Novel Intelligent Optimization Algorithm Based Fractional Order Adaptive Proportional Integral Derivative Controller for Linear Time Invariant based Biological Systems

2021 ◽  
Author(s):  
Wakchaure Vrushali Balasaheb ◽  
Chaskar Uttam
Keyword(s):  
Fractional Order ◽  
Optimization Algorithm ◽  
Linear Time ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Intelligent Optimization ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Intelligent Optimization Algorithm ◽  
Time Invariant

Proportional–integral–derivative controller family for pole placement

2016 ◽  
Vol 231 (20) ◽  
pp. 3791-3797 ◽  
Author(s):  
Chimpalthradi R Ashokkumar ◽  
George WP York ◽  
Scott F Gruber
Keyword(s):  
Closed Loop ◽  
Linear Time ◽  
Pole Placement ◽  
Proportional Integral Derivative ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral ◽  
Linear Time Invariant ◽  
Generalized Eigenvalue ◽  
Square Systems ◽  
Time Invariant

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

Evaluation of fractional order of the discrete integrator. Part II

2020 ◽  
Vol 23 (2) ◽  
pp. 408-426
Author(s):  
Piotr Ostalczyk ◽  
Marcin Bąkała ◽  
Jacek Nowakowski ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Output Signal ◽  
Linear Time ◽  
Mathematical Problem ◽  
Simple Method ◽  
Linear Time Invariant ◽  
Input And Output ◽  
Order Difference Equation ◽  
Time Invariant ◽  
Discrete Integrator

AbstractThis is a continuation (Part II) of our previous paper [19]. In this paper we present a simple method of the fractional-order value calculation of the fractional-order discrete integration element. We assume that the input and output signals are known. The linear time-invariant fractional-order difference equation is reduced to the polynomial in a variable ν with coefficients depending on the measured input and output signal values. One should solve linear algebraic equation or find roots of a polynomial. This simple mathematical problem complicates when the measured output signal contains a noise. Then, the polynomial roots are unsettled because they are very sensitive to coefficients variability. In the paper we show that the discrete integrator fractional-order is very stiff due to the degree of the polynomial. The minimal number of samples guaranteeing the correct order is evaluated. The investigations are supported by a numerical example.

scholarly journals Mixed Order Fractional Observers for Minimal Realizations of Linear Time-Invariant Systems

Algorithms ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 136
Author(s):  
Manuel Duarte-Mermoud ◽  
Javier Gallegos ◽  
Norelys Aguila-Camacho ◽  
Rafael Castro-Linares
Keyword(s):  
Fractional Order ◽  
Performance Optimization ◽  
Degrees Of Freedom ◽  
Linear Time ◽  
Minimal Realization ◽  
Linear Time Invariant ◽  
Mixed Order ◽  
Linear Time Invariant Systems ◽  
Minimal Realizations ◽  
Time Invariant

Adaptive and non-adaptive minimal realization (MR) fractional order observers (FOO) for linear time-invariant systems (LTIS) of a possibly different derivation order (mixed order observers, MOO) are studied in this paper. Conditions on the convergence and robustness are provided using a general framework which allows observing systems defined with any type of fractional order derivative (FOD). A qualitative discussion is presented to show that the derivation orders of the observer structure and for the parameter adjustment are relevant degrees of freedom for performance optimization. A control problem is developed to illustrate the application of the proposed observers.

Fractional order frequency proportional-integral-derivative control of microgrid consisting of renewable energy sources based on multi-objective grasshopper optimization algorithm

2021 ◽  
pp. 014233122110346
Author(s):  
Abdulsamed Tabak
Keyword(s):  
Fractional Order ◽  
Optimization Algorithm ◽  
Frequency Control ◽  
Frequency Deviation ◽  
Control Signal ◽  
Proportional Integral Derivative ◽  
Proportional Integral ◽  
Multi Objective ◽  
Grasshopper Optimization Algorithm ◽  
Grasshopper Optimization

In recent years, fractional order proportional-integral-derivative (FOPID) controllers have been applied in different areas in the academy due to their superior performance over conventional proportional-integral-derivative (PID) controllers. When the literature is reviewed, it has been observed that lack of studies that use swarm-based and multi-objective optimization algorithms together with FOPID controllers in frequency control of micro-grid. The load frequency control (LFC) problem is considered as two objectives in order to eliminate the complications that occur when only the frequency deviation is minimized. In our study, a method called MOGOA-FOPID in which both the frequency deviation and the control signal are minimized together for the frequency control in the microgrid is proposed. By using the multi-objective grasshopper optimization algorithm (MOGOA), both the frequency deviation and the control signal are minimized together, and thus, it is aimed to limit the battery capacity, reduce the flywheel jerk and avoid high diesel fuel consumption as well as an effective frequency control. In order to obtain a more realistic system, not only the photovoltaic (PV) solar and wind power but also the load demand is taken in a stochastic structure. Then, the results of the proposed MOGOA-FOPID are compared with the results of multi-objective genetic algorithm (MOGA)-based PID/FOPID and MOGOA-PID and its superiority is demonstrated. Finally, robustness tests of the system are performed under the perturbed parameters and outperform of MOGOA-FOPID over other methods is seen.

scholarly journals Commensurate and Non-Commensurate Fractional-Order Discrete Models of an Electric Individual-Wheel Drive on an Autonomous Platform

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 300
Author(s):  
Marcin Bąkała ◽  
Piotr Duch ◽  
J. A. Tenreiro Machado ◽  
Piotr Ostalczyk ◽  
Dominik Sankowski
Keyword(s):  
Fractional Order ◽  
Closed Loop ◽  
Linear Time ◽  
Classical Model ◽  
Linear Difference Equation ◽  
Discrete Models ◽  
Measured Velocity ◽  
Linear Time Invariant ◽  
Wheel Drive ◽  
Time Invariant

This paper presents integer and linear time-invariant fractional order (FO) models of a closed-loop electric individual-wheel drive implemented on an autonomous platform. Two discrete-time FO models are tested: non-commensurate and commensurate. A classical model described by the second-order linear difference equation is used as the reference. According to the sum of the squared error criterion (SSE), we compare a two-parameter integer order model with four-parameter non-commensurate and three-parameter commensurate FO descriptions. The computer simulation results are compared with the measured velocity of a real autonomous platform powered by a closed-loop electric individual-wheel drive.

Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Mojtaba Soorki ◽  
Mohammad Tavazoei
Keyword(s):  
Fractional Order ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Time Response ◽  
Response Analysis ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Time Response Analysis ◽  
Necessary And Sufficient ◽  
Time Invariant

AbstractThis paper deals with fractional-order linear time invariant swarm systems. Necessary and sufficient conditions for asymptotic swarm stability of these systems are presented. Also, based on a time response analysis the speed of convergence in an asymptotically swarm stable fractional-order linear time invariant swarm system is investigated and compared with that of its integer-order counterpart. Numerical simulation results are presented to show the effectiveness of the paper results.

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