Control of an electromechanical pendulum subjected to impulsive disturbances using the Melnikov theory approach
The dynamics of an electromechanical pendulum that collides with an external moving mass is considered. The Melnikov function is derived to determine the effects of periodic collisions on the threshold condition for the appearance of Smale horseshoes chaos in the system. In order to counterbalance the action of the collision, a pulse-like periodic controller is used and the results show the efficiency of the controller to reduce the distortions due to collision and change the parameters boundary delineating the chaotic domain.
KeywordsElectromechanical pendulum Horseshoes chaos Collision Impulsive control
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- C. May, H. Janocha, E. Grasso and D. Naso, A pendulum actuator and its force generation capabilities, Proc. 7th Int. Conf. on Multibody Systems, Nonlinear Dynamics, and Control (2009) 1769–1775.Google Scholar
- N. Ida, Design and control of a magnetic pendulum actuator, 13th Int. Conf. on Optimization of Electrical and Electronic Equipment (OPTIM) (2012) Doi: 10.1109/OPTIM. 2012.6231898.Google Scholar
- Y. Guo and A. C. J Luo, Analytical bifurcation trees of a periodically excited pendulum, ASME Proc. Dynamics, Vibration and Control (2016) V04BT05A016, Doi: 10.1115/IMECE 2016-65916.Google Scholar
- J. Xie, S.-H. He, Z.-H. Liu and Y. Chen, On application Melnikov method to detecting the edge of chaos for a microcantilever, New Advances in Mechanisms, Mechanical Transmission and Robotics (2016) 155–163.Google Scholar
- V. K. Melnikov, On the stability of the center for time periodic perturbations, Trans. Moscow Math. SOC, 2 (1963) 1–57.Google Scholar