The modelling and analysis of fractional-order control systems in frequency domain

The modelling and analysis of fractional-order control systems in discrete domain

This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A practical example for modelling the fractional-order control loop is shown and obtained results are discussed in conclusion.

Modelling and analysis of fractional-order regulated systems in the state space

In this paper we present the mathematical description and analysis of a fractional-order regulated system in the state space. A little historical background of our results in the analysis and synthesis of the fractional-order dynamical regulated systems is given. The methods and results of simulations of the fractional-order system described by a state space equation equivalent to three-member fractional-order differential equation with a fractional-order $PD^δ$ regulator are then presented. The possibility of investigating the stability of such systems is also considered.

Fractional Generalized KYP Lemma for Fractional Order System within Finite Frequency Range

The celebrated GKYP is widely used in integer-order control system. However, when it comes to the fractional order system, there exists no such tool to solve problems. This paper prove the FGKYP which can be used in the analysis of problems in fractional order system. The $H_\infty$ and $L_\infty$ of fractional order system are analysed based on the FGKYP.

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is c…

Fractional-Order Modelling and Optimal Control of Cholera Transmission

A Caputo-type fractional-order mathematical model for "metapopulation cholera transmission" was recently proposed in [Chaos Solitons Fractals 117 (2018), 37--49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system …

基于混沌多目标优化的AVR系统分数阶PID控制器频域设计

Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization

本文提出一种基于混沌多目标优化的分数阶PID控制器设计方法，用于AVR系统，通过改进的NSGA-II算法优化控制器参数，保证系统稳定性和鲁棒性。