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EN
Controlling mechanical systems with position and velocity cascade loops is one of the most effective methods to operate this type of systems. However, when using low-rate sampling electronics, the implementation is not trivial and the resulting performance can be poor. This paper proposes effective tuning rules that only require establishing the bandwidth of the inner velocity loop and an estimation of the inertia of the mechanism. Since discrete-time mechatronic systems can also exhibit unstable behavior, several stability conditions are also derived. By using the proposed methodology, a P-PI control algorithm is developed for a desktop haptic device, obtaining good experimental performance with low sampling-rate electronics.
EN
By analyzing the issue of chaos synchronization, it can be noticed the lack of a general approach, which would enable any type of synchronization to be achieved. Similarly, there is the lack of a unified method for synchronizing both continuous-time and discrete-time systems via a scalar signal. This paper aims to bridge all these gaps by presenting a novel general unified framework to synchronize chaotic (hyperchaotic) systems via a scalar signal. By exploiting nonlinear observer design, the approach enables any type of synchronization defined to date to be achieved for both continuous-time and discrete-time systems. Referring to discrete-time systems, the method assures any type of dead beat synchronization (i.e., exact synchronization in finite time), thus providing additional value to the conceived framework. Finally, the topic of synchronizing special type of systems, such as those characterized by the absence of equilibrium points, is also discussed.
EN
In this paper we study the problem of state constraints in discrete time sliding mode control. We present a sufficient condition for the strategy that drives the representative point monotonically to the sliding hyperplane in finite time. The advantage of this strategy is that disturbances do not have to fulfill the matching conditions. Our approach is based on the so-called reaching law technique.
PL
W artykule przeanalizowany został problem ograniczenia zmiennych stanu w dyskretnym sterowaniu ślizgowym. Do zaprojektowania regulatora zastosowano regułę osiągania ruchu ślizgowego. Zaprezentowano warunek dostateczny na monotoniczną zbieżność stanu obiektu do płaszczyzny ślizgowej w skończonym czasie. Zaletą przedstawionej metody jest to, że zakłócenia nie muszą spełniać warunków dopasowania.
EN
In this paper, low cost air levitation project is presented as a teaching tool for control engineering. Air levitation control system is built as a classroom demonstration device and laboratory stand. The laboratory stand provides a new plant to control for students of control engineering.It is comprised of Arduino Mega 2560, plexiglass, metal elements and 3D printed parts.
PL
W pracy przedstawiono projekt stanowiska laboratoryjnego do lewitacji powietrznej. Obiekt został zaprojektowany oraz zbudowany dla celów edukacyjnych oraz naukowych w dziedzinie szeroko pojętej automatyki oraz teorii sterowania. Ukazane w pracy stanowisko wykorzystuje nowoczesne narzędzia inżynierskie: Arduino Mega 2560 oraz MATLAB/Simulink. Celem tego projektu jest umożliwienie studentom wdrażania różnych systemów sterowania. Obejmuje to implementację identyfikacji systemu, opracowanie algorytmów sterowania oraz przeprowadzenie weryfikacji eksperymentalnej.
PL
W pracy przedstawiono wyniki analizy literaturowej zagadnień związanych ze sterowaniem przepływem materiałów w systemach magazynowych. Na podstawie zaproponowanego dyskretnego, niestacjonarnego, dynamicznego modelu systemu magazynowego ze zmiennym w czasie opóźnieniem stworzono układ sterowania. Przedstawiona koncepcja usprawnienia przepływu towarów wykorzystuje predyktor Smitha z regulatorem PID. Do doboru optymalnych nastaw parametrów układu regulacji zastosowany został algorytm genetyczny. Wskaźnik jakości skonstruowano na bazie: kosztów tworzenia i utrzymania zapasów oraz utraconych zysków, tj. różnic między zapotrzebowaniem a sprzedażą produktów. Wskaźnik ten odzwierciedla, jak system sterowania zamówieniami nadąża za zmieniającymi się potrzebami rynku. Problem ten jest istotny w przedsiębiorstwach produkcyjnych i handlowych, które dążą do minimalizacji czasu realizacji operacji magazynowych i maksymalizacji przepustowości magazynu przy zapewnieniu ciągłości procesu produkcyjnego i sprzedaży. Sformułowano opis matematyczny systemu sterowania oraz problemu optymalizacji. Dokonano jego implementacji stosując algorytm genetyczny. Przedstawione zostały wyniki badań symulacyjnych ukazujące jakość zaproponowanego układu regulacji w środowisku MATLAB/Simulink.
