Wyniki wyszukiwania - BazTech

1

Dynamic sliding mode control based on a full-order observer: Underactuated electro-mechanical system regulation

Ordaz Patricio, Romero-Trejo Hugo, Cuvas Carlos, Sandre Omar

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 1

29--43

EN

This paper concerns the synthesis of a nonlinear robust output controller based on a full-order observer for a class of uncertain disturbed systems. The proposed method guarantees that, in finite time, the system trajectories go inside a minimal neighborhood ultimately bounded. To this end, the attractive ellipsoid method is enhanced by applying the dynamic sliding mode control performance properties. Furthermore, in order to guarantee the stability of the trajectory around the trivial solution in the uniform-ultimately bounded sense, the feasibility of a specific matrix inequality problem is provided. With this feasible set of matrix inequalities, the separation principle of the controller/observer scheme considered also holds. To achieve a system performance improvement, a numerical algorithm based on the small size ultimate bound is presented. Finally, to illustrate the theoretical performance of the designed controller/observer, a numerical example dealing with the stabilization of a disturbed electromechanical system with uncertain and unmodeled dynamics is presented.

2

A hierarchical observer for a non-linear uncertain CSTR model of biochemical processes

Czyżniewski Mateusz, Łangowski Rafał

International Journal of Applied Mathematics and Computer Science

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2024

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Vol. 34, no. 1

45--64

EN

The problem of estimation of unmeasured state variables and unknown reaction kinetic functions for selected biochemical processes modelled as a continuous stirred tank reactor is addressed in this paper. In particular, a new hierarchical (sequential) state observer is derived to generate stable and robust estimates of the state variables and kinetic functions. The developed hierarchical observer uses an adjusted asymptotic observer and an adopted super-twisting sliding mode observer. The stability of the proposed hierarchical observer is investigated under uncertainty in the system dynamics. The stability analysis of the estimation error dynamics is carried out based on the methodology associated with linear parameter-varying systems and sliding mode regimes. The developed hierarchical observer is implemented in the Matlab/Simulink environment and its performance is validated via simulation. The obtained satisfactory estimation results demonstrate high effectiveness of the devised hierarchical observer.

3

On the finite time stabilization via robust control for uncertain disturbed systems

Ordaz Patricio, Alazki Hussain, Sánchez Bonifacio, Ordaz-Oliver Mario

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 1

71--82

EN

This paper deals with the finite-time stabilization problem for a class of uncertain disturbed systems using linear robust control. The proposed algorithm is designed to provide the robustness of a linear feedback control scheme such that system trajectories arrive at a small-size attractive set around an unstable equilibrium in a finite time. To this end, an optimization problem with a linear matrix inequality constraint is presented. This means that the effects of external disturbances, as well as matched and mismatched uncertain dynamics, can be significantly reduced. Finally, the performance of the suggested closed-loop control strategies is shown by the trajectory tracking of an unmanned aerial vehicle flight.

4

LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials

Sánchez Marcelino, Bernal Miguel

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

275--283

EN

This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a generalisation of the characteristic polynomial, which proves to outperform former results on the subject. Moreover, the derived conditions have the advantage of being cast as linear matrix inequalities under mild assumptions.

5

Metody opisu niepewności parametrów układu w badaniach systemu elektroenergetycznego

Robak S.

Przegląd Elektrotechniczny

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2006

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R. 82, nr 5

72-76

PL

W artykule omówiono główne czynniki mające wpływ na zmienność parametrów oraz stanów pracy systemu elektroenergetycznego. Przedstawiono metody opisu niepewności, dokonując ogólnej charakterystyki wybranych modeli. Bardziej szczegółowo omówiono zastosowanie analizy przedziałowej w tym twierdzenia Charitonowa. Zawarto przykład obliczeniowy obrazujący zastosowanie przyjętego modelu niepewności w obliczeniach stabilności lokalnej systemu.

EN

The main factors affecting the variability of power system parameters and states are presented in this paper. Uncertainty assessment methods have been outlined by performing an general review of selected models. Later the use of interval stability and especially its application based on Kharitonov theorem is presented in details. Finally an example illustrating the application of the developed uncertainty model in steady-state stability analysis is included.

6

On The Stability of Neutral-type Uncertain Systems With Multiple Time Delays

Liu P. L.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 2

221-229

EN

The problems of both single and multiple delays for neutral-type uncertain systems are considered. First, for single neutral time delay systems, based on a Razumikhin-type theorem, some delay-dependent stability criteria are derived in terms of the Lyapunov equation for various classes of model transformation and decomposition techniques. Second, robust control for neutral systems with multiple time delays is considered. Finally, we demonstrate numerical examples to illustrate the effectiveness of the proposed approaches. Compared with results existing in the literature, our methods are shown to be superior to them.

7

Observer design for systems with unknown inputs

Hui S., Żak S.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

431-446

EN

Design procedures are proposed for two different classes of observers for systems with unknown inputs. In the first approach, the state of the observed system is decomposed into known and unknown components. The unknown component is a projection, not necessarily orthogonal, of the whole state along the subspace in which the available state component resides. Then, a dynamical system to estimate the unknown component is constructed. Combining the output of the dynamical system, which estimates the unknown state component, with the available state information results in an observer that estimates the whole state. It is shown that some previously proposed observer architectures can be obtained using the projection operator approach presented in this paper. The second approach combines sliding modes and the second method of Lyapunov resulting in a nonlinear observer. The nonlinear component of the sliding mode observer forces the observation error into the sliding mode along a manifold in the observation error space. Design algorithms are given for both types of observers.