scholarly journals Backstepping Based Nonlinear Sensorless Control of Induction Motor System

2021 ◽  
Vol 54 (3) ◽  
pp. 495-502
Author(s):  
Farid Berrezzek ◽  
Abdelhak Benheniche
Keyword(s):  
Induction Motor ◽  
Control Strategy ◽  
Sensorless Control ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Asymptotic Convergence ◽  
Matrix Inequalities ◽  
Circle Criterion ◽  
The Stability ◽  
Criterion Approach

This work proposes a sensorless control strategy for the induction motor (IM) using a Backstepping control and a nonlinear observer based on the circle-criterion approach. The Backstepping is a powerful control strategy that deals with nonlinear higher-order systems and includes non-measurable parameters related to the (IM). The nonlinear observer approach is intended to determine these important parameters. The circle-criterion approach is employed to determine the observer gain matrices as a solution of LMI (linear matrix inequalities) that guarantee the stability conditions of the designed observer. The main objective of this method is to solve the problem of the nonlinearities of the system which ensure the global asymptotic convergence of the observed dynamics and to improve the performance of the induction motors. The efficiency and correctness of the proposed scheme are proven by several numerical simulations.

scholarly journals A comparative study of nonlinear circle criterion based observer and H∞ observer for induction motor drive

2019 ◽  
Vol 10 (3) ◽  
pp. 1229
Author(s):  
Farid Berrezzek ◽  
Wafa Bourbia ◽  
Bachir Bensaker
Keyword(s):  
Comparative Study ◽  
Induction Motor ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Linear Matrix ◽  
Optimization Approach ◽  
Lmi Optimization ◽  
Circle Criterion ◽  
True State ◽  
The Stability

<span lang="EN-US">This paper deals with a comparative study of circle criterion based nonlinear observer<em> </em>and <em>H<sub>∞</sub></em> observer for induction motor (IM) drive. The  advantage of the circle criterion approach for nonlinear observer design is that it directly handles the nonlinearities of the system with less restriction  conditions in contrast of the other methods which attempt to eliminate them. However the <em>H<sub>∞</sub></em> observer guaranteed the stability taking into account disturbance and noise attenuation. Linear matrix inequality (LMI) optimization approach is used to compute the gains matrices for the two observers. The simulation results show the superiority of <em>H<sub>∞</sub></em> observer in the sense that it can achieve convergence to the true state, despite the nonlinearity of model and the presence of disturbance.</span>

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

Stability of nonlinear time-delay systems satisfying a quadratic constraint

2016 ◽  
Vol 40 (3) ◽  
pp. 712-718 ◽  
Author(s):  
Mohsen Ekramian ◽  
Mohammad Ataei ◽  
Soroush Talebi
Keyword(s):  
Time Delay ◽  
Uncertain Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Quadratic Constraint ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability

The stability problem of nonlinear time-delay systems is addressed. A quadratic constraint is employed to exploit the structure of nonlinearity in dynamical systems via a set of multiplier matrices. This yields less conservative results concerning stability analysis. By employing a Wirtinger-based inequality, a delay-dependent stability criterion is derived in terms of linear matrix inequalities for the nominal and uncertain systems. A numerical example is used to demonstrate the effectiveness of the proposed stability conditions in dealing with some larger class of nonlinearities.

scholarly journals Temperature Control of Gas Chromatograph Based on Switched Delayed System Techniques

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiao-Liang Wang ◽  
Ming-Xu Zhang ◽  
Kun-Zhi Liu ◽  
Xi-Ming Sun
Keyword(s):  
Temperature Control ◽  
Lyapunov Functional ◽  
Reference Signal ◽  
Pi Controller ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Gas Chromatograph ◽  
Delayed System ◽  
The Stability

We address the temperature control problem of the gas chromatograph. We model the temperature control system of the gas chromatograph into a switched delayed system and analyze the stability by common Lyapunov functional technique. The PI controller parameters can be given based on the proposed linear matrix inequalities (LMIs) condition and the designed controller can make the temperature of gas chromatograph track the reference signal asymptotically. An experiment is given to illustrate the effectiveness of the stability criterion.

scholarly journals New Decentralized Control of Interconnected Systems

2020 ◽  
Vol 9 (4) ◽  
pp. 2252-2260
Keyword(s):  
Closed Loop ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequalities ◽  
Interconnected System ◽  
Local Controller ◽  
The Stability ◽  
Finsler’S Lemma

In this paper, we present a new decentralized H∞ control for interconnected systems, the interconnected system consists of several subsystems. The proposed approach based on Lyapunov functional and a H∞ criterion, employed to reduce the effect of interconnections between subsystems. In the first, we study the stability of the global system in closed loop using a criterion H∞, the stability conditions are presented in terms of LMI. In the second, to improve this approach, a Finsler’s lemma is used for the stability analysis by LMIs. Some sufficient conditions, ensuring all the closed-loop stability are supplied in terms of Linear Matrix Inequalities (LMIs), and the new feedback gain matrix of each local controller is obtained by solving the LMIs. Finally, the practice examples are given to illustrate the efficiency of the present method

scholarly journals Low-Speed Stability Optimization of Full-Order Observer for Induction Motor

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Xiangsheng Liu ◽  
Lin Ren ◽  
Yuanyuan Yang ◽  
Jun He ◽  
Zhengxin Zhou
Keyword(s):  
Induction Motor ◽  
Control Strategy ◽  
System Performance ◽  
System Stability ◽  
Feedback Gain ◽  
Unstable Region ◽  
Low Speed ◽  
Gain Matrix ◽  
Adaptive Law ◽  
The Stability

In terms of the instability of the full-order observer for the induction motor in the low-speed regenerative mode, the low-speed unstable region which leads to the extension of the commissioning cycle cannot be eliminated by the traditional adaptive law which aims at good system performance. It is proposed that the feedback gain matrix can control both the unstable region and the system performance both. To make a trade-off between the stability and performance by designing the feedback gain matrix is still an open problem. To solve this problem, first we analyze the cause of instability and derive constraints to ensure system stability by establishing a transfer function of the adaptive observing system for the speed. Then, with the derived constraints as the design criteria for the feedback gain matrix, a control strategy combining the weighted adaptive law with the improved feedback gain matrix is proposed to improve the stability at low speed. Finally, by comparing the traditional control strategy with the proposed control strategy through simulations and experiments, we show that the proposed control strategy achieves better performance with higher stability.

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