PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 36

Liczba wyników na stronie
first rewind previous Strona / 2 next fast forward last
Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  robust stability
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 2 next fast forward last
1
Content available Design of robust multi-loop PI controller for improved disturbance rejection with constraint on minimum singular value
Arun Pathiran, Muniraj Rathinam, Boselin Prabhu S.R., Jarin T., Willjuice Iruthayarajan M.
Archives of Control Sciences
|
2023
|
Vol. 33, No. 4
839--859
EN
Disturbance rejection performance optimization with constraints on robustness for a multivariable process is commonly encountered in industrial control applications. This paper presents the tuning of a multi-loop Proportional Integral (PI) controller method to enhance the performance of load disturbance rejection using evolutionary optimization. The proposed design methodology is formulated to minimize the load disturbance rejection response and the input control energy under the constraints of robust stability. The minimum singular value of multiplicative uncertainty is considered a multi-loop system robust stability indicator. Optimization is performed to achieve the same, or higher level than the most-explored Direct Synthesis (DS) based multi-loop PI controller, which is derived from a conventional criterion. Simulation analysis clearly proved that the proposed multi-loop PI controller tuning method gives better disturbance rejection, and either, the same or a higher level of robust stability when compared to the DS-based multi-loop PI controller.
2
Content available Stability analysis and H∞ control of discrete T–S fuzzy hyperbolic systems
Duan R., Li J., Zhang Y., Yang Y., Chen G.
International Journal of Applied Mathematics and Computer Science
|
2016
|
Vol. 26, no. 1
133--145
EN
This paper focuses on the problem of constraint control for a class of discrete-time nonlinear systems. Firstly, a new discrete T–S fuzzy hyperbolic model is proposed to represent a class of discrete-time nonlinear systems. By means of the parallel distributed compensation (PDC) method, a novel asymptotic stabilizing control law with the “soft” constraint property is designed. The main advantage is that the proposed control method may achieve a small control amplitude. Secondly, for an uncertain discrete T–S fuzzy hyperbolic system with external disturbances, by the proposed control method, the robust stability and H∞ performance are developed by using a Lyapunov function, and some sufficient conditions are established through seeking feasible solutions of some linear matrix inequalities (LMIs) to obtain several positive diagonally dominant (PDD) matrices. Finally, the validity and feasibility of the proposed schemes are demonstrated by a numerical example and a Van de Vusse one, and some comparisons of the discrete T–S fuzzy hyperbolic model with the discrete T–S fuzzy linear one are also given to illustrate the advantage of our approach.
3
Content available Robust stability of positive linear time delay systems under time-varying perturbations
Ngoc P. H. A., Tinh C. T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
|
Vol. 63, nr 4
947--954
EN
By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.
4
Content available On the existence of a common solution to the Lyapunov equations
Białas S., Góra M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2015
|
Vol. 63, nr 1
163-–168
EN
In this paper, a system of Lyapunov equations A*i P + PAi = −Qi (i = 1, . . . ,m), (A) is considered in which Ai are given n × n complex matrices, Qi are unknown n × n Hermitian positive definite matrices and P, if any, is a common solution to the Lyapunov equations (A). Both sufficient and necessary and sufficient conditions are derived for the existence of such a matrix P. Examples are presented to illustrate the results.
5
Content available Robust stability of a class of uncertain fractional order linear systems with pure delay
Busłowicz M.
Archives of Control Sciences
|
2015
|
Vol. 25, no. 2
177--187
EN
The paper considers the robust stability problem of uncertain continuous-time fractional order linear systems with pure delay in the following two cases: a) the state matrix is a linear convex combination of two known constant matrices, b) the state matrix is an interval matrix. It is shown that the system is robustly stable if and only if all the eigenvalues of the state matrix multiplied by delay in power equal to fractional order are located in the open stability region in the complex plane. Parametric description of boundary of this region is derived. In the case a) the necessary and sufficient computational condition for robust stability is established. This condition is given in terms of eigenvalue-loci of the state matrix, fractional order and time delay. In the case b) the method for determining the rectangle with sides parallel to the axes of the complex plane in which all the eigenvalues of interval matrix are located is given and the sufficient condition for robust stability is proposed. This condition is satisfied if the rectangle multiplied by delay in power equal to fractional order lie in the stability region. The considerations are illustrated by numerical examples.
6
Content available remote Solution of a mixed sensitivity problem with optimized weights and time performance index for a robust servo velocity and position controller
Sarjaš A., Chowdhury A.
