Suppress the vibration of a nonlinear dynamical system subjected to external force using a positive position feedback control.

Vibration suppression using a positive position feedback (PPF) control for a nonlinear dynamical system which subjected to an external force is studied. The proposed model is the vertical dynamic excitation of structures induced by a single pedestrian walking along a straight path on flat and relatively stiff surfaces. The multiple scale perturbation technique was applied to derive the first order approximate solution of the system. The response equation and the stability criteria for the system were derived near the simultaneous primary and internal resonance cases. MATLAB 14.0 have been used for the numerical studying to show the time history of the main system with and without PPF controller. Also, the effect of the system parameters on the response system have been studied. A comparison between the approximate and numerical solutions is illustrated and it show a good agreement between them. It is found that (PPF) controller is very suitable for small natural frequency dynamical systems subjected to primary resonance excitations.