Controlling friction-induced instability by recursive time-delayed acceleration feedback

A novel time-delayed acceleration feedback method of controlling friction-induced instability is proposed. A single degree-of-freedom mechanical oscillator on a moving belt represents the basic friction-driven system. The control force is synthesized based on an infinite weighted sum of the acceleration of the vibrating mass measured at regular intervals in the past. Such a control force can be effectively produced by the recursive summation of the time-delayed acceleration and the time-delayed control signal, and hence the technique is termed as the recursive time-delayed acceleration feedback control. The local stability analysis of the equilibrium reveals nontrivial and beneficial influences of the recursive gain on the system performance. Robustness of the control is shown to improve with the increasing value of the recursive gain. A multiple time scale based analysis of the system elucidates the role of the recursive gain in enhancing the amount of dissipation produced by the control action. The influences of the time-delay and the control gain on the optimized performance of the system are also discussed. Numerical simulations of the system equations corroborate the analytical results. The present method is believed to be applicable to any self-excited system having a large degree of instability that is not removable by an ordinary time-delayed feedback.