Transfer functions for a single flexible link

The authors examine some issues in the transfer function modeling of a single flexible link. Using the assumed-modes approach, it is possible to find the transfer function between the torque input and the net tip deflection. It is shown that when the number of modes is increased for more accurate modeling, the relative degree of the transfer function becomes ill-defined. This can greatly affect the performance of a controller designed using the model. In addition, any attempt to identify the transfer function is also affected. An alternative approach that uses the rigid body deformations minus the elastic deformations as the output is proposed. This solves the above problems and results in a transfer function with a well-defined relative degree of two. Even if three or four vibration modes are used, the leading coefficient in the numerator is much larger with the proposed new output