Przegląd Elektrotechniczny
|
2013
|
R. 89, nr 5
205-208
EN
Robustness of servo control systems in terms of uncertainties and disturbances is still an open issue in feedback control. The concept of an uncertain LTI system is essential for robust control. Model uncertainty arises when system parameters are not precisely known, or can vary over a given range. The article presents a robust velocity and position controller for a servo system with a DC-motor. The aim of the work is to synthesize a feedback control structure with a controller in the direct branch, with which the robustness and stability performance will be ensured. For the design procedure a mixed-sensitivity approach with an additional time performance index is used. The time performance index introduces a subsequent criterion in the mixed sensitivity approach to ensure accurate dynamic performance of the feedback loop. For simplification of the controller structure the evolution optimization will be employed. The control strategy has been tested on real system with use of TI-DSP microcontroller.
PL
W artykule opisano metodę sterowania pozycją i prędkością w zamkniętej pętli dla serwomechanizmu z silnikiem DC. Dla zapewnienia niezawodności i stabilności algorytmu zastosowano optymalizację typu mixed-sensitivity z dodatkowym wskaźnikiem skuteczności w czasie. W celu uproszczenia struktury sterowania zastosowana zostanie także optymalizacja ewolucyjna. Przeprowadzono badania eksperymentalne.
7
Content available remote QFTźbased robust velocity controller design for a SW-OC motor
Igrec D., Sarjaš A., Chowdhury A.
Przegląd Elektrotechniczny
|
2011
|
R. 87, nr 3
81-84
EN
The arlicle presents a robust velocity controller design on the basis of Quantitative Feedback Theory for a series-wound OC motor. The aim of this work is to show the design technique with mathematical modelling of a series-wound OC motor, preparation of performance characteristics, selecting QFT boundaries and choosing the controller structure. The controlled system performance obtained with the presented control strategy has been validated through simulation and the results have shown to be consistent with the expected performance of the linear and nonlinear models.
PL
Artykuł przedstawia projekt sterownika prędkości na bazie teorii ilościowego sprzężenia zwrotnego (QFT) dla silnika szeregowego prądu stałego. Celem pracy jest pokazanie techniki projektowania z matematycznym modelem silnika, przygotowanie charakterystyki działania, wyselekcjonowanie ograniczeń QFT oraz wybór struktury sterownika. Działanie systemu sterowanego otrzymane ze strategii działania zostało walidowane przez symulację i rezultaty nie pokazały sprzeczności z oczekiwanym zachowaniem modeli liniowych i nieliniowych.
8
Content available Odporna stabilność rodziny wielomianów niecałkowitego stopnia o współczynnikach wieloliniowo zależnych od niepewnych parametrów
Kalinowski T., Busłowicz M.
Pomiary Automatyka Robotyka
|
2011
|
R. 15, nr 2
576-585
PL
W pracy rozpatrzono problem odpornej stabilności rodzin wielomianów charakterystycznych niecałkowitego stopnia, których współczynniki zależą wieloliniowo od niepewnych parametrów. Podano komputerowe metody badania odpornej stabilności. Proponowane metody bazują na warunku wykluczenia zera i na twierdzeniu o odwzorowaniu, znanych z teorii odpornej stabilności rodzin wielomianów całkowitych stopni. Rozważania zilustrowano przykładem.
EN
The paper considers the problem of robust stability of families of fractional degree characteristic polynomials with coefficients multilinearly dependent on uncertain parameters. Computer methods for checking of robust stability are given. The methods proposed are based on the Zero Exclusion Condition and on the Mapping Theorem known from the theory of robust stability of families of natural degree polynomials. The considerations are illustrated by example.
9
Content available Improved stability and robust stability conditions for a general model of scalar continuous-discrete linear systems
Busłowicz M.
Pomiary Automatyka Kontrola
|
2011
|
R. 57, nr 2
188-189
EN
The paper improves the main result of the previous authors paper [1]. First it is shown that the conditions for asymptotic stability and for robust stability of a general model of scalar continuous-discrete linear systems given in this paper are only necessary. Next, the necessary and sufficient conditions are established. The conditions are expressed in terms of coefficients of the model.
PL
W pracy podano poprawione warunki stabilności oraz odpornej stabilności modelu ogólnego (1) skalarnych liniowych układów ciągło-dyskretnych, standardowych oraz dodatnich. Pokazano, że podane w pracy [1] warunki są tylko konieczne. Bazują one bowiem na warunku stabilności (7), który jest słuszny dla klasy (5) wielomianów dwóch zmiennych niezależnych. Wielomian charakterystyczny (4) rozpatrywanego układu nie należy do klasy (5), ale do klasy (8) wielomianów. Wobec tego do badania stabilności modelu (1) należy wykorzystać warunki (7) i (9), które są konieczne i wystarczające dla asymptotycznej stabilności klasy (8) wielomianów. Bazując na tych warunkach w twierdzeniu 1 sformułowano kryterium asymptotycznej stabilności analizowanej klasy układów. Warunki asymptotycznej stabilności oraz odpornej stabilności standardowego układu ciągło-dyskretnego podano w twierdzeniu 2 oraz w twierdzeniu 4, odpowiednio. Natomiast warunki asymptotycznej stabilności oraz odpornej stabilności dodatniego układu ciągło-dyskretnego podano w twierdzeniach 3 i 5. Wszystkie warunki są wyrażone w terminach współczynników modelu (1) (lub wartości krańcowych przedziałów (18), z których te współczynniki mogą przyjmować swoje wartości).