EN
There are a number of theorems and techniques that view inventory management from variant perspectives. The recent progress in research has resulted in innovative and more general techniques that can reduce the supply chain costs fundamentally. Modern inventory control is anchored in vastly advanced and complex models, which require considerable computational efforts. In this paper, we use a mathematical model of a warehouse system with time-varying delivery delay and adapt control system in order to apply it to the problem of goods flow in inventory systems. On the basis of the analysis of the inventory system, we propose a control system, then made its initial verification in the way of computer simulation in MATLAB/Simulink. The concept of improving the flow of materials is based on the structure of the Smith predictor and the PID controller. We perform optimization studies using genetic algorithm. Two quality indicators are subjected to minimization: the total costs of creating and maintaining inventories and differences between the demand and sales of products – the value of providing on whether the storage system keep up with the changing needs of the market (avoid stoppages). In this article, we mainly want to show that our idea of control system is able to achieve a high service level with maintaining a given inventory capacity to avoid redundancy.
EN
Modern inventory control is anchored in vastly advanced and complex models, which require considerable computational efforts. In this paper, we use a mathematical model of an inventory system with large supply delay and control system in order to optimize goods flow in inventory systems. The paper proposes the use of automatic control systems to control the system for supplementary orders. A discrete-time, dynamic model of the warehouse system is assumed for the analysis. For the given model, two automatic control systems: adaptive and classical non-adaptive periodic inventory systems , are analyzed. The non-adaptive control system is well known in the literature and the second one is its extension. The parameters of the control system are tuned by minimizing the cost function using a genetic algorithm for the assumed scenario for the market demand. Results of numerical simulations of the dynamical system and selected results in the objective space are presented in the paper.
PL
W pracy dokonano analizy literaturowej zagadnień związanych z modelowaniem systemów magazynowych. Następnie zaproponowano dyskretny, dynamiczny model systemu magazynowego z uwzględnieniem opóźnień dostaw, opóźnień dotyczących realizacji zamówienia oraz zmiennych w czasie opóźnień związanych z oczekiwaniem na transport. Wskazano możliwość rozbudowy modelu w celu optymalizacji fizycznego przepływu produktów od producenta na rynek, począwszy od etapu wytwarzania, skończywszy na etapie doręczenia to waru do klientów. Problem ten jest istotny w przedsiębiorstwach produkcyjnych i handlowych, które dążą do minimalizacji czasu realizacji operacji magazynowych i maksymalizacji przepustowości magazynu przy zapewnieniu ciągłości procesu produkcyjnego i sprzedaży. W końcowej części przedstawione są wyniki symulacji komputerowych w środowisku MATLAB/ Simulink.
EN
This work includes analysis of the literature related to issues in the inventory control. On the basis of the analysis of the inventory system, we proposed mathematical model and then made its initial verification in the way of computer simulation in Matlab / Simulink for different scenarios of the market behavior. The simulation was designed to reflect the dynamic phenomena connected with inventory control. This is a suitable foundation to design a stable control strategy which will minimize lost service favorable circumstances (occurring when only a part of the required demand can be satisfied from the stock available at the distribution center. Such a model enables the use of existing synthesis methods of control to avoid demurrages and minimize their effects. A block diagram of an inventory system with delay varying in time is presented in Fig.1. The last part of this paper presents the results of a simulation of the developed model in Fig.2. The graph of this r esponses i s shown i n Figs. 3,5 a nd 6. The paper presents a mathematical model of a warehouse system with time-varying delivery delay. The aim of this work is to adapt and extend the mathematical model and analyze the mechanism of flow of goods associated with inventory management. The work contains an introduction with literature review, simulation and potential future research directions. The first part of the paper is focused on crucial facts about the inventory phenomena over the years. There are a number of theorems and techniques that view inventory management from variant perspectives. Modern enterprises have to make inventory decisions that benefit the entire supply c hain to maximize profit a nd m inimize costs. I n this article, we want to show not only the mathematics associated with proper inventory control but also the mechanism of managing inventory. Striking a balance between operating savings and the costs and capital requirements associated with larger stock is the fundamental problem of inventory policy.
