Self-Oscillations in Dynamic Systems: A New Methodology via by Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte

By Luis T. Aguilar, Igor Boiko, Leonid Fridman, Rafael Iriarte

This monograph provides an easy and effective two-relay keep watch over set of rules for new release of self-excited oscillations of a wanted amplitude and frequency in dynamic platforms. built by means of the authors, the two-relay controller comprises relays switched by way of the suggestions got from a linear or nonlinear process, and represents a brand new method of the self-generation of periodic motions in underactuated mechanical systems.

The first a part of the publication explains the layout strategies for two-relay keep watch over utilizing 3 assorted methodologies – the describing-function strategy, Poincaré maps, and the locus-of-a perturbed-relay-system technique – and concludes with balance research of designed periodic oscillations.

Two the way to make sure the robustness of two-relay keep watch over algorithms are explored within the moment half, one according to the mix of the high-order sliding mode controller and backstepping, and the opposite on higher-order sliding-modes-based reconstruction of uncertainties and their repayment the place Lyapunov-based balance research of monitoring errors is used. eventually, the 3rd half illustrates purposes of self-oscillation new release by way of a two-relay keep watch over with a Furuta pendulum, wheel pendulum, 3-DOF underactuated robotic, 3-DOF laboratory helicopter, and fixed-phase digital circuits.

Self-Oscillations in Dynamic Systems will attract engineers, researchers, and graduate scholars engaged on the monitoring and self-generation of periodic movement of electromechanical structures, together with non-minimum-phase structures. it's going to even be of curiosity to mathematicians engaged on research of periodic solutions.

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Self-Oscillations in Dynamic Systems: A New Methodology via Two-Relay Controllers

This monograph provides an easy and effective two-relay regulate set of rules for iteration of self-excited oscillations of a wanted amplitude and frequency in dynamic structures. constructed through the authors, the two-relay controller comprises relays switched by means of the suggestions acquired from a linear or nonlinear procedure, and represents a brand new method of the self-generation of periodic motions in underactuated mechanical structures.

Additional info for Self-Oscillations in Dynamic Systems: A New Methodology via Two-Relay Controllers

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3 Describing Function of the Two-Relay Control 21 Fig. 4) is greater than 1. 2) named above as the tworelay controller. / D ! A1 Z 2 =! t/dt C j 0 ! A1 Z 2 =! t/ in our case) and ! t/. However, the analysis of the TRC can utilize the fact that it is a combination of two relay nonlinearities, for which the DFs are known. The TRC can be viewed as the parallel connection of two ideal relays where the input to the first relay is the output variable and the input to the second relay is the derivative of the output variable (see Fig.

2 /2 C 9! 1 3! : ! 2 /2 C 9! j4/g D 0:0325. 15), the values of controller parameters: c1 D 1:1781 and c2 D 0:9425. 5 14 time [s] Fig. 2) is plotted in Fig. 3, where the amplitude of the system output produced through simulations matches the desired amplitude, whereas the frequency of this signal shows some deviation from the desired value: ˝ D 3:6 rad/s. This discrepancy is expected due to the approximate nature of the DF method. / ˇˇ d ln ! 1220. 28), with c1 D 1:1781 and c2 D 0:9425, is orbitally asymptotically stable.

Now, let us derive the Poincaré map from the sets '2 . 0; Á2 ; 10 /, where Á2 < 0, into the sets '3 . Á1 ; 0; 10 / where Á1 < 0 (see region R3 in Fig. 1). Tp ; Á1 ; 0 ; c1 ; c2 / 46 3 Poincaré Map-Based Design smoothly depend on their arguments. Á01 ; 0 ; c1 ; c2 / of '3 . Á1 ; 0; 0 /, Á1 < 0 together with the time C constant Tp < Tsw < Tp can be defined by the similar procedure. 1 ? 1 ; ? 1 D A1 , one needs to solve the set of algebraic equations with respect to c1 , c2 , and 0 : Ä A1 ? 2 =˝; A1 ; ?

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