Control of friction driven oscillation by time-delayed state feedback

An experimental set-up is designed and fabricated to yield a single degree-of-freedom friction-driven oscillator. Self-excited limit cycles obtained experimentally are used to determine the numerical values of the parameters that appear in the mathematical model under pure slip condition. Then the control of the limit cycle using a time-delayed displacement feedback is investigated. The same system under harmonic excitation is also considered. A PD control system with identical time delay in the displacement and velocity feedback is analysed. Only the primary harmonic entrainment region is investigated. Both the best and worst time delays are determined. Stability and bifurcation conditions are discussed. Numerical results are used to verify the analytical results obtained by using the method of multiple time scales and a parametric investigation is included. The proper choice of time delay, which depends on the model parameters, is crucial. It is shown that with appropriate choices of time delay and gain factors, both the limit cycle and the steady-state forced amplitude can be controlled; no time delay or inappropriate time delay can enhance the vibration level.