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The Drazin inverse of the sum of two products
Safae Alaoui Chrifi,Abdelaziz Tajmouati 대한수학회 2022 대한수학회논문집 Vol.37 No.3
In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.
Robust Control of Induction Motor with H<sub>∞</sub>Theory based on Loopshaping
Benderradji, Hadda,Chrifi-Alaoui, Larbi,Mahieddine-Mahmoud, Sofiane,Makouf, Abdessalam The Korean Institute of Electrical Engineers 2011 Journal of Electrical Engineering & Technology Vol.6 No.2
The $H_{\infty}$ approach, adopted in this paper, is based on loop shaping using a normalized coprime factor combined with a field-oriented control to control induction motor. We develop two loops. The first one, the inner loop, controls the stator current by $H{\infty}$ controller in order to obtain good performance. The second loop, the outer one, guarantees stability and tracking performance of speed and rotor flux using a proportional integral controller. When the rotor flux cannot be measured, we introduce a flux observer to estimate the rotor flux. Simulation and experimental results are presented to validate the effectiveness and the good performance of this control technique.
Robust Control of Induction Motor with H<SUB>∞</SUB> Theory based on Loopshaping
Hadda Benderradji,Larbi Chrifi-Alaoui,Sofiane Mahieddine-Mahmoud,Abdessalam Makouf 대한전기학회 2011 Journal of Electrical Engineering & Technology Vol.6 No.2
The H∞ approach, adopted in this paper, is based on loop shaping using a normalized coprime factor combined with a field-oriented control to control induction motor. We develop two loops. The first one, the inner loop, controls the stator current by H∞ controller in order to obtain good performance. The second loop, the outer one, guarantees stability and tracking performance of speed and rotor flux using a proportional integral controller. When the rotor flux cannot be measured, we introduce a flux observer to estimate the rotor flux. Simulation and experimental results are presented to validate the effectiveness and the good performance of this control technique.
Robust Control of Induction Motor with H∞ Theory based on Loopshaping
Hadda Benderradji,Larbi Chrifi-Alaoui,Sofiane Mahieddine-Mahmoud,Abdessalam Makouf 대한전기학회 2011 Journal of Electrical Engineering & Technology Vol.6 No.2
The H_∞ approach, adopted in this paper, is based on loop shaping using a normalized coprime factor combined with a field-oriented control to control induction motor. We develop two loops. The first one, the inner loop, controls the stator current by H_∞ controller in order to obtain good performance. The second loop, the outer one, guarantees stability and tracking performance of speed and rotor flux using a proportional integral controller. When the rotor flux cannot be measured, we introduce a flux observer to estimate the rotor flux. Simulation and experimental results are presented to validate the effectiveness and the good performance of this control technique.
Robust Nonlinear Control of a Mobile Robot
Zidani, Ghania,Drid, Said,Chrifi-Alaoui, Larbi,Arar, Djemai,Bussy, Pascal The Korean Institute of Electrical Engineers 2016 Journal of Electrical Engineering & Technology Vol.11 No.4
A robust control intended for a nonholonomic mobile robot is considered to guarantee good tracking a desired trajectory. The main drawbacks of the mobile robot model are the existence of nonholonomic constraints, uncertain system parameters and un-modeled dynamics. in order to overcome these drawbacks, we propose a robust control based on Lyapunov theory associated with sliding-mode control, this solution shows good robustness with respect to parameter variations, measurement errors, noise and guarantees position and velocity tracking. The global asymptotic stability of the overall system is proven theoretically. The simulation results largely confirm the effectiveness of the proposed control.
Khamari, Dalila,Makouf, Abdesslam,Drid, Said,Chrifi-Alaoui, Larbi The Korean Institute of Electrical Engineers 2013 Journal of Electrical Engineering & Technology Vol.8 No.5
This paper deals with a robust controller for an induction motor (IM) which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback are associated. This approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic LPV system because of speed and rotor resistance affine dependence. Their values can be estimated on line during systems operations. The simulation and experimental results largely confirm the effectiveness of the proposed control.
Dalila Khamari,Abdesslam Makouf,Said Drid,Larbi Chrifi-Alaoui 대한전기학회 2013 Journal of Electrical Engineering & Technology Vol.8 No.5
This paper deals with a robust controller for an induction motor (IM) which is represented as a linear parameter varying systems. To do so linear matrix inequality (LMI) based approach and robust Lyapunov feedback are associated. This approach is related to the fact that the synthesis of a linear parameter varying (LPV) feedback controller for the inner loop take into account rotor resistance and mechanical speed as varying parameter. An LPV flux observer is also synthesized to estimate rotor flux providing reference to cited above regulator. The induction motor is described as a polytopic LPV system because of speed and rotor resistance affine dependence. Their values can be estimated on line during systems operations. The simulation and experimental results largely confirm the effectiveness of the proposed control.
Robust Nonlinear Control of a Mobile Robot
Ghania Zidani,Said Drid,Larbi Chrifi-Alaoui,Djemai Arar,Pascal Bussy 대한전기학회 2016 Journal of Electrical Engineering & Technology Vol.11 No.4
A robust control intended for a nonholonomic mobile robot is considered to guarantee good tracking a desired trajectory. The main drawbacks of the mobile robot model are the existence of nonholonomic constraints, uncertain system parameters and un-modeled dynamics. in order to overcome these drawbacks, we propose a robust control based on Lyapunov theory associated with sliding-mode control, this solution shows good robustness with respect to parameter variations, measurement errors, noise and guarantees position and velocity tracking. The global asymptotic stability of the overall system is proven theoretically. The simulation results largely confirm the effectiveness of the proposed control.