Self Oscillations in Dynamic Systems : A New Methodology via Two Relay Controllers Introduction Part I: Design of Self Oscillations using Two Relay Controller Describing Function Based Design of TRC for Generation of Self Oscillation Poincaré Maps Based Design Self Oscillation via Locus of a Perturbed Relay System Design (LPRS) Part II: Robustification of the Self Oscillation Generated by Two Relay Controller Robustification of the Self Oscillation via Sliding Modes Tracking Controllers Output Based Robust Generation of Self Oscillations Part III: Applications Generating Self Oscillations in Furuta Pendulum Three Link Serial Structure Underactuated Robot Generation of Self Oscillations in Systems with Double Integrator Fixed Phase Loop (FPL) Appendix A: Describing Function Appendix B: The Locus of a Perturbed Relay System (LPRS) Appendix C: Poincaré Map Appendix D: Output Feedback References Index This monograph presents a simple and efficient two relay control algorithm for generation of self excited oscillations of a desired amplitude and frequency in dynamic systems. Developed by the authors the two relay controller consists of two relays switched by the feedback received from a linear or nonlinear system and represents a new approach to the self generation of periodic motions in underactuated mechanical systems. The first part of the book explains the design procedures for two relay control using three different methodologies the describing function method Poincaré maps and the locus of a perturbed relay system method and concludes with stability analysis of designed periodic oscillations. Two methods to ensure the robustness of two relay control algorithms are explored in the second part one based on the combination of the high order sliding mode controller and backstepping and the other on higher order sliding modes based reconstruction of uncertainties and their compensation where Lyapunov based stability analysis of tracking error is used. Finally the third part illustrates applications of self oscillation generation by a two relay control with a Furuta pendulum wheel pendulum 3 DOF underactuated robot 3 DOF laboratory helicopter and fixed phase electronic circuits. Self Oscillations in Dynamic Systems will appeal to engineers researchers and graduate students working on the tracking and self generation of periodic motion of electromechanical systems including non minimum phase systems. It will also be of interest to mathematicians working on analysis of periodic solutions