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1
Content available An adaptive identification method based on the modulating functions technique and exact state observers for modeling and simulation of a nonlinear MISO glass melting process
Byrski Witold, Drapała Michał, Byrski Jędrzej
International Journal of Applied Mathematics and Computer Science
|
2019
|
Vol. 29, no. 4
739--757
EN
The paper presents new concepts of the identification method based on modulating functions and exact state observers with its application for identification of a real continuous-time industrial process. The method enables transformation of a system of differential equations into an algebraic one with the same parameters. Then, these parameters can be estimated using the least-squares approach. The main problem is the nonlinearity of the MISO process and its noticeable transport delays. It requires specific modifications to be introduced into the basic identification algorithm. The main goal of the method is to obtain on-line a temporary linear model of the process around the selected operating point, because fast methods for tuning PID controller parameters for such a model are well known. Hence, a special adaptive identification approach with a moving window is proposed, which involves using on-line registered input and output process data. An optimal identification method for a MISO model assuming decomposition to many inner SISO systems is presented. Additionally, a special version of the modulating functions method, in which both model parameters and unknown delays are identified, is tested on real data sets collected from a glass melting installation.
2
Content available Decentralized stabilization of fractional positive descriptor continuous-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2018
|
Vol. 28, no. 1
135--140
EN
A method for decentralized stabilization of fractional positive descriptor linear systems is proposed. Necessary and sufficient conditions for decentralized stabilization of fractional positive descriptor linear systems are established. The efficiency of the proposed method is demonstrated on a numerical example.
3
Content available State estimation for miso non-linear systems in controller canonical form
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
|
2016
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Vol. 26, no. 3
569--583
EN
We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.
4
Content available Fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative
Kaczorek T., Borawski K.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 3
533--541
EN
The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.
5
Content available Positivity and linearization of a class of nonlinear continuous-time systems by state feedbacks
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2015
|
Vol. 25, no. 4
827--831
EN
The positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback it is possible to obtain an asymptotically stable and controllable linear system, and if the closed-loop system is positive then it is unstable.
6
Content available State estimation for a class of nonlinear systems
Schwaller B., Ensminger D., Dresp-Langley B., Ragot J.
International Journal of Applied Mathematics and Computer Science
|
2013
|
Vol. 23, no. 2
383--394
EN
We propose a new type of Proportional Integral (PI) state observer for a class of nonlinear systems in continuous time which ensures an asymptotic stable convergence of the state estimates. Approximations of non-linearity are not necessary to obtain such results, but the functions must be, at least locally, of the Lipschitz type. The obtained state variables are exact and robust against noise. Naslin’s damping criterion permits synthesizing gains in an algebraically simple and efficient way. Both the speed and damping of the observer response are controlled in this way. Model simulations based on a Sprott strange attractor are discussed as an example.
7
Content available Minimum energy control of positive continuous-time linear systems with bounded inputs
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2013
|
Vol. 23, no. 4
725--730
EN
The minimum energy control problem for positive continuous-time linear systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of a solution to the problem are established. A procedure for solving the problem is proposed and illustrated with a numerical example.
8
Content available Asynchronous distributed state estimation for continuous-time stochastic processes
Kowalczuk Z., Domżalski M.
International Journal of Applied Mathematics and Computer Science
|
2013
|
Vol. 23, no. 2
327--339
EN
The problem of state estimation of a continuous-time stochastic process using an Asynchronous Distributed multi-sensor Estimation (ADE) system is considered. The state of a process of interest is estimated by a group of local estimators constituting the proposed ADE system. Each estimator is based, e.g., on a Kalman filter and performs single sensor filtration and fusion of its local results with the results from other/remote processors to compute possibly the best state estimates. In performing data fusion, however, two important issues need to be addressed namely, the problem of asynchronism of local processors and the issue of unknown correlation between asynchronous data in local processors. Both the problems, along with their solutions, are investigated in this paper. Possible applications and effectiveness of the proposed ADE approach are illustrated by simulated experiments, including a non-complete connection graph of such a distributed estimation system.
9
Content available Application of the shuffle algorithm to analysis of descriptor linear systems with singular pencil art angielski
Kaczorek T.
Autobusy : technika, eksploatacja, systemy transportowe
|
2013
|
R. 14, nr 3
1419-1434
EN
A new method of analysis of descriptor continuous-time and discrete-time linear systems with singular pencil is proposed. The method is based on transformation of singular pencil by the use of the shuffle algorithm. Conditions for transformation of the descriptor linear systems to equivalent standard linear systems are established.