10
Content available Stability and robust stability conditions for a general model of scalar continuous-discrete linear systems
Busłowicz M.
Pomiary Automatyka Kontrola
|
2010
|
R. 56, nr 2
133-135
EN
The problems of asymptotic stability and robust stability of the general model of scalar linear dynamic continuous-discrete systems, standard and positive, are considered. Simple analytic conditions for asymptotic stability and for robust stability are given. These conditions are expressed in terms of coefficients of the model. The considerations are illustrated by numerical examples.
PL
W pracy rozpatrzono problemy stabilności oraz odpornej stabilności modelu ogólnego (1) skalarnych liniowych układów ciągło-dyskretnych, standardowych oraz dodatnich. Bazując na podanym w twierdzeniu 3 kryterium stabilności analizowanej klasy układów, wyprowadzono proste analityczne warunki asymptotycznej stabilności oraz odpornej stabilności. Warunki asymptotycznej stabilności oraz odpornej stabilności standardowego układu ciągło-dyskretnego podano w twierdzeniu 4 oraz w twierdzeniu 6, odpowiednio. Natomiast warunki asymptotycznej stabilności oraz odpornej stabilności dodatniego układu ciągło-dyskretnego podano w twierdzeniach 5 i 8, odpowiednio. Wszystkie warunki są wyrażone w terminach współczynników modelu (1) (lub wartości krańcowych przedziałów (13), z których te współczynniki mogą przyjmować swoje wartości). Rozważania zostały zilustrowane przykładami liczbowymi.
11
Content available remote Robust stability of positive continuous-time linear systems with delays
Busłowicz M.
International Journal of Applied Mathematics and Computer Science
|
2010
|
Vol. 20, no 4
665-670
EN
The paper is devoted to the problem of robust stability of positive continuous-time linear systems with delays with structured perturbations of state matrices. Simple necessary and sufficient conditions for robust stability in the general case and in the case of systems with a linear uncertainty structure in two sub-cases: (i) a unity rank uncertainty structure and (ii) nonnegative perturbation matrices are established. The problems are illustrated with numerical examples.
12
Content available remote Simple conditions for robust stability of positive discrete-time linear systems with delays
Busłowicz M.
Control and Cybernetics
|
2010
|
Vol. 39, no 4
1159-1171
EN
The paper is devoted to the problem of robust stability of positive linear discrete-time systems with delays in the case of structured perturbations of state matrices. Simple new necessary and sufficient conditions for robust stability in the general case and in the case of system with linear uncertainty structure are established for two sub-cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices. It is shown that robust stability of the positive discrete-time linear system with delays is equivalent to: 1) robust stability of the corresponding positive system without delays of the same order as time-delay system - in the general case, 2) asymptotic stability of finite family of the positive vertex systems without delays - in the case of a linear unity rank uncertainty structure, 3) asymptotic stability of only one positive vertex system without delays - in the case of a linear uncertainty structure with non-negative perturbation matrices.
13
Content available remote Schur stability of the convex combination of complex polynomials
Białas S., Białas M.
Control and Cybernetics
|
2010
|
Vol. 39, no 2
551-558
EN
This paper gives a necessary and sufficient condition for Schur stability of the convex combination of complex polynomials. It is a generalization of the work by Ackerman and Barmish (1988).
14
Content available remote Odporna stabilność ukladów ciągło-dyskretnych o funkcji charakterystycznej zależnej liniowo od jednego niepewnego parametru
Busłowicz M., Sokólski M.
Pomiary Automatyka Robotyka
|
2009
|
R. 13, nr 2
435-444
PL
Rozpatrzono problem badania odpornej stabilności liniowego układu hybrydowego ciągło-dyskretnego, którego wielomian charakterystyczny zależy liniowo od jednego niepewnego parametru. Wielomian ten można przedstawić w postaci wypukłej kombinacji dwóch wielomianów dwóch zmiennych niezależnych. Podano częstotliwościowe metody badania odpornej stabilności takiej kombinacji. Bazują one na warunku wykluczenia zera znanym z teorii odpornej stabilności rodzin wielomianów jednej zmiennej. Rozważania zilustrowano przykładem.
