Nonlinear modeling and control of flexible-link manipulators subjected to parametric excitation

This paper presents nonlinear dynamic modeling and control of flexible-link manipulators subjected 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 equations of motion to obtain a reduced-order set of equations. Control strategies, computed torque control and a composite control, based on the singular perturbation formulation developed, are utilized to reduce mechanical 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 simulations supported by real-time experiments show that the singular-perturbation control methodology developed for the nonlinear time-varying system offers better system response over the computed torque control as the manipulator is commanded to follow a certain trajectory.