Wyniki wyszukiwania - Biblioteka Nauki

1

Synteza regulatora ułamkowego rzędu dla określonej klasy obiektów z opóźnieniem

100%

Ruszewski A.

|

tom R. 56, nr 5

400-403

PL

W pracy rozpatrzono problem doboru wartości parametrów regulatora ułamkowego rzędu zapewniającego zadany zapas stabilności układu regulacji z obiektem inercyjnym pierwszego rzędu z całkowaniem i opóźnieniem. Postać transmitancji regulatora wynika z zastosowania idealnej transmitancji Bodego jako transmitancji odniesienia dla układu otwartego z regulatorem. Wykorzystując klasyczną metodę podziału D podano analityczno-komputerowe metody wyznaczania obszarów stabilności na płaszczyźnie parametrów regulatora. Podano także proste zależności analityczne pozwalające wyznaczyć wartości parametrów regulatora, dla których rozpatrywany układ regulacji charakteryzuje się zadanymi wartościami zapasu modułu i fazy.

EN

The paper presents the design problem of a fractional order controller satisfying gain and phase margin of the closed-loop system with time-delay inertial plant with integral term (1). The controller transfer function (2) results from the use of Bode's ideal transfer function as a reference transfer function for the open loop system. The characteristic function of the closed-loop system with plant (1), controller (2) and the gain-phase margin tester (Fig. 1) is given by (3). The closed-loop system is said to be bounded-input bounded-output stable if and only if all the zeros of the characteristic function (3) have negative real parts. Using the classical D-partition method, a simple and efficient computational method for determining stability regions in the controller parameters space (α, kc) is given. Analytical descriptions for boundary of stability regions in the controller parameters space are determined. The stability region is located between the real zero boundary kc = 0 and the complex zero boundary of the form (7), (8). The presented descriptions for the boundary of stability regions are also used for obtaining stability regions for specified gain and phase margins requirements. To determine the stability regions for a given value of the control system gain margin A, one should set α = 0. On the other hand by setting A = 1, there can be obtained the stability regions for a given phase margin α. The stability regions of quasi-polynomial (3) are shown in Figs. 2 and 3. Any point from the stability region provides the gain and phase margins requirements. Moreover, the analytical forms directly expressing the controller parameters for specified gain and phase margin requirements are determined. The numerical examples confirm the results received on the basis of the D-partition method.

2

Stability conditions of fractional discrete-time scalar systems with pure delay

100%

Ruszewski A.

|

2013

|

tom R. 17, nr 2

340-344

EN

In the paper the problem of stability of fractional discrete-time linear scalar systems with state space pure delay is considered. Using the classical D-decomposition method, the necessary and sufficient condition for practical stability as well as the sufficient condition for asymptotic stability are given.

PL

W pracy rozpatrzono problem stabilności liniowych skalarnych układów dyskretnych niecałkowitego rzędu z czystym opóźnieniem zmiennych stanu. Wykorzystując metodę podziału D podano warunek konieczny i wystarczający praktycznej stabilności oraz warunek wystarczający stabilności asymptotycznej.

3

Stabilizacja układów całkujących ułamkowego rzędu z opóźnieniem za pomocą ułamkowego regulatora PD

100%

Ruszewski A.

|

2010

|

tom R. 14, nr 2

501-509

PL

W pracy rozpatrzono problem stabilności układów regulacji automatycznej złożonych z regulatora PD ułamkowego rzędu oraz obiektu całkującego ułamkowego rzędu z opóźnieniem. Wykorzystując klasyczną metodę podziału D podano proste analityczno-komputerowe metody wyznaczania obszarów stabilności na płaszczyźnie parametrów rozpatrywanego układu regulacji. Zaproponowane metody zastosowano także do wyznaczania obszarów stabilności dla zadanych zapasów stabilności modułu i fazy.

EN

The paper presents the stability problem of control systems composed of a fractional-order PD controller and a integrator plant of a fractional order with time delay. Using the classical D-partition method, a simple and efficient computational method for determining stability regions in the controller and plant parameters space is given. The presented method is also used for obtaining stability regions for specified gain and phase margins requirements.

4

Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

100%

Ruszewski A.

|

tom Vol. 26, no. 4

441--452

EN

The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.

5

Stabilization of Inertial Plant with Time Delay Using Fractional Order Controller

63%

Ruszewski A. , Nartowicz T.

|

tom Vol. 5, no. 2

117-121

EN

The paper presents the problem of designing of a fractional order controller satisfying the conditions of gain and phase margins of the closed-loop system with time-delay inertial plant. The transfer function of the controller follows directly from the use of Bode's ideal transfer function as a reference transfer function for the open loop system. Using the classical D-partition method and the gain-phase margin tester, a simple computational method for determining stability regions in the controller parameters plane is given. An efficient analytical procedure to obtain controller parameter values for specified gain and phase margin requirements is also given. The considerations are illustrated by numerical examples computed in MATLAB/Simulink.

6

Necessary and sufficient conditions for stability of fractional discrete-time linear state-space systems

63%

Busłowicz M. , Ruszewski A.

|

tom Vol. 61, nr 4

779--786

EN

In the paper the problems of practical stability and asymptotic stability of fractional discrete-time linear systems are addressed. Necessary and sufficient conditions for practical stability and for asymptotic stability are established. The conditions are given in terms of eigenvalues of the state matrix of the system. In particular, it is shown that (similarly as in the case of fractional continuous-time linear systems) in the complex plane exists such a region, that location of all eigenvalues of the state matrix in this region is necessary and sufficient for asymptotic stability. The parametric description of boundary of this region is given. Moreover, it is shown that Schur stability of the state matrix (all eigenvalues have absolute values less than 1) is not necessary nor sufficient for asymptotic stability of the fractional discrete-time system. The considerations are illustrated by numerical examples.

7

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

63%

Kaczorek T. , Ruszewski A.

|

2020

|

tom Vol. 30, No. 4

667--681

EN

The global stability of discrete-time nonlinear systems with descriptor positive linear parts and positive scalar feedbacks is addressed. Sufficient conditions for the global stability of standard and fractional nonlinear systems are established. The effectiveness of these conditions is illustrated on numerical examples.