EN
The problem of robust stability of linear continuous-discrete systems with characteristic polynomial linearly dependent on one uncertain parameter is considered. This problem is equivalent to the problem of robust stability of convex combination of two polynomials of two independent variables. Frequency domain methods for robust stability analysis of such a combination are given. The method proposed are based on the zero exclusion condition known from the theory of robust stability of families of polynomials of one variable. The considerations are illustrated by numerical example.
15
Content available remote Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties
Rauh A., Minisini J., Hofer E. P.
International Journal of Applied Mathematics and Computer Science
|
2009
|
Vol. 19, no 3
425-439
EN
Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
16
Content available remote Odporna stabilność liniowego ciągłego układu ułamkowego rzędu współmiernego o funkcji charakterystycznej zależnej liniowo od jednego niepewnego parametru
Busłowicz M., Kalinowski T.
Pomiary Automatyka Robotyka
|
2008
|
R. 12, nr 2
465--474
PL
Rozpatrzono zagadnienie badania odpornej stabilności liniowego ciągłego układu ułamkowego rzędu współmiernego, którego wielomian charakterystyczny zależy liniowo od jednego niepewnego parametru. Wielomian ten można przedstawić w postaci wypukłej kombinacji dwóch wielomianów ułamkowego stopnia. Podano częstotliwościowe metody badania odpornej stabilności takiej kombinacji. Bazują one na warunku wykluczenia zera znanym z teorii odpornej stabilności rodzin wielomianów stopnia naturalnego. Rozważania zilustrowano przykładem.
EN
The problem of robust stability of linear continuous-time fractional systems of commensurate order with characteristic polynomial linearly dependent on one uncertain parameter is considered. This problem is equivalent to the problem of robust stability of convex combination of two fractional commensurate degree polynomials. Frequency domain methods for robust stability analysis of such a combination are given. The method proposed are based on the zero exclusion condition known from the theory of robust stability of families of natural degree polynomials. The considerations are illustrated by numerical example.
17
Content available Simple conditions for robust stability of linear positive discrete-time systems with one delay
Busłowicz M.
Journal of Automation Mobile Robotics and Intelligent Systems
|
2008
|
Vol. 2, No. 2
18-22
EN
Simple new necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with one delay in the general case and in the two special cases: 1) linear unity rank uncertainty structure, 2) linear uncertainty structure with non-negative perturbation matrices, are established. The conditions are based on the new simple criterion for asymptotic stability of the positive linear discrete-time systems with one delay, proved in the paper. The considerations are illustrated by numerical examples.
18
Content available remote On parametric Hurwitz stability margin of real polynomials
Husek P.
Control and Cybernetics
|
2008
|
Vol. 37, no 3
549-563
EN
The paper deals with the problem of determining Hurwitz stability of a ball of polynomials defined by a weighted lp norm in the coefficient space where p is an arbitrary positive integer including infinity. The solution of the case when the weights are supposed to be the same for coefficient being above and below its nominal value corresponding to symmetric ball has been given by Tsypkin and Polyak. However, sometimes it seems to be useful to have a possibility to consider these weights as different, resulting in the asymmetric ball. This is, for example, the situation where the weights express our level of confidence that the real value of a coefficient lies in some interval. Such approach is used if the value of a coefficient is estimated by an expert. Solution of the problem is based on frequency domain plot in the complex plane and on applying the Zero Exclusion Theorem. The main idea consists in separation of the original problem into four subproblems and using an appropriate coordinate transformation which makes the value set independent of frequency. This transformation makes it possible to move the relative value set into the origin of the complex plane and to easily formulate the necessary and sufficient condition of Hurwitz stability of asymmetric ball of polynomials with prescribed radius or determine the maximum radius preserving stability. The whole graphical procedure consists of four plots instead of one, needed in the symmetric case.
19
Content available remote Simple stability conditions for linear positive discrete-time systems with delays
Busłowicz M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2008
|
Vol. 56, nr 4
325-328
EN
Simple new necessary and sufficient conditions for asymptotic stability of the positive linear discrete-time systems with delays in states are established. It is shown that asymptotic stability of the system is equivalent to asymptotic stability of the corresponding positive discrete-time system without delays of the same size. The considerations are illustrated by numerical examples.
20
Content available Robust stability of convex combination of two fractional degree characteristic polynomials
Busłowicz M.
Acta Mechanica et Automatica
|
2008
|
Vol. 2, no. 2
5-10
EN
The paper considers the problem of robust stability of convex combination of two fractional degree characteristic polynomials. This problem is equivalent to the problem of robust stability of linear continuous-time fractional systems with characteristic polynomial linearly dependent on one uncertain parameter. Frequency domain methods for robust stability analysis of such a combination are given. The methods proposed are based on the Zero Exclusion Condition known from the theory of robust stability of families of natural degree polynomials. The considerations are illustrated by numerical example.
first rewind previous Strona / 2 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.