Wyniki wyszukiwania - Biblioteka Nauki

1

A problem of robust control of a system with time delay

100%

Blizorukova M. , Kappel F. , Maksimov V.

International Journal of Applied Mathematics and Computer Science

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2001

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tom 11

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nr 4

821-834

EN

A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.

2

Robust Control of Linear Stochastic Systems with Fully Observable State

80%

Poznyak A. S. , Taksar M. I.

Applicationes Mathematicae

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1996-1997

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tom 24

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nr 1

35-46

EN

We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.

3

H control of robot arm with hydraulic drive

80%

Gosiewski Z. , Michałowski G.

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2008

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tom Vol. 2, no. 2

39-44

EN

In the paper an H�‡ velocity control of the robot arm in combination with the hydraulic drive is presented. The open-loop system consists of a manipulator with one rotary degree of freedom, a hydraulic servomotor, and an electrohydraulic amplifier. The mathematical model of the system is derived. Due to the nonlinearity in the model, which is caused by varying operating point parameters and the direction of the servomotor motion, the model of multiplicative uncertainty was defined. The plant model transfer function parameters were assumed to be variable. To limit error signal, control signal, and output signal three weighting functions were designed. The simulation results of the designed H�‡ optimal closed-loop system were compared to the standard PID closed-loop system. The solution ensuring robust performance was achieved and proved.

4

Robust linear controller for dynamic object with two-dimensional uncertain parameters space

80%

Oprzedkiewicz K.

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2006

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tom Vol. 16, no. 4

435-444

EN

Robust linear controller for an uncertain param,eter linear dynamic system is presentedin this paper. Plant is described by finite dimensional linear stste-space equation with interval diagonal state matrix, know control and output matrices and two-dimensional uncertain parameters space. The controllable and observable part of the system can be described by equivqlent transfer function. To control the plant a general linear controller is used. general robustness indices and idea of robutness areas are defined for the control system. First order uncertain parameter system with the PID controller is presented as an illustrative example.

5

A Problem of Robust Control of a System With Time Delay

80%

Blizorukova M. , Kappel F. , Maksimov V.

|

2001

|

tom Vol. 11, no 4

821-834

EN

A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.

6

Optimal control for a plants consisting of two masses and connected with a non-linear spring

80%

Łozowicki A. , Łozowicka-Stupnicka T. , Łozowicka D.

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2010

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tom nr 2

EN

Problem of optimal system controlling a motion of the plant consisting of twomasses connected with a non-linear spring is considered in the paper. For example such plants can be motorcars with trailer or dumb barge pulling by ship. The irregular motion of elements of such plants influences negative on consume energy. In addition, because of safety, the speed of motion should be limited. As a criterion of quality we take the energy of the error signals. Till now the two mass problem (benchmark problem) was considered for linear cases only. The novelty of our work is generalisation of this problem (using the describing function method) for non-linear cases. The H control theory (robust control) is firstly adapted to cope with non-linear plants. High effectiveness of the optimal controller has been confirmed by computer simulation in MATLAB.

PL

W pracy rozważany jest układ sterujący, optymalizujący ruch obiektu składającego się z dwóch elementów o znacznych masach połączonych nieliniową sprężyną. Obiektami takimi są np. samochody z przyczepami lub barki wodne ciągnięte przez statki. Nieregularności ruchu elementów takich obiektów powodują duże straty energii w napędzie i, ze względu na bezpieczeństwo, zmuszają do ograniczania prędkości ruchu, co wydłuża czas trwania transportu. Kryterium jakości jest zużycie energii określone sygnałem błędu. Dla znalezienia optymalnego regulatora przeprowadzono harmoniczną linearyzację układu i dla zlinearyzowanego równania zastosowano metody optymalizacji bazujące na metodach przestrzeni Banacha H i H2 (robust control). Wysoka skuteczność regulatora wyznaczonego opisaną metodą potwierdzona została symulacją komputerową. Dodatkowym efektem zastosowanego sterowania jest zapewnienie stabilności układu.

