lyapunov’s theorem
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Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 403
Author(s):  
Ahmed G. Mahmoud A. Aziz ◽  
Hegazy Rez ◽  
Ahmed A. Zaki Diab

This paper introduces a novel sensorless model-predictive torque-flux control (MPTFC) for two-level inverter-fed induction motor (IM) drives to overcome the high torque ripples issue, which is evidently presented in model-predictive torque control (MPTC). The suggested control approach will be based on a novel modification for the adaptive full-order-observer (AFOO). Moreover, the motor is modeled considering core losses and a compensation term of core loss applied to the suggested observer. In order to mitigate the machine losses, particularly at low speed and light load operations, the loss minimization criterion (LMC) is suggested. A comprehensive comparative analysis between the performance of IM drive under conventional MPTC, and those of the proposed MPTFC approaches (without and with consideration of the LMC) has been carried out to confirm the efficiency of the proposed MPTFC drive. Based on MATLAB® and Simulink® from MathWorks® (2018a, Natick, MA 01760-2098 USA) simulation results, the suggested sensorless system can operate at very low speeds and has the better dynamic and steady-state performance. Moreover, a comparison in detail of MPTC and the proposed MPTFC techniques regarding torque, current, and fluxes ripples is performed. The stability of the modified adaptive closed-loop observer for speed, flux and parameters estimation methodology is proven for a wide range of speeds via Lyapunov’s theorem.



Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1095
Author(s):  
Ángel Hernández-Gómez ◽  
Victor Ramirez ◽  
Belem Saldivar

The fault detection method has been used usually to give a diagnosis of the performance and efficiency in the proton exchange membrane fuel cell (PEMFC) systems. To be able to use this method a lot of sensors are implemented in the PEMFC to measure different parameters like pressure, temperature, voltage, and electrical current. However, despite the high reliability of the sensors, they can fail or give erroneous measurements. To address this problem, an efficient solution to replace the sensors must be found. For this reason, in this work, the immersion and invariance method is proposed to develop an oxygen pressure estimator based on the voltage, electrical current density, and temperature measurements. The estimator stability region is calculated by applying Lyapunov’s Theorem and constraints to achieve stability are established for the oxygen pressure, electrical current density, and temperature. Under these estimator requirements, oxygen pressure measurements of high reliability are obtained to fault diagnosis without the need to use an oxygen sensor.



Author(s):  
Tedjini Hamza ◽  
Messaoud Fatima Zahra ◽  
Kadri Boufeldja

<p>Reactive power compensation is an essential part of a power system and the static synchronous compensator (STATCOM) plays an important role in controlling the reactive power flow over the transmission line. The basic building block of the STATCOM is a voltage source inverter (VSI) that generates a synchronous sinusoidal voltage and because of the high MVA ratings, it would be expensive to provide independent, equal, regulated dc voltage sources to power the multilevel converters which are presently proposed for STATCOMs. Dc voltage sources can be derived from the dc link capacitances which are charged by the rectified ac power. In this paper a new stronger control combined of nonlinear control based Lyapunov’s theorem and Ant Colony Algorithm (ACA) to maintain stability of multilevel STATCOM and the utility.</p>



Author(s):  
Mansour Bechar ◽  
Abdeldjebar Hazzab ◽  
Mohamed Habbab ◽  
Pierre Sicard

In this paper, Reduced-Order Observer For Real-Time Implementation Speed Sensorless Control of Induction Using RT-LAB Softwareis presented. Speed estimation is performed through a reduced-order observer. The stability of the proposed observer is proved based on Lyapunov’s theorem. The model is initially built offline using Matlab/Simulink and implemented in real-time environment using RT-LAB package and an OP5600 digital simulator. RT-LAB configuration has two main subsystems master and console subsystems. These two subsystems were coordinated to achieve the real-time simulation. In order to verify the feasibility and effectiveness of proposed method, experimental results are presented over a wide speed range, including zero speed.





2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Ryosuke Kasai ◽  
Yusaku Yamaguchi ◽  
Takeshi Kojima ◽  
Tetsuya Yoshinaga

Iterative reconstruction (IR) algorithms based on the principle of optimization are known for producing better reconstructed images in computed tomography. In this paper, we present an IR algorithm based on minimizing a symmetrized Kullback-Leibler divergence (SKLD) that is called Jeffreys’ J-divergence. The SKLD with iterative steps is guaranteed to decrease in convergence monotonically using a continuous dynamical method for consistent inverse problems. Specifically, we construct an autonomous differential equation for which the proposed iterative formula gives a first-order numerical discretization and demonstrate the stability of a desired solution using Lyapunov’s theorem. We describe a hybrid Euler method combined with additive and multiplicative calculus for constructing an effective and robust discretization method, thereby enabling us to obtain an approximate solution to the differential equation. We performed experiments and found that the IR algorithm derived from the hybrid discretization achieved high performance.



2018 ◽  
Vol 146 (9) ◽  
pp. 3825-3838 ◽  
Author(s):  
Marcin Bownik


2018 ◽  
Vol 34 ◽  
pp. 304-319 ◽  
Author(s):  
Chandrashekaran Arumugasamy ◽  
Sachindranath Jayaraman ◽  
Vatsalkumar Mer

For a proper cone $K$ in a finite dimensional real Hilbert space $V$, a linear map $L$ is said to be $K$-semipositive if there exists $d \in K^\circ$, the interior of $K$, such that $L(d) \in K^\circ$. The aim of this manuscript is to characterize $K$-semipositivity of linear maps relative to a proper cone. Among several results obtained, $K$-semipositivity is characterized in terms of products of the form $YX^{-1}$ for $K$-positive linear maps ($L(K \setminus \{0\}) \subseteq K^\circ$) with $X$ invertible, semipositivity of matrices relative to the $n$-dimensional Lorentz cone $\mathcal{L}^n_{+}$ is characterized, semipositivity of the following three linear maps relative to the cone $\mathcal{S}^n_{+}$: $X \mapsto AXB$ (denoted by $M_{A,B}$), $X \mapsto AXB + B^tXA^t$ (denoted by $L_{A,B}$), where $A, B \in M_n(\reals)$, and $X \mapsto X - AXA^t$ (denoted by $S_A$, known as the Stein transformation) is characterized. It is also proved that $M_{A,B}$ is semipositive if and only if $B = \alpha A^t$ for some $\alpha > 0$, the map $L_{A,B}$ is semipositive if and only if $A(B^t)^{-1}$ is positive stable. A particular case of the new result generalizes Lyapunov's theorem. Decompositions of the above maps (when they are semipositive) in the form $L_1L_2^{-1}$, where $L_1$ and $L_2$ are both positive and invertible (assuming $A$ is invertible in the case of $S_A$) are presented. Moreover, a question on invariance of the semipositive cone $\mathcal{K}_A$ of a matrix under $A$ is partially answered.



Author(s):  
Peter A. Loeb ◽  
Salim Rashid
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