A simple approach to mathematical modelling of integer order and fractional order fuzzy PID controllers using one-dimensional input space and their experimental realization

2021 ◽  
Vol 358 (7) ◽  
pp. 3726-3756
Author(s):  
Debdoot Sain ◽  
B.M. Mohan
Keyword(s):  
Mathematical Modelling ◽  
Fractional Order ◽  
Simple Approach ◽  
Pid Controllers ◽  
Fuzzy Pid ◽  
Experimental Realization ◽  
One Dimensional ◽  
Input Space ◽  
Integer Order

Grasshopper Algorithm Optimized Fractional Order Fuzzy PID Frequency Controller for Hybrid Power Systems

2019 ◽  
Vol 12 (6) ◽  
pp. 519-531
Author(s):  
Deepak Kumar Lal ◽  
Ajit Kumar Barisal
Keyword(s):  
Power Systems ◽  
Power System ◽  
Fractional Order ◽  
Pid Controller ◽  
Load Frequency Control ◽  
Pid Controllers ◽  
Fuzzy Pid ◽  
Fuzzy Pid Controller ◽  
Hybrid Power ◽  
Increasing Demand

Background: Due to the increasing demand for the electrical power and limitations of conventional energy to produce electricity. Methods: Now the Microgrid (MG) system based on alternative energy sources are used to provide electrical energy to fulfill the increasing demand. The power system frequency deviates from its nominal value when the generation differs the load demand. The paper presents, Load Frequency Control (LFC) of a hybrid power structure consisting of a reheat turbine thermal unit, hydropower generation unit and Distributed Generation (DG) resources. Results: The execution of the proposed fractional order Fuzzy proportional-integral-derivative (FO Fuzzy PID) controller is explored by comparing the results with different types of controllers such as PID, fractional order PID (FOPID) and Fuzzy PID controllers. The controller parameters are optimized with a novel application of Grasshopper Optimization Algorithm (GOA). The robustness of the proposed FO Fuzzy PID controller towards different loading, Step Load Perturbations (SLP) and random step change of wind power is tested. Further, the study is extended to an AC microgrid integrated three region thermal power systems. Conclusion: The performed time domain simulations results demonstrate the effectiveness of the proposed FO Fuzzy PID controller and show that it has better performance than that of PID, FOPID and Fuzzy PID controllers. The suggested approach is reached out to the more practical multi-region power system. Thus, the worthiness and adequacy of the proposed technique are verified effectively.

Exploiting Fractional Order PID Controller Methods in Improving the Performance of Integer Order PID Controllers: A GA Based Approach

2009 ◽  
Author(s):  
Bijoy K. Mukherjee ◽  
Santanu Metia ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Pid Controllers ◽  
Integer Order ◽  
Fractional Order Pid ◽  
Fractional Order Pid Controller

New alternatives for analog implementation of fractional-order integrators, differentiators and PID controllers based on integer-order integrators

2017 ◽  
Vol 90 (1) ◽  
pp. 241-256 ◽  
Author(s):  
Carlos Muñiz-Montero ◽  
Luis V. García-Jiménez ◽  
Luis A. Sánchez-Gaspariano ◽  
Carlos Sánchez-López ◽  
Víctor R. González-Díaz ◽  
...  
Keyword(s):  
Fractional Order ◽  
Pid Controllers ◽  
Integer Order ◽  
Analog Implementation

Analysis, Control and FPGA Implementation of a Fractional-Order Modified Shinriki Circuit

2019 ◽  
Vol 28 (14) ◽  
pp. 1950232 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Fahimeh Nazarimehr ◽  
Laarem Guessas ◽  
Anitha Karthikeyan ◽  
Ashokkumar Srinivasan ◽  
...  
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Dynamic Properties ◽  
Fpga Implementation ◽  
Pid Controllers ◽  
Largest Lyapunov Exponent ◽  
Unknown Parameters ◽  
Integer Order ◽  
Sliding Mode Controllers ◽  
Fractional Orders

