Utilizing the time delayed PPF controller to suppress vibrations of a nonlinear system containing real power exponents in damping and restoring forces

The time delayed Positive Position Feedback (PPF) controller is utilized to suppress the primary resonance of vibrations of an excited base oscillator by real power exponents of the restoring and damping forces. Multiple scales method is conducted to get the frequency response equations. The stability of the system is studied by using the Lyapunov first method. The influences of system parameters and time delay on the system response are investigated to avoid the jump phenomenon for better system performance. Time margin is deduced for most possible values of controller gain. Analytic results are verified by numerical integration of the original system equations.