1202ptimal Control of Nonlinear Vibration Resonances for s1202ptimal Control of Nonlinear Vibration Resonances for s.doc

Optimal Control of Nonlinear Vibration Resonances for s.d.o.f System with Linear and Nonlinear Controllers Abstract: A optimal feedback control methodology is provided to mitigate the primary and superharmonic resonance of a single degree of freedom(s.d.o.f) system with linear and nonlinear vibration controllers. Using the method of multiple scales, the modulation equations that govern the nonlinear dynamic of the s.d.o.f system are derived. The regions of the stable feedback gain are obtained by using the stability conditions of eigenvalue equation. An attenuation ratio is utilized to evaluate the performance of the vibration control by taking the proportion of peak amplitude of primary or superharmonic resonance for the suspension system with and without control. Taking the attenuation ratio and energy function as the objective functions and the regions of the stable feedback gains as constrained conditions, the optimal control parameters are worked out by using minimum optimal method. The optimal controllers are designed to control the dynamic behaviors of the nonlinear dynamical systems. It is found that both the optimal linear feedback gains and suitable nonlinear feedback gain can suppress the vibration of the s.d.o.f vibration system. Keywords: nonlinear vibration; optimal control; primary resonance; superharmonic resonance INTRODUCTION Engineering structure are subjected to vibrations caused by wind, roating engines and cars, or other environmental disturbances. The undesirable large amplitude of the resonance response can induce noise, bad performance or even serve damage. Therefore, it is important to mitigate the resonant vibrations to ensure an appropriate running condition and a desired behaviour of the system. In the literature, the stability of the nonlinear dynamics and control problems of vibration system have been widely studied. The stability of viscoelastic system under stochastic loads were studied by using several numeri