7

Persistent bounded disturbance rejection for uncertain time-delay systems

80%

Sun M. , Jia Y.

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2009

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tom Vol. 38, no 3

593-607

EN

This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems with parametric uncertainty by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L1-performance analysis are given in terms of linear matrix inequalities (LMIs). Based on the results, a simple approach to the design of a linear state-feedback controller is presented to stabilize robustly the uncertain time-delay systems and achieve a desired level of disturbance attenuation. All the obtained conditions are delay-dependent. A numerical example is included to illustrate the proposed method.

8

One-DoF robust control of shaft supported magnetically

80%

Gosiewski Z. , Mystkowski A.

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2006

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tom Vol. 16, no. 3

327-339

EN

The paper presents a robust control of the motion of a shaft supported by magnetic bearings. The dynamics of magnetic suspension systems are characterized by their instability and uncertainly of the plant. Therefore apart from the model of the plant we determined a model of the parametrical uncertainty. The uncertainty is modeled as additive. Current stiffness and displacement stiffness are assumed to be the uncertainty parameters. The performance of the closed-loop system, signals limits, and the disturbances influence are determined with the aid of the weighting functions. Three weighting functions are designed We(S) - penalizing the error signal e, Wu(S) - penalizing the input signal u, and Wy(S) - penalizing the output signal x. For these functions and the uncertainly model we assigned the augmented control model. For the augmented control system we assigned the robust controller. The robust controller assures high quality of control despite of the uncertainty model of the plant, disturbances in the systems, signals limits and high dynamics of the system. Next the H∞ closed-loop system is compared with the standard PID closed-loop system. Finally simulation results show effectiveness of the control system as good initial responses/transient responses and robustness of the designed robust controller.

9

Analysis of nonlinear model following control/internal model control (MFC/IMC) structure for a ship engine speed control

80%

Brzózka J.

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2008

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tom Vol. 34, no 3

25-29

EN

Ship governors are usually designed on the basis of PID (Proportional Integral Derivative) controllers because of their simplicity, reliability and universality. However, their performance in various environmental conditions is not as good as desired. These disadvantages can be overcome by adaptive controllers, although these methods are complex. This article presents a new control loop structure for a ship engine speed control based on the model following control (MFC) and internal model control (IMC) theory. The new structure presented has the advantages of both the PID and robust control methodologies. It is robust for large parameter variations and strong environmental disturbances. Simulations using MATLAB®/Simulink® software for a real ship engine parameters showed high effectiveness of MFC/IMC structure for speed-keeping and speed-changing.

10

Reliable robust path planning with application to mobile robots

80%

Pepy R. , Kieffer M. , Walter E.

International Journal of Applied Mathematics and Computer Science

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2009

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tom 19

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nr 3

413-424

EN

This paper is devoted to path planning when the safety of the system considered has to be guaranteed in the presence of bounded uncertainty affecting its model. A new path planner addresses this problem by combining Rapidly-exploring Random Trees (RRT) and a set representation of uncertain states. An idealized algorithm is presented first, before a description of one of its possible implementations, where compact sets are wrapped into boxes. The resulting path planner is then used for nonholonomic path planning in robotics.

11

Reducing the mast vibration of single-mast stacker cranes by gain-scheduled control

80%

Hajdu S. , Gáspár P.

International Journal of Applied Mathematics and Computer Science

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2016

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tom 26

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nr 4

791-802

EN

In the frame structure of stacker cranes harmful mast vibrations may appear due to the inertial forces of acceleration or the braking movement phase. This effect may reduce the stability and positioning accuracy of these machines. Unfortunately, their dynamic properties also vary with the lifted load magnitude and position. The purpose of the paper is to present a controller design method which can handle the effect of a varying lifted load magnitude and position in a dynamic model and at the same time reveals good reference signal tracking and mast vibration reducing properties. A controller design case study is presented step by step from dynamic modeling through to the validation of the resulting controller. In the paper the dynamic modeling possibilities of single-mast stacker cranes are summarized. The handling of varying dynamical behavior is realized via the polytopic LPV modeling approach. Based on this modeling technique, a gain-scheduled controller design method is proposed, which is suitable for achieving the goals set. Finally, controller validation is presented by means of time domain simulations.

