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    Enhancing the transient performances and stability of three-tank liquid level using a modified pid controller
    (Revue roumaine des sciences techniques — Série électrotechnique et énergétique, 2025) Idir, Abdelhakim; Nesri, Mokhtar; Belhouchet, Khaled; Guedida, Sifelislam; Canale, Laurent
    Managing liquid levels in industrial tanks is crucial, especially for precise component mixing. Traditional PID controllers, though widely used, often exhibit slow settling times and excessive overshoot, which can affect system performance. This study proposes a fractionalized order PID (FrOPID) controller optimized using the Modified Artificial Hummingbird Algorithm (MAHA) to enhance stability and response in a three-tank system. The controller’s effectiveness is evaluated under varying valve coefficient (Kv) and tank cross-sectional area conditions. A comparative analysis with advanced metaheuristic-optimized PID controllers confirms the superiority of the MAHA/FrOPID in terms of accuracy, response speed, and robustness, making it a highly efficient solution for liquid level control.
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    A comparative study between fractionalized and fractional order PID controllers for control of a stable system based on particle swarm optimization algorithm
    (Wydawnictwo SIGMA-NOT, 2023) Idir, Abdelhakim; Berrabah, Fouad; Laurent, Canale
    Most industrial applications use integer-order proportional integral derivative (IOPID) controllers due to well-known characteristics such as simplicity and ease of implementation. However, because of their nonlinear nature and the underlying iso-damping feature of fractional-order operators, fractional-order PID (FOPID) and fractionalized-order PID (FrOPID) controllers outperform the IOPID controllers. In this study, three different controllers based on particle swarm optimization are used to regulate a stable system. While a FrOPID controller only has to optimize four parameters and a normal PID controller only needs to optimize three parameters, a FOPID controller requires the optimization of five parameters. Set-point tracking, and better disturbance rejection are obtained with the fractional PID controller, whereas fractionalized PID outperforms the other controllers in terms of noise attenuation
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    An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise
    (INASS, 2018) Bensafia, Yassine; Khettab, Khatir; Idir, Abdelhakim
    Recently, many research works have focused on fractional order control (FOC) and fractional systems. It has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. In this paper we propose a new approach for robust control by fractionalizing an integer order integrator in the classical PID control scheme and we use the Sub-optimal Approximation of fractional order transfer function to design the parameters of PID controller, after that we study the performance analysis of fractionalized PID controller over integer order PID controller. The implementation of the fractionalized terms is realized by mean of well-established numerical approximation methods. Illustrative simulation examples show that the disturbance rejection is improved by 50%. This approach can also be generalized to a wide range of control methods