Negative Derivative Feedback Controller for Repressing Vibrations of the Hybrid Rayleigh−Van der Pol−Duffing Oscillator
Y. A. Amer, M. A. EL-Sayed, M. N. Abd El-Salam
Abstract
Negative derivative feedback (NDF) controller is presented for suppressing the vibrations of a nonlinear dynamical system at the worst resonance case (Ω=ω1, ω2=ω1). To obtain the approximate solution, we used the multiple scales technique. The behavior of uncontrolled and controlled system is presented using time histories. We used the frequency-response equations to investigate the stability of controlled system. The e.ectiveness of closed loop parameters on the behavior of the main system and NDF controller has been studied. We found that all obtained solutions using multiple scales method are in a good agreement with the numerical solutions.
Topics & Concepts
Van der Pol oscillatorControl theory (sociology)Duffing equationController (irrigation)Nonlinear systemDerivative (finance)Stability (learning theory)Rayleigh scatteringVibrationMathematicsResonance (particle physics)PhysicsMathematical analysisComputer scienceControl (management)Quantum mechanicsEconomicsFinancial economicsAgronomyArtificial intelligenceBiologyMachine learningVibration and Dynamic AnalysisVibration Control and Rheological FluidsDynamics and Control of Mechanical Systems