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1

Maximum amplitudes in transient resonance of distributed-parameter systems

Michalczyk J.

Archives of Mining Sciences

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2012

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Vol. 57, no. 3

657--665

EN

The application of the kinetic energy balance for the estimation maximum amplitudes of continuous systems in the transient resonance excited by the free coasting of unbalanced rotor or piston machines placed on the continuous system - was proposed in the study. The exact as well as the approximate methods were shown. For the typical one- and two-dimensional systems the calculation formulae, useful for the engineering practice, were given.

PL

W pracy wskazano na możliwość zastosowania metody bilansu energii kinetycznej dla oszacowania amplitud maksymalnych w rezonansie przejściowym podczas wybiegu ciężkich maszyn wirnikowych lub tłokowych posadowionych na układach o ciągłym rozkładzie masy. W szczególności rozważono drgania okołorezonansowe przesiewaczy i przenośników wibracyjnych o znacznej długości oraz płytowych i belkowych układów podporowych maszyn o dużym zredukowanym momencie bezwładności, jak wirówki odwadniające czy kruszarki młotkowe, stosowanych w zakładach przeróbki kopalin.

2

An output controllability problem for semilinear distributed hyperbolic systems

Zerrik E., Larhrissi R., Bourray H.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 4

437-446

EN

The paper aims at extending the notion of regional controllability developed for linear systems to the semilinear hyperbolic case. We begin with an asymptotically linear system and the approach is based on an extension of the Hilbert uniqueness method and Schauder’s fixed point theorem. The analytical case is then tackled using generalized inverse techniques and converted to a fixed point problem leading to an algorithm which is successfully implemented numerically and illustrated with examples.

3

Optymalne strategie obserwacji w detekcji uszkodzeń układów o parametrach rozłożonych

Patan M., Uciński D., Baranowski P.

Pomiary Automatyka Kontrola

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2005

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R. 51, nr 9 bis

71--73

PL

W pracy przedstawiono problem optymalizacji trajektorii ruchomych czujników pomiarowych w sposób zapewniający maksymalną moc testu weryfikującego prostą hipotezę parametryczną dotyczącą nominalnych wartości parametrów charakteryzujących normalny stan pracy układu o parametrach rozłożonych zdefiniowany w zadanym obszarze przestrzennym. Opracowane podejście polega na sformułowaniu problemu optymalizacji trajektorii ruchu czujników w kategoriach zadania sterowania optymalnego, a następnie jego efektywnym rozwiązaniu w oparciu o istniejące pakiety numeryczne. Zaprezentowano ogólny schemat takiego podejścia prowadzącego do maksymalizacji wiarygodności detekcji oraz dokonano jego weryfikacji w oparciu o przykład numeryczny dotyczący problemu adwekeji-dyfuzji.

EN

The problem under consideration is to determine the optimal strategics of observation taken with movable sensors in such a way as to maximize the power of a simple parametric hypothesis test, which verifies the nominal state of the considered distributed system specified on a given multi-dimensional spatial domain. The optimal trajectiores of sensors movements are determined based on the Ds-optimality criterion defined on the respective Fisher Information Matrix. The proposed approach consists in reformulating the problem of sensor trajectory design as an optimal control one and its effective solution with the use of some existing numerical packages. In this work, a general scheme of such an approach leading to Maximization of the fault detection efficiency in distributed-parameter systems is delineated and tested via computer simulations regarding an advection-diffusion problem.

4

Spatial Compensation of Boundary Disturbances by Boundary Actuators

Afifi L., Chafiai A., El Jai A.

International Journal of Applied Mathematics and Computer Science

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2001

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Vol. 11, no 4

899-920

EN

In this paper we show how to find convenient boundary actuators, termed boundary efficient actuators, ensuring finite-time space compensation of any boundary disturbance. This is the so-called remediability problem. Then we study the relationship between this remediability notion and controllability by boundary actuators, and hence the relationship between boundary strategic and boundary efficient actuators. We also determine the set of boundary remediable disturbances, and for a boundary disturbance, we give the optimal control ensuring its compensation.

