Abstract
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.
Highlights
The restoring force related to the classical model of linear springs usually obeys Hook’s law i.e., the force needed to deform the spring is proportional to its deflection
Feedback to improve the performance of a vibration isolation system whose restoring and damping forces are in a real-power form
They studied the primary resonance, dynamic stability and transmissibility for this system under base excitation using the method of multiple scales
Summary
The restoring force related to the classical model of linear springs usually obeys Hook’s law i.e., the force needed to deform the spring is proportional to its deflection. UTILIZING THE TIME DELAYED PPF CONTROLLER TO SUPPRESS VIBRATIONS OF A NONLINEAR SYSTEM CONTAINING REAL POWER EXPONENTS IN DAMPING AND RESTORING FORCES. ABDELHAFEZ feedback to improve the performance of a vibration isolation system whose restoring and damping forces are in a real-power form They studied the primary resonance, dynamic stability and transmissibility for this system under base excitation using the method of multiple scales. Abdelhafez and coauthor applied positive position feedback (PPF) controller to reduce the vibrations of a forced and self-excited nonlinear beam [19] They deduced that the time margin of the system depends on the sum of all time delays. The PPF controller is utilized to suppress the primary resonance vibrations of the base excited oscillator with real-power exponents in the restoring and damping forces given [9].
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