Nonlinear Dynamics

, Volume 42, Issue 2, pp 113–136 | Cite as

Control of a Nonlinear System Using the Saturation Phenomenon

  • Mohammad Shoeybi
  • Mehrdaad Ghorashi


In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.


energy transfer internal resonance method of multiple scales saturation stability vibration control 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentSharif University of TechnologyTehranIran
  2. 2.Flow Physics and Computation DivisionDepartment of Mechanical Engineering, Stanford UniversityStanfordU.S.A.
  3. 3.The Rotorcraft Research Group, Department of Mechanical and Aerospace EngineeringCarleton UniversityOttawaCanada

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