Journal of Mechanical Science and Technology 32 (2) (2018) 865~874 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online) DOI 10.1007/s12206-018-0137-x Control of an electromechanical pendulum subjected to impulsive disturbances using the Melnikov theory approach † A. Notué Kadjie * , I. Kemajou and P. Woafo Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, and TWAS Research Unit, Department of Physics, Faculty of Science, University of Yaoundé, I, P.O. Box 812, Yaoundé, Cameroon (Manuscript Received April 4, 2017; Revised October 25, 2017; Accepted November 4, 2017) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract 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. Keywords: Electromechanical pendulum; Horseshoes chaos; Collision; Impulsive control ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Dynamical systems theory provides appropriate tools to analyze and understand the behavior of a diverse range of problems. Some of these systems are non-smooth such as electrical circuits that have switches, mechanical devices in which components impact with each other, systems with fric- tion, sliding or squealing, many control systems and models in social and financial sciences where continuous change can trigger discrete actions [1]. As consequence, many efforts have been concentrated by several authors to study the dynamical behavior of non- smooth systems. There are mainly impact oscillators [2-10] and oscillators colliding with other systems [11-17]. Yang et al. [18] presented a project of dynamic simulation system for vessel collision process based on the technology of Ship han- dling simulator. Taghavifar et al. [11] analyzed the dissipated energy for a traveling wheel at collision time with obstacles while a controlled laboratory condition of the soil bin facility equipped with a single wheel-tester rig was utilized to carry out the experiments. Moreover, concerning robots, Fang et al. [19] dealt with the problems related to self-collision detection and optimal collision-free trajectory planning for a robot arm subjected to dynamic constraints. One of the physical systems of practical interest which is sometimes submitted to collision is the pendulum arm. It can be used as actuator [20-22] when set into oscillating motion through several mechanisms. For instance, its swinging dy- namics can be commanded by an electrical voltage through a magnetic coupling (Electromechanical pendulum) as it is con- sidered in this manuscript. During the actuation process, the pendulum may periodically interact with mechanical load (e.g, The pendulum pushing periodically a load when passing at its equilibrium point). The periodic actuation or collision can be a source of distortions or chaos in the dynamical behavior of the actuator. An interesting problem is to find a control strategy that will mitigate the distortion and change the boundaries of the chaos free parameters space. The Melnikov theory is used to delineate the domains where chaos appears. The Melnikov theory analysis is con- firmed numerically with the basin of attraction. It is one of the rare interesting methods to detect analytically chaos in physi- cal systems. It has been used recently to detect chaos in an inverted pendulum system [23], in a planar hybrid piecewise- smooth system with a switching manifold [24], in a micro- cantilever dynamics [25]. Besides the Melnikov method is the Shilnikov criteria which helps in the determination of parame- ters leading to chaos in three dimensional systems [26, 27]. The chaotification of linear systems can make use of the Shil- nikov criteria [28] and other controlling methods [29, 30]. The goal of this work is twofold. First, we analyze the con- ditions for the appearance of horseshoe chaos in the dynamics of on an electromechanical pendulum excited electrically and subjected to collisions. The second aim is to propose a scheme for control that will counterbalance the collision effects (Dis- tortion and chaos) on the dynamics of the electromechanical pendulum. * Corresponding author. Tel.: +237 691766978, Fax.: +237 691766978 E-mail address: notuekajie@yahoo.fr † Recommended by Associate Editor Hugo Rodrigue © KSME & Springer 2018