Nonlinear Dyn (2010) 62: 769–779 DOI 10.1007/s11071-010-9761-z ORIGINAL PAPER Nonlinear modeling and control of flexible-link manipulators subjected to parametric excitation Ayman A. El-Badawy · Mohamed W. Mehrez · Amir R. Ali Received: 12 October 2009 / Accepted: 9 June 2010 / Published online: 9 July 2010 © Springer Science+Business Media B.V. 2010 Abstract This paper presents nonlinear dynamic mod- eling and control of flexible-link manipulators sub- jected to parametric excitation. The equations of motion are obtained using the Lagrangian-assumed modes method. Singular perturbation methodology is developed for the nonlinear time varying equa- tions of motion to obtain a reduced-order set of equa- tions. Control strategies, computed torque control and a composite control, based on the singular perturbation formulation developed, are utilized to reduce mechan- ical vibrations of the flexible-link and enable better tip positioning. Under the composite control technique, the effect of the value of perturbation parameter on the control signal is investigated. Numerical simula- tions supported by real-time experiments show that the singular-perturbation control methodology devel- oped for the nonlinear time-varying system offers bet- ter system response over the computed torque control as the manipulator is commanded to follow a certain trajectory. A.A. El-Badawy ( ) · M.W. Mehrez · A.R. Ali Faculty of Engineering and Material Science, The German University in Cairo, Cairo, Egypt e-mail: ayman.elbadawy@guc.edu.eg M.W. Mehrez e-mail: mohamed.waleed@guc.edu.eg A.R. Ali e-mail: amir.ali@guc.edu.eg Keywords Parametric excitation · Flexible manipulator · Computed torque · Singular perturbation · Composite control · Perturbation parameter 1 Introduction The performance of a robotic manipulator mounted on a crane, mobile platform, or an autonomous vehicle is affected by base excitation. The oscillating base can be modeled as a spring–mass–damper system and thus a new degree of freedom is added to the system. Al- ternatively, the oscillation of the base can be consid- ered as parametric excitation, where the excitation ap- pears as coefficients in the governing differential equa- tions [1]. The difference between the two modeling strategies is that in the first one the control objective is to achieve suppression of base oscillations [2]. In the second case, the control objective is to reduce the vibrations of the flexible link and maintain the accu- racy of the tip position in the presence of sustained parametric excitation. Young and Moon [3] used a simple robust control strategy that reduces mechanical vibrations of the base and enables better tip positioning. The control algo- rithm uses the sensory feedback of the base oscillation to modulate the manipulator actuator input to induce the inertial damping forces. Active damping control problems of robot manipulators with oscillatory bases