN
The problem of duality in nonlinear and linear systems is considered. In addition to the known duality between controllability and observability, new dual notions and their properties are investigated. A way to refine these properties through an isomorphic transformation of the original systems is suggested.
15
EN
A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.
16
Content available remote A Novel Continuous Model to Approximate Time Petri Nets: Modelling and Analysis
EN
In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented.
18
Content available remote Admissible Disturbance Sets for Discrete Perturbed Systems
EN
We consider a discrete disturbed system given by the difference bilinear equation x^{w}_{i+1} =Ax^{w}_{i} + De_{i} + sum_{j=1}^{q}f^{j}_{i}B_{j}x^{w}_{i}, i geq 0, where w=((e_{i})_{i geq 0}, (f_{i})_{i geq 0}) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y^{w}_{i}=Cx^{w}_{i}, i geq 0. Let varepsilon be a tolerance index on the output. The disturbance w is said to be varepsilon-admissible if ||y^{w}_{i}-y_{i}|| leq varepsilon, forall i geq 0, where (y_{i})_{i geq 0} is the output signal associated with the case of an uninfected system. The set of all varepsilon-admissible disturbances is the admissible set {cal W}(varepsilon). The characterization of {cal W}(varepsilon) is investigated and numerical simulations are given.
19
Content available remote Real-time experiments with discrete sliding-mode control enhanced by AI components
EN
The paper presents some experimental results of a real-time implementation of discrete sliding mode control combined with a fuzzy-logic damper block. The hybrid real-time algorithm developed is aimed at applications to discrete systems. The sliding mode pan of the solution is based on system input and output measurements. The algorithm combines an integral action, a nonlinear output feedback, an adjustable sliding mode, and a fuzzy logic damping control block. Design of the sliding mode controller is based on the asymptotic reaching law method. The determination of the integral gain and the coefficients of the sliding mode hyper-plane are made by a pole assignment procedure. The paper presents both the simulation results and the results of laboratory real-time control experiments. The real-time control experiments are made with the motor speed control system using an DSP based hardware (TMS230C31/60 MHz). The results obtained demonstrate the robustness and superiority of the proposed solution in the motor speed control, as compared to the solution based on the optimally tuned PI controller.
20
Content available remote Zeros in Discrete-Time Mimo Lti Systems and the Output-Zeroing Problem
EN
A geometric interpretation of invariant zeros of MIMO LTI discrete-time systems is provided. The zeros are treated as the triples: complex number, state zero direction, input zero direction. Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case (i.e. when each complex number constitutes an invariant zero). Simply, in the degenerate case, to each complex number we can assign an appropriate real initial condition and an appropriate real input sequence which produce a non-trivial solution to the state equation and a zero system response. Clearly, when zeros are treated merely as complex numbers, such an interpretation is impossible. The proposed definition of invariant zeros is compared with other commonly known definitions. It is shown that each Smith zero of the system matrix is also an invariant zero in the sense of the definition adopted in the paper. On the other hand, simple numerical examples show that the considered definition of invariant zeros and the Davison-Wang definition are not comparable. The output-zeroing problem for systems decouplable by state feedback is also described.
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