Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems

This study aimed to analyze the systematic risks of wind energy investments. Within this framework, E7 countries are included in the scope of the examination. A large literature review was carried out and 12 different systematic risk factors that could exist in wind energy investments were identified. The analysis process of the study consisted of two different stages. First, the specified risk criteria were weighted with the help of the interval type 2 (IT2) fuzzy decision-making trial and evaluation laboratory (DEMATEL) method. Second, E7 countries were ranked according to the risk management effectiveness in wind energy investments. In this process, the IT2 fuzzy Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) approach was taken into consideration. The findings show that volatility in exchange rates and interest rates were the most important risks in wind energy investments. In addition, it was determined that China and Indonesia were the most successful countries in managing risks in wind energy investments. In contrast, India, Russia, and Turkey were determined to be the least successful. Additionally, the IT2 fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method was applied as a robustness check of the extended VIKOR method. It was concluded that the ranking results of the IT2 fuzzy TOPSIS method were similar to the results of the IT2 fuzzy VIKOR. It can be understood that the proposed ranking method was consistent with the comparative analysis results. From this point of view, it was observed that countries should take measures regarding their exchange rate and interest rate risks in order to increase the efficiency in wind energy investments. In this context, companies should first ensure that they do not have a foreign exchange short position in their balance sheets by conducting an effective financial analysis. In addition, it is important to use financial derivatives to minimize the exchange rate and interest rate risks. Using these results, it will be possible to manage this risk by taking the reverse position for the existing foreign currency and interest risk. In this way, it will be possible to increase the efficiency of wind energy investments, which will contribute to the social and economic development of each respective country.Energies 2020, 13, 1423 2 of 25 their own energy resources can benefit from these resources [1]. This situation gives these countries a serious cost advantage. On the other hand, countries that do not have sufficient energy resources have to supply the energy they need from outside, which makes these countries dependent on energy. Because of this problem, countries are developing several strategies to produce their own energy [2].Renewable energy sources are an important alternative that allows countries to produce their own energy. The most important feature of these energy alternatives, which come in different forms, such as wind, solar, biomass, geothermal, and hydroelectricity, is that they obtain their resources from natur...

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“…The third stage of this methodology is related to the defuzzification process. In this step, Equations (19)- (22) are used.…”

Section: Linguistic Scales Interval Type 2 Fuzzy Numbersmentioning

confidence: 99%

“…In addition, many control designs can also be implemented in IT2 fuzzy sets [21]. Moreover, another important advantage of IT2 fuzzy sets is its relatively high flexibility and robustness in comparison with IT1 fuzzy logic [22].…”

Section: Introductionmentioning

confidence: 99%

Multi-Faceted Analysis of Systematic Risk-Based Wind Energy Investment Decisions in E7 Economies Using Modified Hybrid Modeling with IT2 Fuzzy Sets

Qiu¹,

et al. 2020

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“…Many FO sliding mode control methods with different sliding mode manifolds have been studied [16]- [27]. These methods include a special nonsingular second-order sliding mode manifold [16], FO hierarchical sliding mode manifold [17]; FO proportional-integral-derivative (FOPID) sliding mode manifold, which is a family of FO proportional-integral (FOPI) and FO proportional-derivative (FOPD) sliding mode manifold [18]- [23]; and continuous FO nonsingular terminal sliding mode (CFONTSM) manifold, which is a refined version of FO nonsingular terminal sliding mode (FONTSM) manifold [24], [25]. Among them, the FONTSM manifold can overcome singularity while ensuring that the system states converge to the equilibrium point in finite time [26].…”

Section: Introductionmentioning

confidence: 99%

“…As this method has no analytic expression, the other methods such as evolutionary optimization [33] and traditional pole assignment [34] had been studied. The particle swarm optimization (PSO) [35] and multi-tracker optimization algorithm (MTOA) [17] belong to the evolutionary optimization algorithms that mostly proceed based on the slope of the objective function with respect to optimization variables (derivative/gradient-based) and move toward solutions. For example, Tejado et al [34] used the PSO method by constructing a cost function (objective function) that depends on the error's energy.…”

