NDLI: Design of an assemble-type fractional-order unit circuit and its application in Lorenz system

Content Provider	IET Digital Library
Author	Zhang, Xiaohong Qi, Yanli
Abstract	A new generalised Lorenz three-dimensional integer-order non-linear system is constructed, and integer-order derivatives are simply replaced by fractional-order ones. Transfer functions in Laplace domain have been calculated and compared for a set of fractional orders q i in (0, 1) with decrement of 0.025 for the maximum error Y = 1 dB/2 dB/3 dB. A novel basic fractional-order unit circuit named ‘Assemble Type’ is designed consulting to the four existing unit circuits, which are ‘Chain Type’, ‘Tree Type’, ‘Mixed Type’ and ‘New Type’. Meanwhile, it is compared with the four existing unit circuits in circuit theory and applications. The novel fractional-order unit circuit is applied to the circuit simulation of Lorenz system combined with the other four unit circuits, and circuit simulation shows that they have very resemble chaotic behaviours, actually, the scheme can be applied in any tiny values of q i , which shows that the fractional-order system has better effectiveness, flexibility and universality. Finally, using stability analytical method based on two stability theorems and necessary conditions to exhibit validity and feasibility of this novel-type design.
Starting Page	437
Ending Page	445
Page Count	9
ISSN	1751858X
Volume Number	11
e-ISSN	17518598
Issue Number	Issue 5, Sep (2017)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cds/11/5
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cds.2016.0145
Journal	IET Circuits, Devices & Systems
Publisher Date	2016-11-15
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Assemble-type Fractional-order Unit Circuit Design Chain Type Circuit Chaos Chaotic Behaviour in Circuit Chaotic Behaviours Circuit Simulation Circuit Stability Circuit Theory General Circuit Analysis And Synthesis Method Generalised Lorenz Three-dimensional Integer-order Nonlinear System Laplace Domain Laplace Equation Mathematical Analysis Mixed Type Circuit Necessary Condition Network Synthesis New Type Circuit Nonlinear Network Analysis Nonlinear Network Analysis And Design Stability Analytical Method Stability Theorems Transfer Function Tree Type Circuit
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Electrical and Electronic Engineering

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