EN
In this paper, we refer to two definitions of fading memory property, which were published in the literature, for discrete-time circuits and systems. One of these definitions relates to systems working with signals (sequences) defined for both the positive and negative integers, expanding from minus infinity to plus infinity. On the other hand, the second one refers to systems processing sequences defined only for nonnegative integers, that is starting at the discrete-time point equal to zero and expanding to plus infinity. We show here that the second definition follows from the first one. That is they are not independent. Moreover, we also show that if an operator describing a system possesses a fading memory according to the second definition, then its associated operator has this property, too, but in accordance with the first definition.
EN
We investigate a SAT-based bounded model checking (BMC) method for MTL (metric temporal logic) that is interpreted over linear discrete infinite time models generated by discrete timed automata. In particular, we translate the existential model checking problem for MTL to the existential model checking problem for a variant of linear temporal logic (called HLTL), and we provide a SAT-based BMC technique for HLTL. We show how to implement the BMC technique for HLTL and discrete timed automata, and as a case study we apply the technique in the analysis of GTPP, a Generic Timed Pipeline Paradigm modelled by a network of discrete timed automata.
EN
In the paper the positive linear discrete-time noncommensurate fractional-order systems described by the state equations are considered. Definition and necessary and sufficient conditions for the positivity, reachability and controllability to zero are given and proven. The considerations are illustrated by a numerical example.
PL
W pracy rozpatrzono liniowe stacjonarne dodatnie układy dyskretne niecałkowitego niewspółmiernego rzędu. Sformułowano definicje oraz podano warunki konieczne i wystarczające dodatniości, osiągalności i sterowalności układów dyskretnych niewspółmiernego rzeczywistego rzędu oraz współmiernego niecałkowitego rzędu. Rozważania zilustrowano przykładem numerycznym.
PL
W pracy zaproponowano model matematyczny kanału komunikacyjnego z zatorem w węźle zatłoczonym, blokadami w węzłach pośrednich i parametrach zmiennych w czasie. Do opisu matematycznego wykorzystany jest liniowy, niestacjonarny, dyskretny model układu dynamicznego. Umożliwia on modelowanie opóźnień o dowolnie długim czasie trwania. Model taki zapisany w przestrzeni zmiennych stanu daje możliwość wykorzystanie istniejących metod syntezy sterowania do unikania zatorów i minimalizacji ich skutków. W pracy przedstawiono wyniki symulacji komputerowej opracowanego modelu.
EN
The paper presents a mathematical model of a communication channel with frequent congestion in intermediate nodes and time-varying delay. The first part of the paper is focused on description of some TCP protocol modifications, which adapted this protocol to be more effective and fault resistant in data transporting. This efficiency can be observed especially in an environment with frequent congestion and data loss. Regardless of the modifications of different transport protocols and the increase in the link bandwidth, to make full use of the computer network bandwidth it is necessary to develop some mechanisms allowing control of the transmitted packets at the network nodes. There is presented mathematical estimation of a real network segment built of many active network nodes and connections. This solution is a linear, non-stationary, discrete dynamical system model that allows modelling of delays for any long duration. Such a model stored in the state variables enables the use of existing synthesis methods of control to avoid congestion and minimize their effects. A block diagram of a network part with delay varying in time is presented in Fig. 1. A network part participating in packet forwarding may consists of a significant number of nodes. The last part of this paper presents the results of a simulation of the developed model in a form of the step response. The graph of this response is shown in Figs. 2 and 3.
