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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

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.

3

Modified model following control structure

Brzózka J.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 9

1052-1054

EN

This paper presents a modified version of the control system with model following control (MFC). The auxiliary (corrective) controller has been designed for an input signal, which is the difference between the amplified state vectors of a model and process. The values of gain coefficients of the state variables of the model and process have been calculated according to the LQR (Linear Quadratic Regulator) procedure. It has been proved that a new controller improves the properties of the MFC system.

PL

Artykuł dotyczy dwu pętlowego układu regulacji ze śledzeniem modelu typu MFC (Model Following Control). Układ taki posiada dwa regulatory: główny oraz korekcyjny. W klasycznym rozwiązaniu sygnałem wejściowym regulatora pomocniczego jest różnica sygnałów wyjściowych z modelu i procesu. Pozwala to na generowanie korekcyjnego sygnału błędu w przypadku zaistnienia różnic między procesem i modelem. Takie rozwiązanie nie pozwala jednak w jawny sposób kontrolować zmiennych stanu procesu. Dlatego też w artykule przedstawiono zmodyfikowaną wersję układu regulacji MFC, z regulatorem pomocniczym (korekcyjnym), którego sygnałem wejściowym jest różnica odpowiednio wzmocnionych współrzędnych stanu modelu i procesu. Analizowany układ opisano w przestrzeni zmiennych stanu, a regulator korekcyjny został zaprojektowany jako regulator typu LQR (Linear Quadratic Regulator). W dalszej kolejności przeproawdzono analizę porównawczą własności nowego i klasycznego układu MFC (wartości własne, stopień oscylacyjności, stabilności oraz funkcję wrażliwości). Przedstawiono, że układ MFC może być wykorzystywany również jako tolerujący uszkodzenia (a nie tylko w przypadkach zmian dynamiki procesu), co umieszcza go w klasie układów regulacji odpornych na uszkodzenia. Zostało to zilustrowane przeprowadzonymi badaniami symulacyjnymi.

4

Non-Certainty-Equivalent Adaptive Control of a Nonlinear Aeroelastic System

Lee K. W., Singh S. N.

International Journal of Electronics and Telecommunications

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2010

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Vol. 56, No. 4

463-471

EN

The development of a non-certainty-equivalent adaptive control system for the control of a nonlinear aeroelastic system is the subject of this paper. The prototypical aeroelastic wing section considered here includes structural nonlinearity and a single control surface for the purpose of control. Its dynamical model has two-degree-of-freedom and describes the plunge and pitch motion. It is assumed that the model parameters (except the sign of one of the control input coefficients) are not known. The uncontrolled aeroelastic model exhibits limit cycle oscillation beyond a critical free-stream velocity. Based on the attractive manifold, and the immersion and invariance methodologies, a non-certainty-equivalent adaptive state variable feedback control law for the trajectory tracking of the pitch angle is derived. Using the Lyapunov analysis, asymptotic convergence of the state variables to the origin is established. It is shown that the trajectory of the system converges to a manifold. The special feature of the designed control system is that the closed-loop system asymptotically recovers the performance of a deterministic controller. This cannot happen if certainty-equivalent adaptive controllers are used. Simulation results are presented which show that the control system suppresses the oscillatory responses of the system in the presence of large parameter uncertainties.

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

Application of uncertain variables in an adaptive decision system for a complex of operations

Orski D., Sugisaka M.

Systems Science

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2004

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Vol. 30, no 3

85-94

EN

The paper concerns a decision plant consisting of parallel operations, which are described by relational models with unknown parameters. The unknown parameters are assumed to be values of uncertain variables characterized by certainty distributions given by an expert. The solution of a decision problem and, consequently, performance of the knowledge-based decision system is very sensitive to the forms and parameters of certainty distributions. In the paper, it is shown how application of an adaptation process, consisting in step by step changing of parameters in certainty distributions based on current performance evaluation, may improve performance of a decision system under consideration. An illustrative example and results of simulations are included.