Research Article
An Electromechanical Pendulum Robot Arm in Action:
Dynamics and Control
A. Notué Kadjie, P. R. Nwagoum Tuwa, and Paul Woafo
Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Department of Physics,
Faculty of Science, University of Yaound´ e I, P.O. Box 812, Yaound´ e, Cameroon
Correspondence should be addressed to Paul Woafo; pwoafo1@yahoo.fr
Received 22 June 2017; Revised 18 October 2017; Accepted 8 November 2017; Published 5 December 2017
Academic Editor: Francesco Pellicano
Copyright © 2017 A. Notu´ e Kadjie et al. Tis is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Te authors numerically investigate the dynamics and control of an electromechanical robot arm consisting of a pendulum coupled
to an electrical circuit via an electromagnetic mechanism. Te analysis of the dynamical behavior of the electromechanical device
powered by a sinusoidal power source is carried out when the efects of the loads on the arm are neglected. It is found that the
device exhibits period-n T oscillations and high amplitude oscillations when the electric current is at its smallest value. Te specifc
case which considers the efects of the impulsive contact force caused by an external load mass pushed by the arm is also studied.
It is found that the amplitude of the impulse force generates several behaviors such as jump of amplitude and distortions of the
mechanical vibration and electrical signal. For more efcient functioning of the device, both piezoelectric and adaptive backstepping
controls are applied on the system. It is found that the control strategies are able to mitigate the signal distortion and restore the
dynamical behavior to its normal state or reduce the efects of perturbations such as a short time variation of one component or
when the robot system is subject to noises.
1. Introduction
Pendulum motion-driven systems have been intensively
studied recently by both industries and research institutes
because of their applications in diferent felds [1–10]. Some
of these studies concern the analysis of the dynamical
states and the development of control strategies to stabilize
the dynamical state to a prescribed state. Tese pendulum
models comprise the downward pendulum [5], horizontal
pendulum [6], inverted pendulum [7], spherical pendulum
[8], the fexible pendulum [9, 10], the pendulum excited
by an RLC circuit based on nonlinear shaker [11], and
rotating pendulum [12]. When the pendulum is coupled to an
electrical part (electromechanical pendulum), its applications
with and without control are more interesting in robotics and
other felds of engineering. Tis is due to some particular
dynamical states (periodic, quasiperiodic, and chaotic states)
that the electromechanical pendulum can generate because of
intrinsic angular nonlinearity or due to natural or imposed
nonlinearities in the electrical part [5, 9–12].
Te working state of a system with particular dynamics
can be modifed because of the interaction with its envi-
ronment or the application of some constraints or control
laws. In this line, recent years have seen the development
of various control strategies applied on electrical, mechan-
ical, electromechanical, and even biological systems: some
examples are the adaptive control [13], active control [14],
the classical and active-backstepping controls [15, 16], and the
sliding mode control [17]. An interesting contribution dealing
with chaos control of a double pendulum arm powered
through an RLC circuit is reported in [11] where the authors
used the state-dependent Riccati equation control and the
nonlinear saturation control techniques to suppress chaos in
the dynamics of the double pendulum arm. Due to its impor-
tance for engineering and robotic applications, the control of
pendulum motion has been intensively studied using various
approaches, including passivity-based control [18], nonlinear
control [19, 20], sliding mode control [21], motion control of
two pendulums [22], and bifurcation control [23].
In this work, the dynamics and the control of an elec-
tromechanical pendulum with rigid and constant length
Hindawi
Shock and Vibration
Volume 2017, Article ID 3979384, 13 pages
https://doi.org/10.1155/2017/3979384