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Self-oscillations in dynamic systems. A new methodology via two-relay controllers. (English) Zbl 1423.93005

Systems & Control: Foundations & Applications. Cham: Birkhäuser (ISBN 978-3-319-23302-4/hbk; 978-3-319-23303-1/ebook). xiv, 158 p. (2015).
From the preface: How can I generate oscillations of low frequency and particular amplitude using variable structure control?
Boiko and Fridman discovered that describing functions (DF) of the second-order sliding mode control algorithms could shift the point characterizing the oscillatory mode resulting from chattering to the second and third quadrants of the complex plane. With the discovery of this property, a straightforward logical conclusion could be made that the problem of generation of self-oscillations (SO) with desired amplitude and frequency could be defined as an inverse problem with respect to the one previously studied.
In this book, the two-relay controller (TRC) is proposed, which is intended for the generation of SO in dynamic systems.

MSC:

93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory
93B35 Sensitivity (robustness)
93B12 Variable structure systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
93C15 Control/observation systems governed by ordinary differential equations
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
93C80 Frequency-response methods in control theory
70Q05 Control of mechanical systems
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