Control Lorenz System with Vibration Estimation with Averaging Method

Chun Zhou

doi:10.4028/www.scientific.net/AMM.43.36

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 43Control Lorenz System with Vibration Estimation...

Control Lorenz System with Vibration Estimation with Averaging Method

Abstract:

The vibrational control theory stems from the well-known of stabilization of the upper unstable equilibrium position of the inverted pendulum having suspension point vibration along the vertical line with amplitude as small as desired and a frequency reason high. Chaotic phenomena have been found in many nonlinear systems including continuous time and discrete time. The chaotic systems are characterized by their extreme sensitivity to initial conditions, nonperiodic and boundary. The trajectories start even from close initial states will diverge from each other at an exponential rate as time goes. The vibrational control method was applied to Lorenz system. The effect of the control can be estimated with the APAZ method. It was showed that vibrational control brought the controlled Lorenz system to stable equilibrium with appropriate parameters. Numerical simulation demonstrated validity of the proposed method.