Fractional-order Systems and Controls

By Concepción A. Monje, YangQuan Chen, Blas M. Vinagre, Dingyu Xue, V. Feliu. 2010

1,881 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/368bda603bf8279fb5cbd63acede9fafb883e843

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In Control and Systems Engineering

Citations in the corpus

A Fractional Order Proportional and Derivative (FOPD) Motion Controller: Tuning Rule and Experiments (2010, background): “For example, the fractional order controllers are realized by the analogue circuits in [7]; the controller was proposed in [2], where a better control performance was demonstrated in comparison with the classical proportional–integral–differential (PID) controller because of extra real parameters an”
Fractional order models of leaves (2014, methodology): “During the last decade FC has been found to play a fundamental role in the modeling of a considerable number of phenomena (Oustaloup, 1991; Zaslavsky, 2005; Magin, 2006; Mainardi, 2010; Monje et al., 2010; Tenreiro Machado et al., 2011a), and has emerged as an important tool for the study of dynamic”
Approximate controllability of fractional order semilinear systems with bounded delay (2012, background): “It is clear that the linear system corresponding to (11) is controllable as the rank of the matrix [B, AB] is 2, see [3,4].”
Design of a Fractional Order Frequency PID Controller for an Islanded Microgrid: A Multi-Objective Extremal Optimization Method (2017, methodology): “FOPID Controller As one of three widely used definitions for fractional differentiation and integration, the Riemann Liouville (RL) definition is presented as follows [19]: 1 1 ( ) ( ) , 1 ( ) ( ) n t r a t n r n a d f D f t d n r n n r dt t τ τ τ − + = − < < Γ − −  (1) where Γ(.”
Fractional systems state space description: some wrong ideas and proposed solutions (2014, methodology): “…mentioned and with null initial conditions, description (2) can be used to obtain the system forced solution in terms of the MittagLeffler function (Monje et al., 2010): yf tð Þ ¼ C Z t 0 E A t ð Þ ð ÞBu ð Þd þDu tð Þ with E xð Þ ¼ X1 k¼0 zk kþ 1ð Þ ð37Þ but is wrong to consider that yiðtÞ ¼ E…”
The Chronicles of Fractional Calculus (2017, neutral): “2009 [6, 90, 122, 27, 89, 77, 155] [109, 17] 2010 [111, 31, 133, 165, 46] [98, 106, 63] 2011 [156, 144, 87, 65, 126, 92, 3, 187, 207, 78, 44, 93] [86, 18]”