5

Optimal Selection of Measurement Locations for Parameter Estimation in Distributed Processes

Uciński D.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 2

357-379

EN

The problem of locating pointwise sensor measurements so as to optimally estimate unknown parameters in a class of distributed systems is studied. Based on a scalar measure of performance defined on the corresponding Fisher information matrix, two approaches are developed for this problem: introduction of continuous designs, which allows for adaptation of well-known sequential algorithms of classical optimum experimental design, and application of standard non-linear programming techniques. In each case, particular algorithms are delineated and analysis of the appropriate sensor placements is made. The relative advantages and shortcomings of both the approaches are discussed and demonstrated by applying them to a two-dimensional diffusion process.

6

Detection and Control Problems for Non-Linear Distributed-Parameter Systems With Delays

Namir A., Lahmidi F., Labriji E. H.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 3

437-464

EN

First, we consider non-linear discrete-time and continuous-time systems with unknown inputs. The problem of reconstructing an input using the information given by an output equation is investigated. Then we examine a control problem for non-linear discrete-time hereditary systems, i.e. the problem of finding a control which drives the state of the system from its initial value to a given desired final state. The methods used to solve these problems are based on the state-space technique and fixed-point theorems. To illustrate the outlined ideas, various numerical simulation results are presented.

7

Identification and suboptimal control of heat exchanger using generalized back propagation through time

Fujarewicz K.

Archives of Control Sciences

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2000

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Vol. 10, no. 3/4

167-183

EN

This paper deals with a problem of identification and suboptimal control of a counterflow heat exchanger. From the point of view of control theory the heat exchanger is a nonlinear, multidimensional, distributed parameter, dynamical system, and due to its complexity it is difficult to identify it as a black box. In this paper a hybrid model containing neural networks is identified. Its complicated structure makes the analytical calculation of the gradient of performance index with respect to neural network weights very difficult. This problem is solved using a special, structural formulation of sensitivity analysis called generalized back propagation through time (GBPTT). This method is universal, can be used for searching suboptimal parameters (weights) or suboptimal control signals in continuous or discrete time, nonlinear, dynamical systems. Moreover, the presented method is fully mnemonic. The obtained model of the heat exchanger and the same methodology is used during the gradient calculation of the suboptimal control signal of the heat exchanger. Numerical examples are presented.

8

Constrained Controllability of Dynamic Systems

Klamka J.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

231-244

EN

The present paper is devoted to a study of constrained controllability and controllability for linear dynamic systems if the controls are taken to be non-negative. By analogy to the usual definition of controllability it is possible to introduce the concept of positive controllability. Weshall concentrate on approximate positive controllability for linear infinite-dimensional dynamic systems when the values of controls are taken from a positive closed convex cone and the operator of the system is normal and has pure discrete point spectrum. Special attention is paid to positive infinite-dimensional linear dynamic systems. General approximate constrained controllability results are then applied to distributed-parameter dynamic systems described by linear partial-differential equations of parabolic type with various kinds of boundary conditions. Several remarks and comments on the relationships between different concepts of controllability are given. Finally, a simple illustrative example is also presented.

9

Source identification in distributed parameter systems

Skliar M., Ramirez W. F.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 4

733-754

EN

In this paper, we solve the problem of the pointwise source identification of the convection-diffusion transport processes. This is done by converting the identification problem into an optimization problem of finding a spatial location and the capacity of a point source which results in the best match of model-predicted measurements to actual observed measurements.

10

Observer design for distributed-parameter dissipative bilinear systems

Bounit H., Hammouri H.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 2

381-402

EN

This paper deals with the problem of observer synthesis for a class of infinitedimensional dissipative bilinear systems working for a class of inputs. First, a simple observer (the estimation error converges strongly asymptotically to zero) for strongly persistent input signals is presented. Next, sufficient conditions are given which guarantee the existence of an exponential observer for skew-adjoint bilinear systems based on the time-varying differential Riccati (or Lyapunov) equations working for strongly regularly persistent inputs. These results are illustrated by means of partial-differential systems.