PL
Podano nową metodę analizy deskryptowych liniowych układów ciągłych i dyskretnych z pękami singularnymi. Proponowana metoda jest oparta na redukcji deskryptowych układów o pękach singularnych do równoważnych układów standardowych za pomocą algorytmu przesuwania. Podano warunki istnienia tej redukcji oraz ilustrowano proponowaną metodę przykładem numerycznym.
10
Content available remote Positive stable realizations of fractional continuous-time linear systems
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2011
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Vol. 21, no 4
697-702
EN
Conditions for the existence of positive stable realizations with system Metzler matrices for fractional continuous-time linear systems are established. A procedure based on the Gilbert method for computation of positive stable realizations of proper transfer matrices is proposed. It is shown that linear minimum-phase systems with real negative poles and zeros always have positive stable realizations.
11
Układ ciągły równoważny układowi ze sterowaniem poślizgowym
Gessing R.
Zeszyty Naukowe. Automatyka / Politechnika Śląska
|
2008
|
z. 151
37-47
PL
W pracy pokazuje się, jak utworzyć układ ciągły równoważny układowi ze sterowaniem poślizgowym, przy małej histerezie przekaźnika. Układ ten powstaje przez zastąpienie przekaźnika odpowiednim elementem z nasyceniem. Ten ostatni może być zrealizowany przez wzmacniacz o dużym wzmocnieniu połączony szeregowo z elementem z nasyceniami sterowania określonymi przez przełączane amplitudy przekaźnika. W równoważnym układzie ciągłym efekt szarpania charakterystyczny dla układów ze sterowaniem poślizgowym nie występuje. Zasada konstrukcji obu układów została sformułowana w postaci Podstawowej zasady sterowania.
EN
It is shown how to create the continuous system equivalent to the system with sliding mode control (under small hysteresis of the relay). The system arises from the replacement of the relay by some appropriate saturation-type nonlinearity. The latter may be implemented by the amplifier with high gain in series connected with saturation, with constraints of the control determined by the switched magnitudes of the relay. In the equivalent continuous systems the chattering effect, related with sliding mode control doesn't exist. The principle of construction of both the systems is formulated in the form of the Basic principle of control.
12
Content available remote Span’s low damped vibrations and vibration’s damping by modal disparity inducted by cable stays temporal addition
Lipiński K.
Vibrations in Physical Systems
|
2008
|
Vol. 23
235--240
EN
The paper presents low damped vibrations of a continuous system. Such vibrations are present in many structures, and effective elimination method is requested. In the paper, temporal stiffness modification is proposed in order to distribute the energy amount different modes of the system (for example to these that are better damped). The method is tested with a bridge span numerical model.
13
Content available remote Problem częstotliwości drgań własnych w wirujących ^ układach mechanicznych pojazdów szynowych
Dżuła S.
Pojazdy Szynowe
|
2005
|
nr 1
1-5
EN
On the example of the vibrating railway wheel the results of numerical caiculations of the problem of boundary system of the eąuations describing the wheel vibration are presented. The vibrating wheel was modelled as the countinuous system. The few variants of the physical and mathematical model of the wheel were formulated beginning from the simplest model in which the complete symmetry of the structure of the vibrating wheel up to the model with the asymmetry of the structure (unbalances of the wheel plate and rim with the countinuous weight distribution) in the rolling motion and the cooperation with the track. In dependence on the accepted model the results of caiculations show the big quantitative differences, first of all the qualitative ones. This work was made within the research project financed from the means of the State Committee for Scientific Research in 2003 - 2006.
14
Content available Nowa metoda obliczeń kinetostatycznych przesztywnionych łańcuchów kinematycznych
Jaworowski H., Felis J.
Mechanics / AGH University of Science and Technology
|
2005
|
Vol. 24, no. 4
252-260
PL
W pracy przedstawiono zastosowanie pewnej nowej metody rozwiązywania ciągłych jednowymiarowych struktur sprężystych do obliczeń kinetostatycznych przesztywnionych łańcuchów kinematycznych. Sformułowano i rozwiązano problem brzegowy z uwzględnieniem sił bezwładności unoszenia dla płaskiego przesztywnionego mechanizmu czworoboku przegubowego. Wyznaczone zostały przemieszczenia członów mechanizmu, siły reakcji w parach kinematycznych oraz uogólniona siła równoważąca.