PL
W pracy omówiono zagadnienia związane z mechanizmami powstawania zatorów komunikacyjnych oraz blokad w przepływie informacji w rozległych sieciach komputerowych. Na podstawie przeprowadzonej analizy zaproponowano struktury modelowe dla poszczególnych segmentów rozpatrywanego kanału komunikacyjnego. W pracy podano podstawowe zależności matematyczne niezbędne do wykorzystania zaproponowanego modelu.
EN
The paper describes an issue connected with mechanism of forming communication congestion and blockades in information flow. A new model structure for specific segments of the considered communication channel was proposed on the basis of the conducted analysis. The paper presents the basic mathematical relationships necessary for using the proposed model. Implementing QoS politics does not solve the problem of network congestion avoidance and congestion elimination. The main difficulty in this field is the delay in a communication channel as well as the delay jitter. Regardless of the modification of different transport protocols and increase in the links bandwidth, it is necessary to develop some mechanisms to control the packet forwarding at the network nodes if we want to utilize the full throughput of computer networks. The mechanisms of forming network congestion and blockages described in this paper allow us to create an advanced dynamic mathematical model of the communication channel with a time-varying delay. Such a model stored in the state space will enable the use of existing methods of linear-time varying systems to control the queue length in order to avoid congestions and minimize their effects. A block diagram of the network part with delay varying in time is presented in Fig. 2. The network part participating in packet forwarding may consists of a significant number of nodes. It can be considered as a set of logical nodes as shown in Fig. 5. Each logical node in a specific time can either forward all data to the next node or store it in an egress buffer.
EN
The optimization problem for fractional discrete-time systems with a quadratic performance index has been formulated and solved. The case of fixed final time and a free final state has been considered. A method for numerical computation of optimization problems has been presented. The presented method is a generalization of the well-known method for discrete-time systems of integer order. The efficiency of the method has been demonstrated on numerical examples and illustrated by graphs. Graphs also show the differences between the fractional and classical (standard) systems theory. Results for other cases of the fractional system order (coefficient ) and not illustrated with numerical examples have been obtained through a computer algorithm written for this purpose.
PL
W pracy dokonano analizy wpływu złożoności przybliżonego modelu odcinkami afinicznego służącego do syntezy regulatora sektorami afinicznego na własności układu sterowania w sytuacji, gdy sterowany obiekt jest nieliniowy. Zaproponowano metodę wyznaczania przybliżonego modelu odcinkami afinicznego, umożliwiającego optymalny dobór węzłów, minimalizującego odchylenie pomiędzy funkcją nieliniową i jej przybliżeniem. Rozważania przeprowadzono na podstawie dyskretnego modelu pojazdu na nieliniowym wzgórzu.
EN
The paper presents analysis of the impact of the complexity of the approximate piece-wise affine (PWA) model used to compute PWA regulator on the eon troI system properties with nonlinear plant. The method for de termin ing the approximate piece-wise affine model is proposed. The method allows the optimal nodes selection and minimize the deviation between the nonlinear function and its piece-wise affine approximation. Considerations are based on the car on nonlinear hill discrete-time model. (Effeet of the partitions of approximate seeant pieee-wise affine model on eon troI quality for non-lineer, state-dependent system).
EN
The paper concerns an application of regulation theory methods to modeling and effective control of connection-oriented data transmission networks. In particular the problem of congestion control in a single virtual circuit of such a network is considered and new discrete-time sliding mode data flow rate controllers are proposed. The controllers are designed in such a way that packet losses are explicitly accounted for. The closed-loop system stability and finitetime error convergence are proved. Moreover, a number of favorable properties of the proposed controllers are stated as theorems, formally proved and verified in a simulation example. It is demonstrated that the proposed controllers guarantee full utilization of the available bandwidth and eliminates the risk of bottleneck node buffer overflow. Application of time-varying sliding hyperplanes helps avoid excessive transmission rates at the beginning of the control process.
EN
The paper proposes a novel method for feedback stability evaluation for linear time-varying, discrete-time control systems. It is assumed that the time-varying system can be described by the general discrete-time, time-varying state space model and by the equivalent linear input-output (transfer) operator. The method extends feedback stability concepts for systems given in a general linear time-varying, discrete-time form, not only in the Lurie form. In the paper selected short-time stability concepts are employed for inference about feedback stability of systems defined on an infinite time-horizon. Theoretical considerations are complemented by numerical examples.
