An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

In this paper, a new optimal reduced order fractionalized PID (ROFPID) controller based on the Harris Hawks Optimization Algorithm (HHOA) is proposed for aircraft pitch angle control. Statistical tests, analysis of the index of performance, and disturbance rejection, as well as transient and frequency responses, were all used to validate the effectiveness of the proposed approach. The performance of the proposed HHOA-ROFPID and HHOA-ROFPID controllers with Oustaloup and Matsuda approximations was then compared not only to the PID controller tuned by the original HHO algorithm but also to other controllers tuned by cutting-edge meta-heuristic algorithms such as the atom search optimization algorithm (ASOA), Salp Swarm Algorithm (SSA), sine-cosine algorithm (SCA), and Grey wolf optimization algorithm (GOA). Simulation results show that the proposed controller with the Matsuda approximation provides better and more robust performance compared to the proposed controller with the Oustaloup approximation and other existing controllers in terms of percentage overshoot, settling time, rise time, and disturbance rejection.

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“…Our present goal is to find a low‐order approximation integer‐order model, as stated below [61–63]:

{G}_{r/m}(s)&#x0003D;\frac{\beta_1{s}&#x0005E;r&#x0002B;\dots &#x0002B;{\beta}_rs&#x0002B;{\beta}_{r&#x0002B;1}}{s&#x0005E;m&#x0002B;{\alpha}_1{s}&#x0005E;{m-1}&#x0002B;\dots &#x0002B;{\alpha}_{m-1}s&#x0002B;{\alpha}_m}.

…”

Section: Proposed Reduced Order Fractionalized Pid Controllermentioning

confidence: 99%

Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller

Idir

Bensafia

Khettab

et al. 2022

Asian Journal of Control

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“…It is worth mentioning that as far as the problems of real-world applications are concerned, specifically applications from the field of physical and engineering sciences, the Riemann-Liouville and Grünwald-Letnikov definitions are taken as equivalent [6,[25][26][27][28].…”

Section: Fractional Order Systems 21 Fractional Calculusmentioning

confidence: 99%

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

Bensafia

Idir

Khettab

et al. 2022

IJEEI

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Recent advances in fractional order calculus led to the improvement of control theory and resulted in the potential use of a fractional adaptive proportional integral derivative (FAPID) controller in advanced academic and industrial applications as compared to the conventional adaptive PID (APID) controller. Basically, a fractional order adaptive PID controller is an improved version of a classical integer order adaptive PID controller that outperformed its classical counterpart. In the case of a closed loop system, a minor change would result in overall system instability. An efficient PID controller can be used to control the response of such a system. Among various parameters of an instable system, the speed of the system is an important parameter to be controlled efficiently. The current research work presents the speed control mechanism for an uncertain, instable system by using a fractional-order adaptive PID controller. To validate the arguments, the effectiveness and robustness of the proposed fractional order adaptive PID controller have been studied in comparison to the classical adaptive PID controller using the criterion of quadratic error. Simulation findings and comparisons demonstrated that the proposed controller has superior control performance and outstanding robustness in terms of percentage overshoot, settling time, rising time, and disturbance rejection.

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“…In the subject of fractional calculus, the Grünwald-Letnikov definition is considered one of the most frequently used definitions. Considering its good usability for discrete control algorithms and its wide application in engineering, 25 the Grünwald-Letnikov fractional derivative are employed as our main tools in this study.…”

Section: Preliminarymentioning

confidence: 99%

“…In the subject of fractional calculus, the Grünwald‐Letnikov definition is considered one of the most frequently used definitions. Considering its good usability for discrete control algorithms and its wide application in engineering, 25 the Grünwald‐Letnikov fractional derivative are employed as our main tools in this study.Definition The Grünwald‐Letnikov fractional derivative with

αth - order

on the half axis

ℝ^{+}

of the function

normalφ ((), t)

is elaborated as follows 26

{D_{t_{0}}^{italicGL}}_{t}^{β} φ ((), t) goodbreak= \lim_{h \to 0} h^{- β} \sum_{j = 0}^{k} {(- 1)}^{j} ((), \binom{β}{j}) φ ((), italickh goodbreak- italicjh), for ((), β \in R),

where

Γ (() .)

represents Gamma function and

{D_{t_{0}}^{italicGL}}_{t}^{β}

is the Grünwald‐Letnikov derivative operator, which is abbreviated as

D^{β}

when

t_{0} = 0

.…”

Section: Preliminarymentioning

confidence: 99%

Design of neural network fractional‐order backstepping controller for MPPT of PV systems using fractional‐order boost converter

Youcef

Khettab

Bensafia

2021

Int Trans Electr Energ Syst

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The main objective of this article is to apply the fractional calculus for establishing a novel design of photovoltaic (PV) system. In order to enhance the efficiency and robustness of the maximum power point tracking (MPPT) approach, a fractional-order (FO) DC-DC boost converter is proposed for a PV system. Due to the nonlinearity of the PV module, an artificial neural network (ANN) loop has been used to consistently generate an optimal reference voltage. Using FO control, an incommensurate FO backstepping controller (FO-BSC) has been ultimately integrated for tracking the maximum power point in the presence of tremendously atmospheric conditions and load changes. In this

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An Improved Robust Fractionalized PID Controller for a Class of Fractional-Order Systems with Measurement Noise

Cited by 6 publications

References 23 publications

Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller

Performance improvement of aircraft pitch angle control using a new reduced order fractionalized PID controller

Novel Robust Control Using a Fractional Adaptive PID Regulator for an unstable system

Design of neural network fractional‐order backstepping controller for MPPT of PV systems using fractional‐order boost converter

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