Self-Oscillation via Locus of a Perturbed Relay System Design (LPRS)

  • Luis T. Aguilar
  • Igor Boiko
  • Leonid Fridman
  • Rafael Iriarte
Part of the Systems & Control: Foundations & Applications book series (SCFA)


The Poincaré map considered above is a precise tool to find gains of the TRC . The drawback of this approach is in its complexity, which entails extensive computations. This chapter presents an alternative approach—based on the LPRS method, which in the solution of the analysis problem provides exact values of the parameters of self-excited oscillations and a precise solution of the input–output problem, when the plant is linear. Application of this method involved the use of specific computation formulas available within the LPRS method. Unlike other publications on the LPRS method that were focused on analysis, this chapter provides LPRS-based design of self-excited periodic motions. The experiments with inertia wheel pendulum are presented below to illustrate the results of this design.


Inertia Wheel Pendulum Input Output Problem Self-excited Oscillations Specific Calculation Formula Relay Feedback System 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Luis T. Aguilar
    • 1
  • Igor Boiko
    • 2
  • Leonid Fridman
    • 3
  • Rafael Iriarte
    • 3
  1. 1.CITEDIInstituto Politecnico NacionalTijuanaMexico
  2. 2.Department of Electrical EngineeringThe Petroleum InstituteAbu DhabiUAE
  3. 3.Division de Ingenieria ElectricaUniversidad Nacional Autonoma de MexicoMexico CityMexico

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