Closed-Form Mathematical Representations of Interval Type-2 Fuzzy Logic Systems with Application to Inverted Pendulum Stabilization

Abuelenin, Sherif M.; Abdel-Kader, Rabab Farouk

doi:10.1080/16168658.2022.2152922

Cited by 3 publications

(5 citation statements)

References 41 publications

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“…In the context of the MPPT mechanism, the closed form fuzzy counterpart has been illustrated and designed for the present work. The researchers (refer 36,38 ) have investigated various closed mathematical forms of FL. A closed type formation of fuzzy inference engine might be favoured in control system formulation.…”

Section: Mppt Control Under Pscmentioning

confidence: 99%

“…A closed type formation of fuzzy inference engine might be favoured in control system formulation. In Reference 36, a novel closed‐form representation of IT2‐FL has been evolved based on approximating the GC method in which the type reduction is bypassed based on the finding of the centre‐of‐area of the output FOU. The output (as shown in Reference 36) may be presented by (12)

y goodbreak= \frac{\sum_{k = 1}^{n} {\overset{true¯}{b}}_{k} ((), {\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\overset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2})) - \sum_{k = 1}^{n} {\underset{true¯}{b}}_{k} ((), {\underset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\underset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}))}{\sum_{k = 1}^{n} ((), {\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\overset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}) goodbreak- {\underset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\underset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}))}

where

y

represents the crisp output,

{\overset{true¯}{b}}_{k}

and

{\underset{true¯}{b}}_{k}

indicate the singleton centers of output MFs for upper MFs (UMFs) and lower MFs (LMFs), respectively,

{\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}}

and

\underset{true¯}{μ}

…”

Section: Mppt Control Under Pscmentioning

confidence: 99%

“…In this table, N, P, Az, S, M, and B stand for negative, positive, approximate zero, small, medium, and big, respectively. However, the computation procedure of the GC‐based CLT2‐FL is similar, as stated in Reference 36. The outputs are assumed as singletons having their own upper and lower limits representing the centers of the output MFs.…”

Section: Mppt Control Under Pscmentioning

confidence: 99%

“…The present research realizes the idea of the combination of neural networks with the closed‐loop version of T2‐FL (CLT2‐FL) to intensify the adaptability and flexibility in the MPPT control surface. The closed loop structure of interval T2‐FL was developed in Reference 36. The geometric centroid (GC) approach for CLT2‐FL is instigated systematically inside the MPPT mechanism in order to obtain efficacious fast tracking ability.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Artificially intelligent MPPT ‐based photovoltaic integrated smart dynamic voltage restorer

Mallick

Mukherjee

2021

Int Trans Electr Energ Syst

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Complexity and sensitivity related to modern machinery navigate electrical engineers more apprehensive owing to upraise power quality. In this effort, a series-connected voltage regulating arrangement furnishes apposite aids towards this sizeable interconnected system. Consequently, a dynamic voltage restorer (DVR) is realized to proffer customized power to the end-users.In accordance, the present research illustrates a student psychology-based optimization modulated DVR control mechanism. In the context of real-time realization, artificial neural network (ANN) is also embodied herein to obtain optimized online results. To intensify the potential of the implemented DVR, combined ANN and closed-loop type 2 fuzzy logic (CLT2-FL) modified maximum power point tracking-based partially shaded photovoltaic (PV) aided energy storage unit is also realized in the test network topology. This hybrid CLT2-FL module is adopted herein to trace the optimal power effectively under distinct practical scenarios. In order to assist the PV array, a supercapacitor-based charge controller is also incorporated. Consequently, the results are evaluated to divulge the potency of the propounded mechanism against the oddity seen in the voltage waveform, thereby, exhibiting better voltage regulation and lesser harmonics with effectual optimal power tracking.

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Section: Mppt Control Under Pscmentioning

confidence: 99%

y goodbreak= \frac{\sum_{k = 1}^{n} {\overset{true¯}{b}}_{k} ((), {\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\overset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2})) - \sum_{k = 1}^{n} {\underset{true¯}{b}}_{k} ((), {\underset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\underset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}))}{\sum_{k = 1}^{n} ((), {\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\overset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}) goodbreak- {\underset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}} ((), x_{1}) \cdot {\underset{true¯}{μ}}_{{\overset{A}{true}}_{2}^{j}} ((), x_{2}))}

where

y

represents the crisp output,

{\overset{true¯}{b}}_{k}

and

{\underset{true¯}{b}}_{k}

indicate the singleton centers of output MFs for upper MFs (UMFs) and lower MFs (LMFs), respectively,

{\overset{true¯}{μ}}_{{\overset{A}{true}}_{1}^{i}}

and

\underset{true¯}{μ}

…”

Section: Mppt Control Under Pscmentioning

confidence: 99%

Section: Mppt Control Under Pscmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Artificially intelligent MPPT ‐based photovoltaic integrated smart dynamic voltage restorer

Mallick

Mukherjee

2021

Int Trans Electr Energ Syst

View full text Add to dashboard Cite

show abstract

“…These fuzzy sets are also known as secondary membership functions (MF) and when these become a unit interval for the primary membership function, it is termed as interval type‐2 fuzzy set (IT2FS). A fuzzy system that uses, in any event, one IT2FS in the predecessor or subsequent piece of its rule base is known as an “interval type‐2 fuzzy logic system (IT2FLS)” [39].…”

Section: Introductionmentioning

confidence: 99%

Frequency control in hybrid distributed power systems via type‐2 fuzzy PID controller

Khadanga

Kumar²,

Panda

2021

IET Renewable Power Gen

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In this research article, a novel approach is proposed by considering a modified equilibrium optimization (MEO) algorithm based “interval type‐2 fuzzy proportional integral derivative (IT2FPID) controller” for the load frequency control of the multi‐area hybrid power system. The performance of the modified algorithm is tested by comparing it with the standard EO algorithm considering various standard benchmark test functions. Further, the efficacy of the MEO algorithm is tried by planning an IT2FPID controller for frequency regulation of the said hybrid system. The supremacy of the MEO‐based IT2FPID controller is introduced by comparing its outcomes with MEO‐based T1FPID structure, MEO‐based conventional PID and EO‐based PID controller techniques. It is observed that the MEO‐based IT2FPID controller is more effective compared to others.

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Improved frequency regulation of dual-area hybrid power system with the influence of energy storage devices

Baral,

Nayak,

Mohanty

et al. 2024

Electr Eng

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Closed-Form Mathematical Representations of Interval Type-2 Fuzzy Logic Systems with Application to Inverted Pendulum Stabilization

Cited by 3 publications

References 41 publications

Artificially intelligent MPPT ‐based photovoltaic integrated smart dynamic voltage restorer

Artificially intelligent MPPT ‐based photovoltaic integrated smart dynamic voltage restorer

Frequency control in hybrid distributed power systems via type‐2 fuzzy PID controller

Improved frequency regulation of dual-area hybrid power system with the influence of energy storage devices

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