EN
In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.
18
Content available Positive fractional linear systems
EN
An overview of some recent published and unpublished results on positive fractional continuous-time and discrete-time linear systems is given. The first part of the paper is devoted to the positive continuous-time fractional systems. For those systems the solutions to the fractional state equations are proposed. Necessary and sufficient conditions for the positivity, reachability and stability are established. In the second part similar problems are considered for positive discrete-time fractional systems.
PL
W pracy dokonano syntetycznego przeglądu nowych publikowanych i niepublikowanych wyników dotyczących dodatnich ciągłych i dyskretnych układów liniowych niecałkowitego rzędu. W części pierwszej poświęconej układom ciągłym podano rozwiązanie układu równań stanu, warunki konieczne i wystarczające dodatniości, osiągalności i stabilności układów dodatnich. W części drugiej przedstawiono podobne wyniki dla układów dyskretnych.
PL
Idea Aktywnej Redukcji Hałasu (ARH) jest związana z redukcją niepożądanego niskoczęstotliwościowego dźwięku, w rezultacie tworzona jest przestrzenna strefa ciszy wokół wybranego mikrofonu. Artykuł opisuje praktyczną implementacje systemu ARH pracującego pod kontrolą systemu operacyjnego uClinux na dwurdzeniowym procesorze sygnałowym Blackfin firmy Analog Devices. System operacyjny uClinux okazuje się być tanim, dynamicznym środowiskiem rozwojowym dla procesorów sygnałowych Blackfin, dodatkowo wykorzystując wielordzeniowe procesory jest możliwe pokonanie głównej wady Linux'a mianowicie braku funkcjonalności systemu operacyjnego czasu rzeczywistego niezbędnej do zastosowań przetwarzania sygnałów. Można to osiągnąć poprzez oddzielenie kodu który musi być wykonywany w czasie rzeczywistym i uruchamianie go na osobnym rdzeniu podczas gdy drugi rdzeń jest wykorzystywany przez systemem operacyjny Linux. Zastosowanie systemu operacyjnego Linux w implementacji układu ARH przynosi szereg korzyści zwłaszcza zwiększa możliwości rozwoju i debuggingu oprogramowania, Linux daje również dostęp do ogromnej ilości otwartego oprogramowania. W prezentowanym rozwiązaniu w oparciu o system operacyjny Linux stworzono aplikację integrującą funkcje webserwera z układem aktywnej redukcji hałasu, dynamicznie tworzone strony internetowe tworzą graficzny interfejs użytkownika systemu ARH dostępny poprzez przeglądarkę internetową.
EN
The idea of ANC is concerned with attenuation of unwanted low frequency sound (noise). As a result, a three-dimensional zone of quiet is created around the selected microphones. The paper describes ANC system implementation running under the uClinux system on dual core Analog Devices Blackfin DSP. The uClinux is proving to be a low-cost, dynamic development environment. On multi-core Blackfin DSPs, it is possible to overcome the main disadvantage of Linux - lack of hard-real time functionality indispensable for signal processing applications. It can be achieved by separation of the real-time signal processing code and handling it on a dedicated core, while the other core is running Linux. Such a solution offers advantages to designers, most notably by opening up a wide range of applications, drivers and protocols which often are open-source or free software. In most cases, only a compilation or some minor tweaking is necessary to get that software up and running. The advantages for using Linux in the ANC system are ease of use, better system control, easy possibility of creating web based user interfaces and improved debugging capabilities. In this particular application, use of Linux enables a Web server integration into the ANC system. Dynamically created web pages can be accessed by any web browser and become the graphical user interface to the ANC system.
EN
Reduction of singular fractional systems to standard fractional systems and decomposition of singular fractional discrete-time linear systems into dynamic and static parts are addressed. It is shown that if the pencil of singular fractional linear discrete-time system is regular then the singular system can be reduced to standard one and it can be decomposed into dynamic and static parts The proposed procedures are based on modified version of the shuffle algorithm and illustrated by numerical examples.
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