Trajectory Synthesis and Inverse Dynamics Formulation for Minimal Vibrational Excitation for Flexible Structures based on Trajectory Patterns

A new approach to trajectory synthesis and formulation of the inverse dynamics model of flexible structures for point to point motions with minimal high frequency component of the actuating torques (forces) is presented. Trajectories are synthesized such that the flexible structure comes to rest undeformed at the completion of motion. The developed method is based on the Trajectory Pattern Method [1-2]. In this approach, an appropriate trajectory pattern is selected and described in parametric form. The inverse dynamics model of the system is formulated in terms of the trajectory parameters. The trajectory patterns used are in terms of a number of basic sinusoidal time functions and their harmonics. The basic frequencies are selected such that the harmonics appearing in the actuating torques do not excite the natural modes of vibration of the system. For each motion, the trajectory parameters are determined for minimal amplitudes of the higher actuating torque harmonics, noting that from the vibration and control points of view, such trajectories are more desirable. The higher harmonics refers to the harmonics of the actuating torques with frequencies above the highest trajectory harmonic frequency. As an example, a flexible beam undergoing large displacements and rotations in a plane is considered. The effectiveness of the approach is illustrated by an example.