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1

An improvement of Gamma approximation for reduction of continuous interval systems

Bokam Jagadish Kumar, Singh Vinay Pratap, Devarapalli Ramesh, García Márquez Fausto Pedro

Archives of Control Sciences

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2021

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Vol. 31, No. 2

347--373

EN

In recent, modeling practical systems as interval systems is gaining more attention of control researchers due to various advantages of interval systems. This research work presents a new approach for reducing the high-order continuous interval system (HOCIS) utilizing improved Gamma approximation. The denominator polynomial of reduced-order continuous interval model (ROCIM) is obtained using modified Routh table, while the numerator polynomial is derived using Gamma parameters. The distinctive features of this approach are: (i) It always generates a stable model for stable HOCIS in contrast to other recent existing techniques; (ii) It always produces interval models for interval systems in contrast to other relevant methods, and, (iii) The proposed technique can be applied to any system in opposite to some existing techniques which are applicable to second-order and third-order systems only. The accuracy and effectiveness of the proposed method are demonstrated by considering test cases of single-inputsingle-output (SISO) and multi-input-multi-output (MIMO) continuous interval systems. The robust stability analysis for ROCIM is also presented to support the effectiveness of proposed technique.

2

Modeling of MIMO system over fast fading channels

Pawelec J., Krawczyk Z., Kosmowski K.

TTS Technika Transportu Szynowego

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2012

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R. 19, nr 9

285--290, CD

EN

Two models of the Alamouti multiple input – multiple output (MIMO) system have been formed: the analytical and simulation one. The first model is simple and it reflects the quasi-static Rayleigh fading phenomena, while the second one is advanced and it expresses the fast fading effects. The results of analysis and simulations show that the Alamouti MIMO architecture significantly over performs the SISO systems (the SNR gain ~20 dB), but mainly within the quasi-static environment. In mobile conditions this gain and/or the overall system capacity under go a sharp decline.

PL

W referacie poddano eksperymentom symulacyjnym dwa modele MIMO Almaoutiego. Model funkcjonujący w warunkach quasi-statycznych zaników Rayleigha oraz w warunkach zaników szybkich Nakagami’ego. Dokonano oszacowania jaki jest rzeczywisty zysk zastosowania MIMO względem systemu jednokanałowego SISO. W modelowaniu wykorzystano Metodę Monte Carlo.

3

On the effect of chattering in the sliding mode control systems.

Bartoszewicz A.

Systems Science

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2000

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Vol. 26, nr 1

29-42

EN

Variable structure control systems with the ideal sliding motion are perfectly robust with respect to matched disturbance and parameter uncertainty. However, this mode of operation is not achieved in practice. Thus, in this paper the non-ideal sliding motion actually taking place in variable structure systems is investigated. The phenomenon of chattering, i.e., high frequency oscillations which inevitably occur in the systems with ideal relays, is analysed. It is shown that the oscillations are caused by fast usually neglected dynamics of the system, for instance, unmodelled delay or inertia. The describing function method is used to predict the amplitude and the frequency of the oscillations. Furthermore, a simple method is given to determine how the ideal relay input-output characteristics should be modified to eliminate the chattering without introducing excessive control errors. Simulation results confirming the theoretical analysis presented.

4

Beta Fuzzy Logic Systems: Approximation Properties in the Siso Case

Alimi A. M., Hassine R., Selmi M.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 4

857-875

EN

In this paper, a Single-Input Single-Output (SISO) Sugeno fuzzy model of the zeroth order with Beta membership functions for input variables is adopted. After the introduction of Beta Fuzzy Logic Systems (BFLS) a constructive theory is developed to establish the fact that they are universal approximators. Based on this theory, an algorithm, which can actually construct a BFLS approximating a given continuous function with an arbitrary degree of accuracy, is described. We then show that BFLSs satisfy more critical properties which are the best approximation property and the interpolation property. We complete the paper with a series of numerical comparisons between the approximation performances of BFLSs and other classes of widely used fuzzy logic systems. These comparisons confirm that BFLSs perform best in all the cases studied.