PID controller design for fractional-order systems with time delays

Cataloged from PDF version of article.Classical proper PID controllers are designed for linear time invariant plants whose transfer functions are rational functions of s(alpha), where 0 < alpha < 1, and s is the Laplace transform variable. Effect of input-output time delay on the range of allowable controller parameters is investigated. The allowable PID controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants. (C) 2011 Elsevier B.V. All rights reserved

Robust stability of fractional order polynomials with complicated uncertainty structure

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. © 2017 Matusu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/ 2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303, MSMT-7778/2014

Stability Analysis of Fractional Differential Systems with Order Lying in (1, 2)

Raw OTU counts from Il17ra animals at 14 days after colonization. (CSV 49 kb

Robust Stability and Stabilization of Interval Uncertain Descriptor Fractional-Order Systems with the Fractional-Order α

Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimension n only need to solve one 4n-by-4n LMI. Numerical examples are presented to shown the effectiveness of our results

Stability of Linear Multiple‎ Different Order Caputo Fractional System ‎‏

In this paper, we introduce a new equivalent system to the higher order Caputo fractional system ‎‎(CFS) . This equivalent system has multiple order Caputo fractional derivatives ‎‎(CFDs). These CFDs are lying between zero and one.‎ As well ‎as, we find the fundamental solution for linear CFS with multiple order CFDs. Also, we introduce new criteria of studying the stability (asymptotic stability) of the ‎linear CFS with multiple order CFDs. These criteria can be applied in three cases: ‎the first, all CFDs is lying between zero and one. The second, all CFDs are lying ‎between one and two. Finally, some of CFDs are lying between zero and one, ‎and the rest of these derivatives are lying between one and two. The criteria are ‎depending on the position of eigenvalues of the matrix system in the complex plane. ‎These criteria are considered as a generalized of the classical criteria which is ‎used to study the stability of linear first ODEs. Also, these criteria are considered ‎as generalized of the criteria which used to study the stability same order CFS in ‎case when all CFDs lying between zero and one, also in case when all CFDs lying ‎between one and two. Several examples are given to show the behavior of the ‎solution near the equilibrium point.‎ Keywords: Caputo fractional derivatives; Linear Caputo fractional system ‎; Fundamental solution Stability analysis

Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations

Fractional Order Identification Method and Control: Development of Control for Non-Minimum Phase Fractional Order System

The increasing use of renewable energy has resulted in the need for improved a dc-dc converters. This type of electronic-based equipment is needed to interface the dc voltages normally encountered with solar arrays and battery systems to voltage levels suitable for connecting three phase inverters to distribution level networks. As grid-connected solar power levels continue to increase, there is a corresponding need for improved modeling and control of power electronic converters. In particular, higher levels of boost ratios are needed to connect low voltage circuits (less than 1000 V) to medium voltage levels in the range of 13 kV to 34 kV. With boost ratios now exceeding a factor of 10, the inherent nonlinearities of boost converter circuits become more prominent and thereby lead to stability concerns under variable load conditions. This dissertation presents a new method for analyzing dc-dc converters using fractional order calculus. This provides control systems designers the ability to analyze converter frequency response with Bode plots that have pole-zero contributions other than +/- 20 dB/decade. This dissertation details a systematic method of deriving the optimal frequency-domain fit of nonlinear dc-dc converter operation by use of a modified describing function technique. Results are presented by comparing a conventional linearization technique (i.e., integer-order transfer functions) to the describing-function derived equivalent fractional-order model. The benefits of this approach in achieving improved stability margins with high-ratio dc-dc converters are presented