The fractional - order controllers: Methods for their synthesis and application

By Ivo Petrás. 2000

255 citations recorded by the source corpus.

This paper deals with fractional-order controllers. We outline mathematical description of fractional controllers and methods of their synthesis and application. Synthesis method is a modified root locus method for fractional-order systems and fractional-order controllers. In the next section we describe how to apply the fractional controller on control systems.

Subfields: Algebra and Number Theory, Applied Mathematics, Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/29484e69902d87f7a92af87f06a8ef75fd1af2cd

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In Algebra and Number Theory

In Applied Mathematics

In Artificial Intelligence

Citations in the corpus

Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review (2004, methodology): “Another example is the PID controller [24, 26], an extension of PID controller.”
Tuning and implementation methods for fractional-order controllers (2012, methodology): “The controller design was done in [27], according to the method (poles placement) described in [24], for desired stability measure σ = 2.”
Using Fractional Order Adjustment Rules and Fractional Order Reference Models in Model-Reference Adaptive Control (2002, methodology): “Taking the conventional PID controller as an example, its fractional order version, PIλDµ controller, was studied in time domain in [13] and in frequency domain in [ 12 ].”
Fractional order control - A tutorial (2009, background): “PIλ Dμ controller, also known as PIλ Dδ controller, was studied in time domain in [77] and in frequency domain in [67].”
UBIQUITOUS FRACTIONAL ORDER CONTROLS (2006, background): “PI λ D µ controller, also known as PI λ D δ controller, was studied in time domain in (Podlubny, 1999) and in frequency domain in (Petráš, 1999).”
Discretization schemes for fractional-order differentiators and integrators (2002, background): “Another example is the PI D controller [6], [17], an extension of PID controller.”
Network Model of the CPE (2011, background): “The phenomena described by such equations are frequent for instance in biochemistry or biomedicine [6-8], in electrochemistry [9], [10], in modern control technique [11-15], in acoustic or optical signal processing [16], [17] and in many other practical domains.”
Design of a fractional order PID controller for an AVR using particle swarm optimization (2009, methodology): “Different design methods have been reported including pole distribution (Petras, 1999), frequency domain approach (Vinagre, Podlubny, Dorcak, & Feliu, 2000), state-space design (Dorcak, Petras, Kostial, & Terpak, 2001) and two-stage or hybrid approach ll rights reserved.”