Transfer Functions for a Single Flexible Link

This article examines some issues in the transfer function modeling of a single flexible link. Using the assumed- modes approach to represent the elastic deformation, one can find the transfer function between the torque input and the net tip deflection. It is shown here that when the number of modes is increased for more accurate model ing, the relative degree of the transfer function becomes ill defined. This can greatly affect the performance of a controller designed using this model. It is then shown that this problem occurs regardless of the method used to rep resent the elastic deformation. An alternate modeling approach is proposed that uses the rigid body deforma tions minus the elastic deformations as the output. This solves this problem and results in a transfer function with a well-defined relative degree of two. Simulation results are presented that illustrate the advantages of using the proposed alternate transfer function.