Design of robust fractional order PID controller using fractional weights in the mixed sensitivity problem

Amieur, Toufik; Younsi, Abdelaziz; Aidoud, Mohammed; Sedraoui, Moussa; Amieur, Oualid

doi:10.1109/ssd.2017.8166986

Cited by 3 publications

(4 citation statements)

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“…This can be done by a good selection of both adequate integer weights W S ( s ) and W T ( s ) , which are sometimes quite complicated when an integer dimensional space is used. This problem can be avoided by proposing two adjustable fractional weights (Amieur et al, 2017; Sedraoui et al, 2017). Their parameters are given by the PSO algorithm, in which some proposed tuning rules, described later, are well satisfied.…”

Section: Design Of the Primary H∞ Controllermentioning

confidence: 99%

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A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

Guessoum

Feraga

Mehennaoui

et al. 2019

Transactions of the Institute of Measurement and Control

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This paper proposes a new robustification strategy of a primary H∞ controller based on a systematic selection of adequate fractional weights. Its robust performance (RP) margin is well enhanced with respect to unstructured multiplicative uncertainties presented in linear feedback systems. The proposed robustification strategy provides a robustified H∞ controller when following proposed hierarchical control is well respected. First, the primary H ∞ controller is synthesized from solving a weighted-mixed sensitivity H∞ problem using initial integer weights. Thus, an initial RP margin is obtained. Second, an automatic selection of adjustable fractional weights is performed by the particle swarm optimization algorithm, in which some proposed tuning rules are accordingly well satisfied. Third, frequency response data of these weights are computed and then fitted by corresponding approximated integer weights using a frequency identification technique. Finally, these weights reformulate a new weighted-mixed sensitivity problem. The optimal solution to this problem updates the previous initial RP margin. These last three steps are repeated as the updated RP margin is diminished. Otherwise, the proposed hierarchical control is achieved by selecting the best adjustable fractional weights, providing, therefore, the best approximated integer weights and leading, therefore, to the robustified H∞ controller. In order to confirm the effectiveness of our proposed hierarchical control, primary and robustified H∞ controllers are applied on a permanent magnet synchronous motor where its actual behavior is modeled by an unstructured multiplicative uncertain model. The results obtained are compared in frequency domains using the singular value plots of their sensitivity functions. Otherwise, the same results are compared in time domains using the Powersim® software.

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Section: Design Of the Primary H∞ Controllermentioning

confidence: 99%

“…Nevertheless, optimal integer weights cannot be guaranteed because the convergence of the optimization algorithm slows down as the optimal solution approaches. This is generally due to the high number of selected integer weights or specifications to be quantified (Amieur et al, 2017; Sedraoui et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

Guessoum

Feraga

Mehennaoui

et al. 2019

Transactions of the Institute of Measurement and Control

Self Cite

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“…Amieur the trade-off between nominal performance and robust stability within closed-loop systems. Their approach involved the utilization of a min-max optimization algorithm to fine-tune the robust controller [23]. While Reference [22] employs controllers with integer orders, Reference [23] utilizes controllers with fractional orders and fractional weights in the H ∞ method.…”

Section: Introduction 1the Contex Of Researchmentioning

confidence: 99%

“…Their approach involved the utilization of a min-max optimization algorithm to fine-tune the robust controller [23]. While Reference [22] employs controllers with integer orders, Reference [23] utilizes controllers with fractional orders and fractional weights in the H ∞ method. Menak and Tan introduced a novel fitness function that combines constraints related to H ∞ robust performance and Bode's ideal transfer function.…”

Section: Introduction 1the Contex Of Researchmentioning

confidence: 99%

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

Ilten

2023

Fractal Fract

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This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.

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A new robust tilt-PID controller based upon an automatic selection of adjustable fractional weights for permanent magnet synchronous motor drive control

et al. 2021

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Design of robust fractional order PID controller using fractional weights in the mixed sensitivity problem

Cited by 3 publications

References 14 publications

A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

A new robust tilt-PID controller based upon an automatic selection of adjustable fractional weights for permanent magnet synchronous motor drive control

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Design of robust fractional order PID controller using fractional weights in the mixed sensitivity problem

Cited by 3 publications

References 14 publications

A robust performance enhancement of primaryH∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

A robust performance enhancement of primaryH∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

A new robust tilt-PID controller based upon an automatic selection of adjustable fractional weights for permanent magnet synchronous motor drive control

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A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor

A robust performance enhancement of primaryH_∞controller based on auto-selection of adjustable fractional weights: Application on a permanent magnet synchronous motor