scholarly journals Analysis and Modeling of Fractional-Order Buck Converter Based on Riemann-Liouville Derivative

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 162768-162777 ◽  
Author(s):  
Zhihao Wei ◽  
Bo Zhang ◽  
Yanwei Jiang
2021 ◽  
Vol 4 (3) ◽  
pp. 50
Author(s):  
Preeti Warrier ◽  
Pritesh Shah

The control of power converters is difficult due to their non-linear nature and, hence, the quest for smart and efficient controllers is continuous and ongoing. Fractional-order controllers have demonstrated superior performance in power electronic systems in recent years. However, it is a challenge to attain optimal parameters of the fractional-order controller for such types of systems. This article describes the optimal design of a fractional order PID (FOPID) controller for a buck converter using the cohort intelligence (CI) optimization approach. The CI is an artificial intelligence-based socio-inspired meta-heuristic algorithm, which has been inspired by the behavior of a group of candidates called a cohort. The FOPID controller parameters are designed for the minimization of various performance indices, with more emphasis on the integral squared error (ISE) performance index. The FOPID controller shows faster transient and dynamic response characteristics in comparison to the conventional PID controller. Comparison of the proposed method with different optimization techniques like the GA, PSO, ABC, and SA shows good results in lesser computational time. Hence the CI method can be effectively used for the optimal tuning of FOPID controllers, as it gives comparable results to other optimization algorithms at a much faster rate. Such controllers can be optimized for multiple objectives and used in the control of various power converters giving rise to more efficient systems catering to the Industry 4.0 standards.


Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 629 ◽  
Author(s):  
Allan G. Soriano-Sánchez ◽  
Martín A. Rodríguez-Licea ◽  
Francisco J. Pérez-Pinal ◽  
José A. Vázquez-López

In this paper, the approximation of a fractional-order PIDcontroller is proposed to control a DC–DC converter. The synthesis and tuning process of the non-integer PID controller is described step by step. A biquadratic approximation is used to produce a flat phase response in a band-limited frequency spectrum. The proposed method takes into consideration both robustness and desired closed-loop characteristics, keeping the tuning process simple. The transfer function of the fractional-order PID controller and its time domain representation are described and analyzed. The step response of the fractional-order PID approximation shows a faster and stable regulation capacity. The comparison between typical PID controllers and the non-integer PID controller is provided to quantify the regulation speed introduced by the fractional-order PID approximation. Numerical simulations are provided to corroborate the effectiveness of the non-integer PID controller.


2020 ◽  
Vol 107 ◽  
pp. 370-384
Author(s):  
Florindo A. de C. Ayres ◽  
Iury Bessa ◽  
Vinicius Matheus Batista Pereira ◽  
Nei Junior da Silva Farias ◽  
Alessandra Ribeiro de Menezes ◽  
...  

2017 ◽  
Vol 22 (4) ◽  
pp. 503-513 ◽  
Author(s):  
Fei Wang ◽  
Yongqing Yang

This paper investigates fractional order Barbalat’s lemma and its applications for the stability of fractional order nonlinear systems with Caputo fractional derivative at first. Then, based on the relationship between Caputo fractional derivative and Riemann-Liouville fractional derivative, fractional order Barbalat’s lemma with Riemann-Liouville derivative is derived. Furthermore, according to these results, a set of new formulations of Lyapunov-like lemmas for fractional order nonlinear systems are established. Finally, an example is presented to verify the theoretical results in this paper.


In this study, we have successfully found some travelling wave solutions of the variant Boussinesq system and fractional system of two-dimensional Burgers' equations of fractional order by using the -expansion method. These exact solutions contain hyperbolic, trigonometric and rational function solutions. The fractional complex transform is generally used to convert a partial fractional differential equation (FDEs) with modified Riemann-Liouville derivative into ordinary differential equation. We showed that the considered transform and method are very reliable, efficient and powerful in solving wide classes of other nonlinear fractional order equations and systems.


2016 ◽  
Vol 35 (6) ◽  
pp. 2189-2211 ◽  
Author(s):  
Swapnil Khubalkar ◽  
Amit Chopade ◽  
Anjali Junghare ◽  
Mohan Aware ◽  
Shantanu Das

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
V. A. Kubyshkin ◽  
S. S. Postnov

This paper studies two optimal control problems for linear time-invariant systems of fractional order with lumped parameters whose dynamics is described by equations which contain Riemann-Liouville derivative. The first problem is to find control with minimal norm and the second one is to find control with minimal control time at given restriction for control norm. The problem setting with nonlocal initial conditions is considered which differs from other known settings for integer-order systems and fractional-order systems described in terms of equations with Caputo derivative. Admissible controls are allowed to belong to the class of functions which arep-integrable on half segment. The basic investigation approach is the moment method. The correctness and solvability of moment problem are validated for considered problem setting for the system of arbitrary dimension. It is shown that corresponding conditions are analogous to those derived for systems which are described in terms of equations with Caputo derivative. For several particular cases of one- and two-dimensional systems the posed problems are solved explicitly. The dependencies of basic values from derivative index and control time are analyzed. The comparison is performed of obtained results with known results for analogous integer-order systems and fractional-order systems which are described by equations with Caputo derivative.


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