Section: Introductionmentioning

confidence: 99%

Novel Dynamic-Sliding-Mode-Manifold-Based Continuous Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

Deng

Zhang

2020

IEEE Access

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A novel dynamic-sliding-mode-manifold-based continuous fractional-order nonsingular terminal sliding mode control is proposed for a class of second-order nonlinear systems. By designing the parameter in the continuous fractional-order nonsingular terminal sliding mode manifold as an exponential function of the tracking error, a dynamic sliding mode manifold can be obtained by adjusting the parameter online. Even if reference signals change, the parameter does not need repetitive offline optimization. By combining the fast-terminal-sliding-mode-type reaching law, the system states are attracted to the manifold quickly, enhancing the controller's robustness. When a large initial error exists, the control system can still accelerate response and reduce overshoot simultaneously owing to the dynamic changing characteristic of the manifold. The stability and finite-time convergence of the closed-loop system are proven by the Lyapunov stability theory. Simulation results on SISO and MIMO nonlinear systems show that for different reference signals, the proposed method has a better tracking performance than the general fractional-order nonsingular terminal sliding mode control. INDEX TERMS Dynamic sliding mode manifold, fractional-order, nonsingular terminal sliding mode control, nonlinear systems.

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“…Adaptive fractional fuzzy sliding mode control was explained to address the strategy of permanent magnet synchronous motor motion control [24]- [25]. The adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control was presented in [26] for demonstrating the solution of perturbation rejection for a nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

Efficient Fractional Order Reference Model of Adaptive Controller Design for Multi-input Multi-output Thermal System

Chaoraingern

Tipsuwanporn

Numsomran

2020

Int. J. Adv. Sci. Eng. Inf. Technol.

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The diverse control techniques have been combined with fractional calculus to enhance the control system performance. This paper presents an efficient fractional-order model reference adaptive controller (FOMRAC) design, which aims to demonstrate the solution for temperature reference tracking and cross-coupling rejection in the multi-input multi-output thermal system as well as cognizing of power consumption saving constraints. The mathematical modeling, nonlinear dynamic characteristic details, and system identification of the thermal system are described while the fractional-order controller combined with a model reference adaptive control (FOMRAC) based on MIT rule is developed so that to create the nonlinear adaptive mechanism which enables the excellent performance to control the multi-input multi-output thermal system. Likewise, a decoupling compensator is constructed to remunerate the effect of the cross-coupling interaction. The validation of the proposed control scheme is performed through the Matlab simulation and the experiment on the multi-input multi-output thermal system. The results illustrated the FOMRAC technique in which the controller's adjustable parameters can provide efficiency stability and performance to minimize the settling time and percent overshoot of the control system response. Besides, the analysis of the power consumption in the control system is addressed to reinforce the useful ability of the proposed method compared with the integral-order model reference adaptive controller (IOMRAC) and the traditional PID controller. The results revealed that the proposed FOMRAC technique exhibited much better than other methods because of the effective optimization of adaptive gain mechanism and fractional-order operators.

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Optimal adaptive interval type-2 fuzzy fractional-order backstepping sliding mode control method for some classes of nonlinear systems

Cited by 38 publications

References 46 publications

Multi-Faceted Analysis of Systematic Risk-Based Wind Energy Investment Decisions in E7 Economies Using Modified Hybrid Modeling with IT2 Fuzzy Sets

Multi-Faceted Analysis of Systematic Risk-Based Wind Energy Investment Decisions in E7 Economies Using Modified Hybrid Modeling with IT2 Fuzzy Sets

Novel Dynamic-Sliding-Mode-Manifold-Based Continuous Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

Efficient Fractional Order Reference Model of Adaptive Controller Design for Multi-input Multi-output Thermal System

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