In this paper, we introduce a novel integer-order memristor-modified Shinriki circuit (MMSC). We investigate the dynamic properties of the MMSC system and the existence of chaos is proved with positive largest Lyapunov exponent. Bifurcation plots are derived to analyze the parameter dependence of the MMSC system. The fractional-order model of the MMSC system (FOMMSC) is derived and the bifurcation analysis of the FOMMSC system with the fractional orders is carried out. Fractional-order adaptive sliding-mode controllers (FOASMCs) and genetically optimized PID controllers are designed to synchronize identical FOMMSC systems with unknown parameters. Numerical simulations are conducted to validate the theoretical results. FPGA implementation of the FOASMC controllers is presented to show that the proposed control algorithm is hardware realizable. MMSC has trigonometric functions which make the system more complex and the optimization and synchronization of such systems in the integer order itself are harder, so the paper does the same in fractional order. The proposed system is a memristive circuit which can show special features such as multistability, hyperchaos, and multiscroll attractor. Such a system with these features is very rare in the literature.

scholarly journals Invariant Image Representation Using Novel Fractional-Order Polar Harmonic Fourier Moments

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1544
Author(s):  
Chunpeng Wang ◽  
Hongling Gao ◽  
Meihong Yang ◽  
Jian Li ◽  
Bin Ma ◽  
...  
Keyword(s):  
Image Reconstruction ◽  
Fractional Order ◽  
Continuous Functions ◽  
Kernel Functions ◽  
Superior Performance ◽  
Image Description ◽  
Orthogonal Moments ◽  
Integer Order ◽  
Geometric Invariance ◽  
Order Continuous

Continuous orthogonal moments, for which continuous functions are used as kernel functions, are invariant to rotation and scaling, and they have been greatly developed over the recent years. Among continuous orthogonal moments, polar harmonic Fourier moments (PHFMs) have superior performance and strong image description ability. In order to improve the performance of PHFMs in noise resistance and image reconstruction, PHFMs, which can only take integer numbers, are extended to fractional-order polar harmonic Fourier moments (FrPHFMs) in this paper. Firstly, the radial polynomials of integer-order PHFMs are modified to obtain fractional-order radial polynomials, and FrPHFMs are constructed based on the fractional-order radial polynomials; subsequently, the strong reconstruction ability, orthogonality, and geometric invariance of the proposed FrPHFMs are proven; and, finally, the performance of the proposed FrPHFMs is compared with that of integer-order PHFMs, fractional-order radial harmonic Fourier moments (FrRHFMs), fractional-order polar harmonic transforms (FrPHTs), and fractional-order Zernike moments (FrZMs). The experimental results show that the FrPHFMs constructed in this paper are superior to integer-order PHFMs and other fractional-order continuous orthogonal moments in terms of performance in image reconstruction and object recognition, as well as that the proposed FrPHFMs have strong image description ability and good stability.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

Generalized Frequency Domain Robust Tuning of a Family of Fractional Order PI/PID Controllers to Handle Higher Order Process Dynamics

2011 ◽  
Vol 403-408 ◽  
pp. 4859-4866 ◽  
Author(s):  
Saptarshi Das ◽  
Amitava Gupta ◽  
Shantanu Das
Keyword(s):  
Frequency Domain ◽  
Fractional Order ◽  
Test Bench ◽  
Standard Test ◽  
Higher Order ◽  
Pid Controllers ◽  
Order Process ◽  
Controller Tuning ◽  
Process Dynamics ◽  
The Family

Generalization of the frequency domain robust tuning has been proposed in this paper for a family of fractional order (FO) PI/PID controllers. The controller tuning is enhanced with two new FO reduced parameter templates which are capable of capturing higher order process dynamics with much better accuracy. The paper validates the proposed methodology with a standard test-bench of higher order processes to show the relative merits of the family of FO controller structures.

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