12

Iterative Learning Control - monotonicity and optimization

80%

Owens D. , Daley S.

International Journal of Applied Mathematics and Computer Science

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2008

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tom 18

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nr 3

279-293

EN

The area if Iterative Learning Control (ILC) has great potential for applications to systems with a naturally repetitive action where the transfer of data from repetition (trial or iteration) can lead to substantial improvements in tracking performance. There are several serious issues arising from the "2D" structure of ILC and a number of new problems requiring new ways of thinking and design. This paper introduces some of these issues from the point of view of the research group at Sheffield University and concentrates on linear systems and the potential for the use of optimization methods and switching strategies to achieve effective control.

13

Robust stability of systems with parametric uncertainty

70%

Matusu R. , Prokop R.

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2008

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tom Vol. 18, no. 1

73-87

EN

Systems with parametric uncertainty represent an important class of uncertain objects that are characterized by mathematical model containing parameters which are not precisely known, but the values thereof lie within given intervals. This type of uncertainty can arise during the control of real processes, e.g. as a consequence of imprecise measuring or of the influence of certain external conditions. If individual uncertain coefficients (in polynomial, in transfer function etc.) are mutually independent, the uncertainty has a simple interval structure. This article presents several possibilities of interval uncertainty for systems description as well as the tools for robust stability analysis, emphasizing advantages and limitations connected with the use of this simple structures, even for more complex problems.

14

Bounding approach to parameter estimation without prior knowledge on modeling error and application to quality modeling in drinking water distribution systems

70%

Duzinkiewicz K.

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2006

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tom Vol. 16, no. 1

51-70

EN

Parameter estimation of an autoregressive with moving average and exogenous variable ARMAX model is discussed in this paper by using bounding approach. Bounds on the model structure error are assumed unknown, or known but too conservative. To reduce this conservatism, a point-parametric model concept is proposed, where there exist a set model parameters and modeling error corresponding to each input. Feasible parameter sets are defined for point-parametric model. bounded values on the model parameters and modeling error can then be computed jointly by tightening the feasible set using observations under deliberately designed input excitations. Finally, a constantly bounded parameter model is established, which can be used for robust output prediction and control.

15

The steering of the ship motion: a Μ-synthesis approach

70%

Gierusz W.

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2006

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tom Vol. 16, no. 1

87-109

EN

The main goal of this task was synthesis of the multivariable regulator for precise steering of the real, training ship. However such object is strongly nonlinear and its characteristics depends on current work conditions. Therefore one of possible ways to build a proper ship's controller can be the robust control theory approach. It enables the introduction of the effects of the modeling errors, unknown nonlinearities, unawareness of the particular object phenomena into the controller synthesis process. First part of the paper describes the meaning of the weighting functions in the system, the conditions for computing of the H∞ controller and the parametric and nonparametric uncertainties. The next part presents the requirements which should be fulfilled by regulator to the robust one and it describes the way how to calculate the multivariable robust controller via D-K iteration. In the last part of the paper exemplary results of the steering process from simulation and the real-time illustrates the control quality of the obtained closed-loop system.

16

Designing the subsets of signals and its application in systems theory

70%

Łozowicki A. , Łozowicka-Stupnicka T. , Łozowicka D.

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2009

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tom Vol. 35, no 1

47-55

EN

In the paper, simplified models of signals are introduced. The set of signals belonging to the class considered is divided into abstract subsets. Every subset of signals has a representative signal of a very simple form. These representative signals are next used as simplified models of signals and they can be applied to very complicated considerations in systems theory and control theory. For example, they are applied to designing high precision, state feedback control systems. In consequence, such systems approximate (for large gain in feedback loop) the inverse operation to the plant P considered. For solving this problem, the sum of differences of state variables of system and state of control signal are taken into consideration. Based on the simplified models of signals the linear combination of the state variables of system and state of control signal (not only sum of difference) can be used. This is important if the gain in the feedback tends to infinity. A scheme of such systems is presented in the paper.