EN
In the paper is presented application of a new method of solution of one-dimensional continuous elastic beam structures in kinetostatic calculations of over-rigid kinematic chains. There was formulated and solved boundary problem with the application of inertia forces in convection motion for the plane over-rigid four-bar linkage mechanism. There were evaluated the displacements of mechanism links, reactive forces in kinematic pairs and generalized equilibrating force.
15
Content available remote Realization problem for a class of positive continuous-time systems with delays
Kaczorek T.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 4
447-453
EN
The realization problem for a class of positive, continuous-time linear SISO systems with one delay is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for the computation of positive minimal realizations is presented and illustrated by an example.
16
Content available remote Finite horizon nonlinear predictive control by the Taylor approximation: Application to robot tracking trajectory
Hedjar R., Toumi R., Boucher P., Dumur D.
International Journal of Applied Mathematics and Computer Science
|
2005
|
Vol. 15, no 4
527-540
EN
In industrial control systems, practical interest is driven by the fact that today’s processes need to be operated under tighter performance specifications. Often these demands can only be met when process nonlinearities are explicitly considered in the controller. Nonlinear predictive control, the extension of well-established linear predictive control to nonlinear systems, appears to be a well-suited approach for this kind of problems. In this paper, an optimal nonlinear predictive control structure, which provides asymptotic tracking of smooth reference trajectories, is presented. The controller is based on a finite–horizon continuous time minimization of nonlinear predicted tracking errors. A key feature of the control law is that its implementation does not need to perform on-line optimization, and asymptotic tracking of smooth reference signal is guaranteed. An integral action is used to increase the robustness of the closed-loop system with respect to uncertainties and parameters variations. The proposed control scheme is first applied to planning motions problem of a mobile robot and, afterwards, to the trajectory tracking problem of a rigid link manipulator. Simulation results are performed to validate the tracking performance of the proposed controller.
17
Zastosowanie jednolitej metody rozwiązywania ciągłych prętowych struktur sprężystych w obliczeniach kinetostatycznych przesztywnionych łańcuchów kinematycznych
Jaworowski H., Felis J.
Prace Naukowe Instytutu Konstrukcji i Eksploatacji Maszyn Politechniki Wrocławskiej. Konferencje
|
2002
|
Vol. 85, nr 25
209-216
PL
W pracy przedstawiono zastosowanie pewnej nowej metody rozwiązywania ciągłych jednowymiarowych struktur sprężystych do obliczeń kinetostatycznych przesztywnionych łańcuchów kinematycznych. Sformułowano i rozwiązano problem statyczno-brzegowy z uwzględnieniem sił bezwładności unoszenia dla płaskiego przesztywnionego mechanizmu czworoboku przegubowego. Wyznaczone zostały przemieszczenia członów mechanizmu, siły reakcji w parach kinematycznych oraz uogólniona siła równoważąca.
EN
In the paper is presented application of a new method of solution of one-dimensional continuous elastic beam structures in kinetostatic calculations of over-rigid kinematic chains. There was formulated and solved static-boundary problem with the application of inertia forces in convection motion for the plane over-rigid four-bar linkage mechanism. There were evaluated the displacements of mechanism links, reactive forces in kinematic pairs and generalized equilibrating force.
18
Content available remote Controllability, Observability and Optimal Control of Continuous-Time 2-D Systems
Jank G.
International Journal of Applied Mathematics and Computer Science
|
2002
|
Vol. 12, no 2
181-195
EN
We consider linear 2-D systems of Fornasini-Marchesini type in the continuous-time case with non-constant coefficients. Using an explicit representation of the solutions by utilizing the Riemann-kernel of the equation under consideration, we obtain controllability and observability criteria in the case of the inhomogeneous equation, where control is obtained by choosing the inhomogeneity appropriately, but also for the homogeneous equation, where control is obtained by steering with Goursat data. The optimal control problem with a quadratic cost functional is also solved.
19
Modelowanie oddziaływań między ogniwami robota w reprezentacji szkieletów hipergrafów
Buchacz A.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2001
|
z. 64
65-72
PL
W pracy porównano klasyczne i nieklasyczne metody modelowania układów ciągłych.
EN
Classical and unclassical methods of modelling of contiuous systems have been compared.
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