Positive position feedback (PPF) controller for suppression of nonlinear system vibration

In this paper, a study for positive position feedback controller is presented that is used to suppress the vibration amplitude of a nonlinear dynamic model at primary resonance and the presence of 1:1 internal resonance. We obtained an approximate solution by applying the multiple scales method. Then we conducted bifurcation analyses for open and closed loop systems. The stability of the system is investigated by applying the frequency-response equations. The effects of the different controller parameters on the behavior of the main system have been studied. Optimum working conditions of the system were extracted to be used in the design of such systems. Finally, numerical simulations are performed to demonstrate and validate the control law. We found that all predictions from analytical solutions are in good agreement with the numerical simulation. A comparison with the available published work is included at the end of the work.