17

Optimal control of active rotor suspension system

70%

Gosiewski Z. , Mystkowski A.

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2007

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tom Vol. 17, no. 4

459-468

EN

In the paper active magnetic bearings system was used for non-contact suspension of a rigid rotor. Optimal robust control method was applied to stabilize and reduce the rotor vibrations. The rotor is supported by two radial heteropolar magnetic bearings and additionally with one axial passive bearing with permanent magnets. The position of the rotor was measured in two radial directions of each active magnetic bearing and in axial direction of the passive magnetic bearing by the eddy-current sensors. The power amplifiers (PWM) were used to generate a current control signals. For pre-investigations a simple local PID controllers were designed. The PID controllers were used to stabilize nominal model of unstable open-loop system. Based on the performances of the PID closed-loop system the H-infinity optimal control laws were derived. The robust controllers were designed for augmented model of the plant. Next, the computer simulations and experimental investigations were carried out. The robust controller was designed according to Safonov, Limebeer and Chiang formulae. The control algorithm was implemented in a digital signal processor. The experimental and simulation results show the magnetic suspension system has good transient responses and tracking abilities. The H-infinity controller ensures the robust performance and stability of the closed-loop system in spite of disturbances and good vibration compensation.

18

Rationale for mu-synthesis control of flexible rotor-magnetic bearing systems

60%

Sawicki J. T.

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2008

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tom Vol. 2, no. 2

67-74

EN

The emergence of sophisticated formal control synthesis tools provokes important questions for any prospective user: why learn to use these new tools, what will they offer me? In synthesis of magnetic bearing controllers, it turns out that the range of stabilizing controllers is often quite narrow so that the difference between a poor controller and an “optimal” one may be small. Hence, the product of formal control synthesis tools often looks and performs much like what a reasonably clever control engineer would produce by hand. This paper demonstrates that the real value of these tools lies in a) generation of a performance benchmark which can be used to firmly establish the best performance relative to a specification and b) change of design parameter space to one which is relatively easy to maintain and represents a durable investment from an engineering process view.

19

Adaptive state feedback control for a class of linear systems with unknown bounds of uncertainties.

60%

Fenlin L. , Hao W. , Qingxian W. , Mingwu S. , Siying Z.

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2001

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tom Vol. 27, nr 3

23-34

EN

The problem of adaptive robust stabilization for a class of linear time-varying systems with disturbance and nonlinear uncertainties is considered. The bounds of the disturbance and uncertainties are assumed to be unknown, being even arbitrary. For such uncertain dynamical systems, the adaptive robust state feedback controller is obtained. And the resulting closed-loop systems are asymptotically stable in theory. Moreover, an adaptive robust state feedback control scheme is given. The scheme ensures the closed-loop systems exponentially practically stable and can be used in practical engineering. Finally, simulations show that the control scheme is effective.

20

Napęd bezpośredni z silnikiem synchronicznym o magnesach trwałych

60%

Zawirski K.

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2006

|

tom Nr 60

131-138

PL

W artykule omówiono zagadnienia sterowania i właściwości napędów elektrycznych bezpośrednich (bezprzekladniowych) z silnikami synchronicznymi o magnesach trwałych. Szczególną uwagę zwrócono na sterowanie odporne prędkością obrotową przy zmianach momentu bezwładności oraz na precyzyjne sterownie położeniem kątowym. Pokazane wyniki badań eksperymentalnych dobrze ilustrują właściwości napędu.

EN

The paper deals with problems of control and properties of electrical direct drive (without gear) based on permanent magnet synchronous motor. Methods of robust speed control against moment of inertia variation and precise position control have been elaborated. Presented experimental results illustrate gained drive characteristics.