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Analysis and shaping of the self-sustained oscillations in relay controlled fractional-order systems

2012; Springer Science+Business Media; Volume: 16; Issue: 1 Linguagem: Inglês

10.2478/s13540-013-0007-x

1311-0454

Riccardo Caponetto, Guido Maione, Alessandro Pisano, Milan R. Rapaić, Elio Usai,

Extremum Seeking Control Systems

This work deals with Single-Input-Single-Output (SISO) fractional order systems with a discontinuous relay control element in the feedback loop. Stable self-sustained oscillations often occur in the closed loop relay system, and this work takes advantage of Describing Function (DF) analysis and of another more accurate approach, called Locus of a Perturbed Relay System (LPRS) method, for analyzing in the frequency domain the characteristics of the limit cycle oscillations. The use of fractional lead compensator is also suggested for the purpose of shaping the characteristics of the limit cycle. The proposed analysis and design procedures will be supported by thoroughly discussed simulation examples.